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<Input><Text-field style="Text" bold="true" size="16" layout="Normal"><Font size="16" bold="true">This Maple session comes with the paper &quot;Refined enumeration of planar Eulerian orientations&quot;.
The main objective is to count height labelled quandrangulations, with variables t (faces), omega (bicoloured faces) and v (local minima)</Font></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">libname:=&quot;/home/bousquet/Calculs/Gfun/gfun&quot;, libname</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(gfun):</Text-field>
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<Input><Text-field style="Text" layout="Normal">We begin in Section 3 with functional equations.</Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">Refining earlier equations (Section 3.2)</Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal">We work with the &quot;calligraphic&quot; series of Section 3.5. That is, the series that appear in the session, compared to those of the system given in Section 3.2, are tP(yt), C(x,yt)/v and D(x,yt)/v.
The functions below give the series up to the coefficient of t^n.</Text-field>
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<Input><Text-field style="Text" layout="Normal">v appears here in the equation for P (and only here)</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pser:=proc(n) option remember:
if n=0 then 0 else normal(t*(v-1)+1/y*coeff(Cser(n),x)): fi: end:</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cser:=proc(n) option remember:
if n=0 then 0
else map(factor,convert(subs(x=1-1/x,series(1-1/Dser(n),t,n+1)),polynom))
fi: end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30020" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Here we determine D up to t^n, except for the coefficient of y, for which we will use the initial condition later.</Text-field><Text-field style="Text" layout="Normal">We leave this missing term as  y * D1(t,x,n)</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30013" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dserinit:=proc(n) local i,res,res1,resser: option remember:
if n=0 then 1
else res:=y/x*Dser(n-1)*subs(y=1/x,Pser(n-1)):
resser:=convert(series(res,x,3*n+1),polynom):
res:=convert(series(res-add(coeff(resser,x,i)*x^i,i=ldegree(resser,x)..-1),t,n+1),polynom):
res1:= convert(series(collect(1+ y*Dser(n-1)*coeff(Dser(n-1),y) + res,t,normal),t,n+1),polynom):
res1-y*coeff(res1,y)+y*D1(t,x,n):
fi: end:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30024" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Initial condition: D1 is the coefficient of y in D. Omega appears here (and only here)</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30023" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">D1ser:=proc(n) local D1subs: option remember:
if n=0 then 0:
else 
D1subs:=subs(x=1/y,convert(series(D1ser(n-1),x,2*n),polynom)):
map(factor,convert(series(
t/(1-x)+ omega/(1-x)*coeff(Dserinit(n),y,2)+ 1/(1-x)*coeff(D1subs*Dser(n-1),y,1)
,t,n+1),polynom)):
fi:
end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30022" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">To complete the calculation of D up to order t^n</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30011" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dser:=proc(n)
collect(subs(D1(t,x,n)= D1ser(n), Dserinit(n)),t,factor): end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30014" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Back to quadrangulations</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L29995" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Qser:=proc(n)
collect(1/t^2*coeff(Pser(n+2),y,1)-v,t,normal):end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30025" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30004" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">How the system works: one should call the functions in this order</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30002" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dserinit(1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYiIiJGIyomSSJ5RzYiRiMtSSNEMUdGJjYlSSJ0R0YmSSJ4R0YmRiNGI0Yj</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30012" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">D1ser(1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJkkidEc2IiIiIiwmISIiRiZJInhHRiVGJkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30001" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dser(1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYiIiJGIyooSSJ5RzYiRiNJInRHRiZGIywmISIiRiNJInhHRiZGI0YpRik=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30007" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cser(1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ4RidGL0YyRjUtRiw2JVEidEYnRi9GMkY5">KihJInlHNiIiIiJJInhHRiRGJUkidEdGJEYl</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L29999" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pser(1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ2RidGL0YyRjk=">KiZJInRHNiIiIiJJInZHRiRGJQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30026" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us now iterate this</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30009" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=1:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L29992" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 7 do n:=n+1: Dserinit(n):D1ser(n):Dser(n):Cser(n):Pser(n); od:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L32948" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We have reached n=8</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30005" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">nops(collect(Pser(n),t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiOEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIp</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35768" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30028" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(8,collect(Pser(n),t));
op(5,collect(Pser(n),t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ2RidGL0YyRjk=">KiZJInRHNiIiIiJJInZHRiRGJQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KihJInZHNiIiIiIsQCooSSZvbWVnYUdGJCIiI0YjRilJInlHRiRGJUYpKihGKEYlRiNGKUYqRilGKSomRiNGKUYqIiIkRiUqKEYoRilGI0YlRipGJSIiJiooRihGJUYjRiVGKkYpRi8qJkYjRiVGKkYtRi0qJkYoRilGKkYlRikqKEYoRiVGI0YlRipGJSIiKSomRihGJUYqRilGKSomRiNGJUYqRikiIiUqJEYqRi1GJSomRihGJUYqRiVGNComRiNGJUYqRiVGKSokRipGKUY3RipGNEYlSSJ0R0YkRjc=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30008" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Qser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKEkidkc2IiIiIiwwKiZJJm9tZWdhR0YlIiIjRiRGKkYqKiZGKUYqRiRGJiIiJiokRilGKkYqKiZGKUYmRiRGJiIiKUYpRi9GJEYqRi9GJkYmSSJ0R0YlRipGJiooRiRGJiwoRi5GJkYpRiZGKkYmRiZGMEYmRiY=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L32942" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">More terms</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30016" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 7 do n:=n+1: Dserinit(n):D1ser(n):Dser(n):Cser(n):Pser(n); od:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L32949" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We have reached n=15</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L29991" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(Pser(15))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCZJJm9tZWdhRzYiSSJ0R0YkSSJ2R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L32943" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Q is thus known up to the coefficient of t^13</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L32945" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q0ser:=subs(omega=0,Qser(13))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L32947" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q1ser:=subs(omega=1,Qser(13))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L32944" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L29989" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
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<Group view="presentation" inline-output="false" labelreference="L29983" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(x=0,D1ser(4))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCpJInRHNiIiIiIqJiwoKiZJJm9tZWdhR0YkRiVJInZHRiRGJSEiIkYpRitGK0YlRiVGIyIiI0YrKiYsMComRilGLEYqRiwhIiMqJkYpRixGKkYlISImKiRGKUYsRjBGKEYyRikhIiVGKkYrISIkRiVGJUYjIiIkRisqJiw8KiZGKUY2RipGNkYyKiZGKUY2RipGLCEjQSomRilGNkYqRiVGO0YvISNAKiRGKUY2RjJGMSEjWComRilGJUYqRiwhIihGMyEjOkYoISNRKiRGKkYsRitGKUY7RiohIzUhIzdGJUYlRiMiIiVGKw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30039" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(y=0,Pser(5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ2RidGL0YyRjk=">KiZJInRHNiIiIiJJInZHRiRGJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35281" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Qser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqKEkidkc2IiIiIiw8KiZJJm9tZWdhR0YlIiIkRiRGKiIiJiomRilGKkYkIiIjIiNBKiZGKUYqRiRGJkYuKiZGKUYtRiRGLSIjSSokRilGKkYrKiZGKUYtRiRGJiIjcyomRilGJkYkRi0iIzcqJEYpRi1GMSomRilGJkYkRiYiI3kqJEYkRi1GLUYpIiNnRiQiI0MiI1NGJkYmSSJ0R0YlRipGJiooRiRGJiwwRjBGLUYzRitGN0YtRjgiIilGKUZBRiRGLUZBRiZGJkY+Ri1GJiooRiRGJiwoRjhGJkYpRiZGLUYmRiZGPkYmRiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35280" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30040" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now that we can generate terms in the GF of quadrangulations, we can check if our results</Text-field><Text-field style="Text" layout="Normal">for omega=0, 1 and v=1 seem correct.</Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">Checking the three theorems in the introduction</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30085" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30102" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The case omega=0</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30117" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(omega=0, Qser(5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqKEkidkc2IiIiIiwsKiRGJCIiJUYmKiRGJCIiJCIjUyokRiQiIiMiJHYkRiQiJT81IiRzJ0YmRiZJInRHRiUiIiZGLiooRiRGJiwqRipGLkYtIiNbRiQiJEkjIiRDI0YmRiZGMkYpRiYqKEYkRiYsKEYtRi5GJCIjQ0YsRiZGJkYyRitGJiooRiRGJiwmRiRGLiIiKUYmRiZGMkYuRiYqJkYyRiZGJEYmRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30119" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write R0=t*S and determine the first coefficients of R0 using the implicit equation that defines it</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30122" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:pol:=-t+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k,n)*t^k*(v-1)^k*t^(n+1)*S^(n+1),k=0..N),n=0..N):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30114" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(algeqtoseries(pol,t,S,N,true))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzVJInRHNiIiIiIiIiEsJkkidkdGJCEiIkYpRiVGJSwmRighIiRGKUYlIiIjLCgqJEYoRixGK0YoISM5RitGJSIiJCwqKiRGKEYwRitGLiEjUkYoISN5ISM3RiUiIiUsLCokRihGNkYrRjIhI3dGLiEkKlJGKCEkdSUhI2NGJSIiJiwuKiRGKEY9RitGOCEkRCJGMiElWDdGLiElTlBGKCElT0khJClHRiUiIicsMCokRihGRUYrRj8hJCc9RjghJStJRjIhJlluIkYuISZITSRGKCEmWywjISUlZSJGJSIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIp</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30115" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R0ser:=series(t*%,t,N+1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZSMHNlckdGKCs1SSJ0R0YoIiIiRjAsJkkidkdGKCEiIkYzRjAiIiMsJkYyISIkRjNGMCIiJCwoKiRGMkY0RjZGMiEjOUY2RjAiIiUsKiokRjJGN0Y2RjkhI1JGMiEjeSEjN0YwIiImLCwqJEYyRjtGNkY9ISN3RjkhJCpSRjIhJHUlISNjRjAiIicsLiokRjJGQUY2RkMhJEQiRj0hJVg3RjkhJU5QRjIhJU9JISQpR0YwIiIoLDAqJEYyRkhGNkZKISQnPUZDISUrSUY9ISZZbiJGOSEmSE0kRjIhJlssIyElJWUiRjAiIiktSSJPR0YlNiNGMCIiKjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44866" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we want to expand the series G. Let us first check what the sum would give for k=n=0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30123" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:='n': k:='k':eval(subs(n=0,k=0,1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k-1,n)*t^k*(v-1)^k*R^(n+1)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJSRzYi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30113" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:Gser:=normal(series(-v/2-R0ser/2/t^2+1/t^2*add(add(1/2/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k-1,n)*t^k*(v-1)^k*R0ser^(n+1),k=0..N),n=0..N),t,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVHc2VyR0YoKy9JInRHRihJInZHRigiIiIsJiokRjAiIiNGMUYwIiIlRjQsKCokRjAiIiRGMUYzIiM3RjAiIz9GOCwqKiRGMEY1RjFGNyIjQ0YzIiQ6IkYwIiQ3IkY1LCwqJEYwIiImRjFGPCIjU0Y3IiR2JEYzIiU/NUYwIiRzJ0ZCLUkiT0dGJTYjRjEiIic3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35268" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiJJInZHRiQiIiIqJkYlRiYsJkYlRiYiIiVGJkYmIiIjKihGJUYmLCZGJUYmIiM1RiZGJiwmRiVGJkYqRiZGJiIiJComRiVGJiwqKiRGJUYvRiYqJEYlRioiI0NGJSIkOiIiJDciRiZGJkYpKiZGJUYmLCwqJEYlRilGJkYyIiNTRjMiJHYkRiUiJT81IiRzJ0YmRiYiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJiIiJw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30124" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This should coincide with half the series of labelled quadrangulations: good!</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30116" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(normal,subs(omega=0, Qser(5)/2))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqKEkidkc2IiIiIiwsKiRGJCIiJUYmKiRGJCIiJCIjUyokRiQiIiMiJHYkRiQiJT81IiRzJ0YmRiZJInRHRiUiIiZGJiooRiRGJiwqRipGJkYtIiNDRiQiJDoiIiQ3IkYmRiZGMkYpRiYqKEYkRiYsKEYtRiZGJCIjNyIjP0YmRiZGMkYrRiYqKEYkRiYsJkYkRiZGKUYmRiZGMkYuRiYqJkYyRiZGJEYmRiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L44867" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%-%%,t,6))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30118" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">In the OEIS: A324312</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30120" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">seriestolist(series(subs(v=1,%%),t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NygiIiEiIiIiIiYiI0wiJF8jIiUzQA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30121" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Later we will be happy to have more terms of R0 to check the differential equation, so let us compute a few more</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L31042" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10:pol:=-t+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k,n)*t^k*(v-1)^k*t^(n+1)*S^(n+1),k=0..N),n=0..N):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31043" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(algeqtoseries(pol,t,S,N,true))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31040" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R0ser:=series(t*%,t,N+1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31041" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30112" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30111" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check the alternative expression for G</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30110" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=6: t-R+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k+1,n)*R^(n+1)*(t*v-t)^(k+1), k=0..N),n=0..N):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34168" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(subs(R=R0ser,%),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUYjNiYtRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGMy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZLLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0YzRjYtSSVtc3VwR0YkNiUtRk82JVEidEYnRlJGVUYvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YzLUY3Ni1RJyZwbHVzO0YnRjNGOkY9Rj9GQUZDRkVGRy9GSlEsMC4yMjIyMjIyZW1GJy9GTUZeby1GIzYoLUYwNiRRIjRGJ0YzRjZGTkY2LUZYNiVGWi1GMDYkUSIzRidGM0ZnbkYzRmpuLUYjNihGYm9GNi1GIzYmRk5GNi1JKG1mZW5jZWRHRiQ2JC1GIzYmRk5Gam5GYm9GM0YzRjNGNi1GWDYlRlpGYm9GZ25GM0Zqbi1GIzYoRmJvRjYtRiM2KEZORjYtRl9wNiQtRiM2JkZORmpuLUYwNiRRIzEwRidGM0YzRjNGNi1GX3A2JC1GIzYmRk5Gam5GL0YzRjNGM0Y2LUZYNiVGWi1GMDYkUSI1RidGM0ZnbkYzRmpuLUYjNihGYm9GNi1GIzYmRk5GNi1GX3A2JC1GIzYqLUZYNiVGTkZnb0ZnbkZqbi1GIzYmLUYwNiRRIzI0RidGM0Y2LUZYNiVGTkYvRmduRjNGam4tRiM2Ji1GMDYkUSQxMTVGJ0YzRjZGTkYzRmpuLUYwNiRRJDExMkYnRjNGM0YzRjNGNi1GWDYlRlotRjA2JFEiNkYnRjNGZ25GM0Zqbi1GIzYmLUY3Ni1RIk9GJ0YzRjpGPUY/RkFGQ0ZFRkdGSUZMLUY3Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjNGOkY9Rj9GQUZDRkVGR0ZJRkwtRl9wNiQtRiM2Jy1GWDYlRlotRjA2JFEiN0YnRjNGZ24vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPEYzRjNGM0Yz">Ky9JInRHNiIsJEkidkdGJCIiI0YnLCRGJiIiJSIiJCwkKiZGJiIiIiwmRiZGLUYpRi1GLUYpRiksJCooRiZGLSwmRiZGLSIjNUYtRi0sJkYmRi1GJ0YtRi1GKSIiJiwkKiZGJkYtLCoqJEYmRipGLSokRiZGJyIjQ0YmIiQ6IiIkNyJGLUYtRikiIictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGLSIiKA==</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(2*t^2*(subs(omega=0,Qser(N))+v),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiIsJEkidkdGJCIiI0YnLCRGJiIiJSIiJCwkKiZGJiIiIiwmRiZGLUYpRi1GLUYpRiksJCooRiZGLSwmRiZGLSIjNUYtRi0sJkYmRi1GJ0YtRi1GKSIiJiwkKiZGJkYtLCoqJEYmRipGLSokRiZGJyIjQ0YmIiQ6IiIkNyJGLUYtRikiIictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGLSIiKA==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%-%%,t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34452" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L34451" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L34450" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L30109" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L34459" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L30101" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The case omega=1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30130" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write R1=t*S and determine the first coefficients of R1 using its implicit defintion</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30129" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:pol:=-t+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(3*n+2*k,n+k)*t^k*(v-1)^k*t^(n+1)*S^(n+1),k=0..N),n=0..N):</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30133" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,op(algeqtoseries(pol,t,S,N,true)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzVJInRHNiIiIiIiIiEsJkkidkdGJCEiIyEiIkYlRiUsKCokRigiIiNGKUYoISIpRilGJUYtLCoqJEYoIiIkISIlRiwhI09GKCEjYyEiKkYlRjEsLCokRigiIiUhIzVGMCEkXyJGLCEkQyZGKCEkbSUhI2FGJUY4LC4qJEYoIiImISNHRjchJEcnRjAhJVtPRiwhJSkzKEYoISVLVSEkeSRGJUZALDAqJEYoIiInISMlKUY/ISVvREY3ISY/PyNGMCEmZzwoRiwhJktEKkYoISZPMCUhJTtIRiVGSSwyKiRGKCIiKCEkayNGSCEmUy8iRj8hJ2dAN0Y3ISdnbGVGMCEoY0dFIkYsIShPTj0iRighJy9EUyEmZFMjRiVGUy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIp</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R1ser:=series(t*%,t,N+1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZSMXNlckdGKCs1SSJ0R0YoIiIiRjAsJkkidkdGKCEiIyEiIkYwIiIjLCgqJEYyRjVGM0YyISIpRjNGMCIiJCwqKiRGMkY5ISIlRjchI09GMiEjYyEiKkYwIiIlLCwqJEYyRkAhIzVGOyEkXyJGNyEkQyZGMiEkbSUhI2FGMCIiJiwuKiRGMkZIISNHRkIhJEcnRjshJVtPRjchJSkzKEYyISVLVSEkeSRGMCIiJywwKiRGMkZRISMlKUZKISVvREZCISY/PyNGOyEmZzwoRjchJktEKkYyISZPMCUhJTtIRjAiIigsMiokRjJGZW4hJGsjRlMhJlMvIkZKISdnQDdGQiEnZ2xlRjshKGNHRSJGNyEoT049IkYyIScvRFMhJmRTI0YwIiIpLUkiT0dGJTYjRjAiIio3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44868" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">we check what the term k=n=0 in the sum that gives Q1 would be</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30136" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:='n': k:='k':eval(subs(n=0,k=0,1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(3*n+2*k-1,2*n+k)*t^k*(v-1)^k*R^(n+1)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJSRzYi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30131" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:Q1ser:=map(factor,normal(series(-v-R1ser/t^2+1/t^2*add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(3*n+2*k-1,2*n+k)*t^k*(v-1)^k*R1ser^(n+1),k=0..N),n=0..N),t,N)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEmUTFzZXJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNiYtRiM2Ji1GLDYlUSJ2RidGL0YyLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GWi1JKG1mZW5jZWRHRiQ2JC1GIzYmRlMtRjY2LVEnJnBsdXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl9vLUkjbW5HRiQ2JFEiM0YnRjlGOUY5RjlGVi1GLDYlUSJ0RidGL0YyRjlGW28tRiM2Ji1GIzYoRlNGVi1GZ242JC1GIzYmRlNGW28tRmJvNiRRIjZGJ0Y5RjlGOUZWLUZnbjYkLUYjNiYtRiM2Ji1GYm82JFEiMkYnRjlGVkZTRjlGW29GYW9GOUY5RjlGVi1JJW1zdXBHRiQ2JUZlb0ZpcC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOUZbby1GIzYmLUYjNihGU0ZWLUZnbjYkLUYjNiZGU0Zbby1GYm82JFEiMUYnRjlGOUY5RlYtRmduNiQtRiM2KC1GIzYmLUZibzYkUSI1RidGOUZWLUZdcTYlRlNGaXBGX3FGOUZbby1GIzYmLUZibzYkUSM2MUYnRjlGVkZTRjlGW28tRmJvNiRRJDEzNUYnRjlGOUY5RjlGVi1GXXE2JUZlb0Zhb0ZfcUY5RltvLUYjNiYtRiM2JkZTRlYtRmduNiQtRiM2LC1GIzYmLUZibzYkUSMxNEYnRjlGVi1GXXE2JUZTLUZibzYkUSI0RidGOUZfcUY5RltvLUYjNiYtRmJvNiRRJDI3OUYnRjlGVi1GXXE2JUZTRmFvRl9xRjlGW28tRiM2Ji1GYm82JFElMTQ1MkYnRjlGVkZmckY5RltvLUYjNiYtRmJvNiRRJTI0NTVGJ0Y5RlZGU0Y5RltvLUZibzYkUSUxMTM0RidGOUY5RjlGOUZWLUZdcTYlRmVvRmF0Rl9xRjlGW28tRiM2KEZpcEZWLUYjNiZGU0ZWLUZnbjYkLUYjNi4tRiM2Ji1GYm82JFEjMjFGJ0Y5RlYtRl1xNiVGU0ZjckZfcUY5RltvLUYjNiYtRmJvNiRRJDU3OUYnRjlGVkZfdEY5RltvLUYjNiYtRmJvNiRRJTQ1NDBGJ0Y5RlZGaXRGOUZbby1GIzYmLUZibzYkUSYxMzQwMEYnRjlGVkZmckY5RltvLUYjNiYtRmJvNiRRJjE1MDkzRidGOUZWRlNGOUZbby1GYm82JFElNTEwM0YnRjlGOUY5RjlGVi1GXXE2JUZlb0ZjckZfcUY5RltvLUYjNiYtRjY2LVEiT0YnRjlGO0Y+RkBGQkZERkZGSEZZRmVuLUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZZRmVuLUZnbjYkLUYjNictRl1xNiVGZW9GYHBGX3EvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RjlGOUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZRMXNlckdGKCsvSSJ0R0YoKiZJInZHRigiIiIsJkYxRjIiIiRGMkYyRjIqKEYxRjIsJkYxRjIiIidGMkYyLCZGMSIiI0Y0RjJGMkY5KihGMUYyLCZGMUYyRjJGMkYyLCgqJEYxRjkiIiZGMSIjaCIkTiJGMkYyRjQqJkYxRjIsLCokRjEiIiUiIzkqJEYxRjQiJHojRj0iJV85RjEiJWJDIiVNNkYyRjJGRCwkKiZGMUYyLC4qJEYxRj4iI0BGQyIkeiZGRiIlU1hGPSImK00iRjEiJiQ0OiIlLl5GMkYyRjlGPi1JIk9HRiU2I0YyRjc3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30135" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This should coincide with the series of labelled quadrangulations: good!</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30128" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(normal,subs(omega=1, Qser(5)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqKEkidkc2IiIiIiwuKiRGJCIiJiIjQCokRiQiIiUiJHomKiRGJCIiJCIlU1gqJEYkIiIjIiYrTSJGJCImJDQ6IiUuXkYmRiZJInRHRiVGKUYyKihGJEYmLCxGKyIjOUYuIiR6I0YxIiVfOUYkIiViQyIlTTZGJkYmRjZGLEYmKihGJEYmLCpGLkYpRjEiI21GJCIkJz4iJE4iRiZGJkY2Ri9GJiooRiRGJiwoRjFGMkYkIiM6IiM9RiZGJkY2RjJGJiooRiRGJiwmRiRGJkYvRiZGJkY2RiZGJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30127" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%%-%,t,6))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30137" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">OEIS: A324314</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30138" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=5:subs(omega=1, v=1, Qser(n))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJEkidEc2IiIiJiImc3UoKiRGJCIiJSIlTWAqJEYkIiIkIiQtJSokRiQiIiMiI05GJEYp</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30134" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">seriestolist(series(%,t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NygiIiEiIiUiI04iJC0lIiVNYCImc3Uo</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33820" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Later we will be happy to have more terms of R1 to check the differential equation, so let's compute a few more</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33819" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10:pol:=-t+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(3*n+2*k,k+n)*t^k*(v-1)^k*t^(n+1)*S^(n+1),k=0..N),n=0..N):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33818" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(algeqtoseries(pol,t,S,N,true))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33822" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R1ser:=series(t*%,t,N+1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33821" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33823" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Checking the alternative expression of Q1</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30126" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=5: t-R+add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(3*n+2*k+1,k+n+1)*t^(k+1)*(v-1)^(k+1)*R^(n+1),k=0..N),n=0..N):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30125" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(subs(R=R1ser,%),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIsJEkidkdGJCIiJCIiIywkKiZGJiIiIiwmRiZGK0YnRitGK0YnRicsJCooRiZGKywmRiZGKyIiJ0YrRissJkYmRihGJ0YrRitGJyIiJSwkKihGJkYrLCZGJkYrRitGK0YrLCgqJEYmRigiIiZGJiIjaCIkTiJGK0YrRidGOC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YrRjA=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34172" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(3*t^2*(v+subs(omega=1,Qser(N))),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIsJEkidkdGJCIiJCIiIywkKiZGJiIiIiwmRiZGK0YnRitGK0YnRicsJCooRiZGKywmRiZGKyIiJ0YrRissJkYmRihGJ0YrRitGJyIiJSwkKihGJkYrLCZGJkYrRitGK0YrLCgqJEYmRigiIiZGJiIjaCIkTiJGK0YrRidGOC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YrRjA=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34171" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%%-%,t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35446" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35374" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34817" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34170" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34169" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L30095" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" labelreference="L30089" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30091" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30245" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The case v=1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30250" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">thetaser:=proc(N) local n: add((-1)^n*q^(n*(n+1)/2)*sin(z*(2*n+1)),n=0..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30240" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">thetaser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCotSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiekdGKCIiIiomSSJxR0YoRistRiQ2IywkRioiIiRGKyEiIiomRi1GMS1GJDYjLCRGKiIiJkYrRisqJkYtIiInLUYkNiMsJEYqIiIoRitGMg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30325" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The alternative product expressions</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30258" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">prod:=proc(N) local n: 
sin(z)*product((1-q^n)*(1-q^n*exp(2*I*z))*(1-q^n/exp(2*I*z)),n=1..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30253" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">prod(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KjYtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiekdGKCIiIiwmRitGK0kicUdGKCEiIkYrLCZGK0YrKiZGLUYrLUkkZXhwR0YlNiMqJl4jIiIjRitGKkYrRitGLkYrLCZGK0YrKiZGLUYrRjFGLkYuRissJiokRi1GNkYuRitGK0YrLCZGK0YrKiZGLUY2RjFGK0YuRissJkYrRisqJkYtRjZGMUYuRi5GKywmKiRGLSIiJEYuRitGK0YrLCZGK0YrKiZGLUZBRjFGK0YuRissJkYrRisqJkYtRkFGMUYuRi5GKw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30247" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=7: simplify(convert(map(expand,simplify(series(thetaser(n)/prod(n),q,n+1))),trig),trig)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInFHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30256" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Expression of t in terms of q</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30277" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tqser:=proc(N)
simplify(factor(series(cos(alpha)/64/sin(alpha)^3*
(subs(z=alpha,diff(thetaser(N),z$2)/diff(thetaser(N),z)-thetaser(N)*diff(thetaser(N),z$3)/diff(thetaser(N),z)^2)),q,N))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tqser(5)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIiIiJGJSwmKiQtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kmYWxwaGFHRiQiIiMiI0MhIz1GJUYvLCgqJEYoIiIlIiRLJUYnISRzJyIkXyNGJSIiJCwqKiRGKCIiJyIlN3BGMyEmY2kiRiciJidcNyElQ0pGJUY0LUkiT0dGKjYjRiUiIiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30316" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Inversion of the above relation: we write q=t*S and use omega=-2*cos(2a)= 2(1-2*cos(a)^2)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30315" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">qtser:=proc(N)
factor(series(t*subs(cos(alpha)=sqrt(2-omega)/2,
op(algeqtoseries(subs(q=t*S,convert(tqser(N+2),polynom))-t,t,S,N,true))),t,N+1)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30313" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">qtser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIiIiJGJSwmIiInRiVJJm9tZWdhR0YkRiciIiMsKCokRihGKSIjWEYoIiMlKSIjW0YlIiIkLCoqJEYoRi8iJHkkRisiJCkqKkYoIiV3NSIkTyVGJSIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIm</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30251" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Another calculation for q(t)</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30260" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">qtseralt:=proc(N) local csol: option remember:
if N=1 then t
else coeff(series(subs(q=qtseralt(N-1)+t^N*c, t-tqser(N+3)),t,N+3),t,N);
csol:=solve(%,c):
qtseralt(N-1)+t^N*csol:
fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30326" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8: normal(series(subs(cos(alpha)=sqrt(2-omega)/2,qtser(N)-qtseralt(N)),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30327" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This new procedure allows us to compute faster and further</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30263" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">qtseralt(20):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30267" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series R in terms of q</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30279" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rser:=proc(N)
simplify(factor(series(
cos(alpha)^2/96/sin(alpha)^4*subs(z=alpha,thetaser(N))^2/ subs(z=alpha, diff(thetaser(N),z)^2)*
(subs(z=0,diff(thetaser(N),z$3))/subs(z=0,(cos(alpha)=sqrt(2-omega)/2,diff(thetaser(N),z)))-subs(z=alpha,diff(thetaser(N),z$3))/subs(z=alpha,diff(thetaser(N),z))),q,N))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30287" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInFHNiIiIiJGJSwmKiQtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kmYWxwaGFHRiQiIiMiI0chI0FGJUYvLUkiT0dGKjYjRiUiIiQ=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now R in terms of t</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35275" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:factor(subs(cos(alpha)=sqrt(2-omega)/2,series(subs(q=qtser(N+2),Rser(N)),t,N+1)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzNJInRHNiIiIiJGJSwmISIjRiVJJm9tZWdhR0YkISIiIiIjLCQqJiwmRihGJUYqRiVGJSwmRihGJUYlRiVGJUYnIiIkLCQqJkYtRiUsKCokRihGKiIiKkYoIiM7IiM1RiVGJUYpIiIlLCQqJkYtRiUsKiokRihGL0Y0RjMiI0FGKCIjRCIjNkYlRiUhIiciIiYsJComRi1GJSwsKiRGKEY3IiNqRjsiJCM+RjMiJC0kRigiJFsjIiMlKUYlRiVGPyIiJywkKiZGLUYlLC4qJEYoRkAiJWU5RkQiJWxfRjsiJjUuIkYzIiZOPiJGKCIlZ3ciJTNARiVGJUYnIiIoLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIik=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35274" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30329" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series Q in terms of q</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30274" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Qserq:=proc(N) simplify(factor(series(subs(t=tqser(N+2), 
1/t^2/(omega+2)*(t-Rser(N+3))-1),q,N+2))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=6: factor(subs(cos(alpha)=sqrt(2-omega)/2,sin(alpha)=sqrt(2+omega)/2,Qserq(N+2)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzNJInFHNiIsJkkmb21lZ2FHRiQiIiNGJyIiIkYoLCgqJEYmRichIiRGJiEiKSEiI0YoRicsKEYqIiInRiZGLyEiJ0YoIiIkLCQqJiwmRiZGKEYoRihGKCwoRioiIiZGJiEiIkYoRihGKCIiJUY4LCwqJEYmRjgiIzcqJEYmRjEhIyUpRipGMEYmIiNvIiM/RihGNiwsRjohJDsjRjwiJFciRiohI3lGJiEjJypGO0YoRi8sLiokRiZGNiEkZyJGOiIlKzZGPCEkZyhGKiEkUSNGJkZDISNVRigiIigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiKQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30328" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check with the expression of Q derived from functional equations</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30284" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(cos(alpha)=sqrt(2-omega)/2,series(subs(v=1,t=tqser(N+4),Qser(N+2)),q,N)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIsJkkmb21lZ2FHRiQiIiNGJyIiIkYoLCgqJEYmRichIiRGJiEiKSEiI0YoRicsKEYqIiInRiZGLyEiJ0YoIiIkLCQqJiwmRiZGKEYoRihGKCwoRioiIiZGJiEiIkYoRihGKCIiJUY4LCwqJEYmRjgiIzcqJEYmRjEhIyUpRipGMEYmIiNvIiM/RihGNi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRi8=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30224" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Good</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30309" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%%-%,q))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30330" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now the series Q in terms of t</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30223" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=4:map(factor,series(subs(q=convert(qtser(N+4),polynom),factor(subs(cos(alpha)=sqrt(2-omega)/2,sin(alpha)=sqrt(2+omega)/2,convert(Qserq(N+4),polynom)))),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIsJkkmb21lZ2FHRiQiIiNGJyIiIkYoLCgqJEYmRiciIipGJiIjOyIjNUYoRicsKiokRiYiIiQiI2FGKiIkSyJGJiIkXSIiI21GKEYwLCwqJEYmIiIlIiR5JEYvIiVfNkYqIiU3PUYmIiUpWyIiJC8mRihGNy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30308" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(subs(v=1,Qser(4)),t,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCoqJiwsKiRJJm9tZWdhRzYiIiIlIiR5JCokRiYiIiQiJV82KiRGJiIiIyIlNz1GJiIlKVsiIiQvJiIiIkYySSJ0R0YnRihGMiomLCpGKiIjYUYtIiRLIkYmIiRdIiIjbUYyRjJGM0YrRjIqJiwoRi0iIipGJiIjOyIjNUYyRjJGM0YuRjIqJiwmRiZGLkYuRjJGMkYzRjJGMg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30332" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%%-%,t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35277" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Comparison of the series R, R0 and R1 (when v=1)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30481" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:Rse:=factor(subs(cos(alpha)=sqrt(2-omega)/2,series(subs(q=qtser(N+2),Rser(N)),t,N+1)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSc2VHRigrM0kidEdGKCIiIkYwLCYhIiNGMEkmb21lZ2FHRighIiIiIiMsJComLCZGM0YwRjVGMEYwLCZGM0YwRjBGMEYwRjIiIiQsJComRjhGMCwoKiRGM0Y1IiIqRjMiIzsiIzVGMEYwRjQiIiUsJComRjhGMCwqKiRGM0Y6Rj9GPiIjQUYzIiNEIiM2RjBGMCEiJyIiJiwkKiZGOEYwLCwqJEYzRkIiI2pGRiIkIz5GPiIkLSRGMyIkWyMiIyUpRjBGMEZKIiInLCQqJkY4RjAsLiokRjNGSyIlZTlGTyIlbF9GRiImNS4iRj4iJk4+IkYzIiVndyIlM0BGMEYwRjIiIigtSSJPR0YlNiNGMCIiKTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30486" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(omega=0,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzNJInRHNiIiIiJGJSEiIyIiIyEiJSIiJCEjPyIiJSEkSyIiIiYhJTM1IiInISVLJSkiIigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30485" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(v=1,R0ser)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%-%%,t,8))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(omega=1,Rse)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzlJInRHNiIiIiJGJSEiJCIiIyEjNyIiJCEkMCIiIiUhJTE3IiImISYtZyIiIichJztDQiIiKCEoeEJmJCIiKSEpK0k2ZSIiKiEqJ29zTCgqIiM1LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIzY=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%-%%,t,8))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2"></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">A second equation between P and D (Section 3.3)</Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal">Again, ve use the &quot;calligraphic&quot; series, namely tP(yt) and D(x,yt)/v.</Text-field>
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<Input><Text-field style="Text" layout="Normal">Let us check the new equation on D (Proposition 3.6)
#In the second line we replace y by 1/y</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: last0:=subs(y=1/y,Dser(n))*convert(series(subs(x=y,D1ser(n)),y,2*n),polynom):
last:= convert(factor(series(add(coeff(last0,y,-i)*y^(i),i=1..n),t,n+1)),polynom):
factor(series((-Dser(n)+1)*(1-x)+y*Dser(n)*(Pser(n)+t-t*v)+omega/y*(Dser(n)-1-y*D1ser(n))
+last,t,n+1));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIig=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30528" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30571" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" hide-output="false" inline-output="false" labelreference="L30539" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The two equations between P and D define both series (Prop. 3.6)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L44870" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Again, we work with the &quot;calligraphic&quot; series of Section 3.5</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30545" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dser(2);Dser(4): seq(degree(coeff(Dser(n),t,m),y),m=0..3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyoqSSJ5RzYiRiMsNiooSSJ2R0YmRiNJInhHRiYiIiNGJUYjISIiKihJJm9tZWdhR0YmRiNGKUYjRipGI0YjKihGKUYjRipGI0YlRiNGKyomRi5GI0YpRiNGLComRilGI0YlRiNGLComRipGI0YlRiNGI0YuRixGKkYjRiVGLEYsRiNGIywmRixGI0YqRiMhIiRJInRHRiZGK0YjKihGJUYjRjVGI0YzRixGLA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKCZjb21tYTtGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiRRIjFGJ0YvRjItRiw2JFEiMkYnRi9GMi1GLDYkUSIzRidGL0Yv">NiYiIiEiIiIiIiMiIiQ=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30540" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pser(2); collect(Pser(4),t,factor): seq(degree(coeff(Pser(n),t,m),y),m=0..4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsJiomSSJ0RzYiIiIiSSJ5R0YmRidGJ0YnRidGJ0YlRidJInZHRiZGJw==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NicsJEkpaW5maW5pdHlHJSpwcm90ZWN0ZWRHISIiIiIhIiIiIiIjIiIk</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30534" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">unassign('coD','coP'):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30578" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Here we give D(y)=1 (which anyway follows from the equations) and bound the degree in y of the coefficient of t^n by n</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30544" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dexp:=proc(N) local j,n: 1+add(add(coD[j,n]*t^n*y^j,j=1..n),n=1..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30532" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dexp(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDAqKEkidEc2IiIiJEkieUdGJUYmJkkkY29ER0YlNiRGJkYmIiIiRisqKEYkRiZGJyIiIyZGKTYkRi1GJkYrRisqKEYkRiZGJ0YrJkYpNiRGK0YmRitGKyooRiRGLUYnRi0mRik2JEYtRi1GK0YrKihGJEYtRidGKyZGKTYkRitGLUYrRisqKEYkRitGJ0YrJkYpNiRGK0YrRitGK0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30579" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Here we give the first term in P(y) (namely, tv) and bound the degree in y of the coefficient of t^n</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30531" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pexp:=proc(N) local j,n: t*v+add(add(coP[j,n]*t^n*y^j,j=1..n),n=2..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30529" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pexp(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDYqKEkidEc2IiIiJUkieUdGJUYmJkkkY29QR0YlNiRGJkYmIiIiRisqKEYkRiZGJyIiJCZGKTYkRi1GJkYrRisqKEYkRiZGJyIiIyZGKTYkRjFGJkYrRisqKEYkRi1GJ0YtJkYpNiRGLUYtRitGKyooRiRGJkYnRismRik2JEYrRiZGK0YrKihGJEYtRidGMSZGKTYkRjFGLUYrRisqKEYkRi1GJ0YrJkYpNiRGK0YtRitGKyooRiRGMUYnRjEmRik2JEYxRjFGK0YrKihGJEYxRidGKyZGKTYkRitGMUYrRisqJkYkRitJInZHRiVGK0Yr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30536" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">First equation on D, taken at order n: nothing comes out here when n=1</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30535" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=1: res:=convert(factor(series(1+ y* Dexp(n)/x*subs(y=1/x,Pexp(n))+y*coeff(Dexp(n),y,1)*Dexp(n) -Dexp(n),t,n+1)),polynom):
collect(res-add(coeff(res,x,-i)/x^i,i=1..n),t,factor);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30549" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">New equation on D</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30538" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">last0:= convert(factor(series(subs(y=1/y,Dexp(n))*subs(x=y,coeff(Dexpr(n),y,1)),t,n+1)),polynom):
last:=add(coeff(last0,y,-i)*y^i,i=1..n):
res:=convert(factor(series((1-x)*(1-Dexp(n))+y*Dexp(n)*(Pexp(n)+t-t*v)+omega/y*(Dexp(n)-1-y*coeff(Dexp(n),y,1))+ last,t,n+1)),polynom):
collect(res,t,factor);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KihJInlHNiIiIiIsKComSSJ4R0YkRiUmSSRjb0RHRiQ2JEYlRiVGJUYlRikhIiJGJUYlRiVJInRHRiRGJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30558" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">coD[1,1]:=factor(solve(%,coD[1,1])); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkkY29ER0YoNiQiIiJGMCwkKiQsJiEiIkYwSSJ4R0YoRjBGNEY0NyNGMQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30557" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">coeff(Dexp(1),y,1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJkkidEc2IiIiIiwmISIiRiZJInhHRiVGJkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30553" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we iterate the following lines (till the word HERE)
Short/first equation </Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30559" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=n+1: res:=convert(factor(series(1+ y* Dexp(n)/x*subs(y=1/x,Pexp(n))+y*coeff(Dexp(n),y,1)*Dexp(n) -Dexp(n),t,n+1)),polynom):
resser:=factor(series(res,x,2*n)):
collect(res-add(coeff(resser,x,-i)/x^i,i=1..n),t,factor):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30560" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">co:=collect(numer(%),y,factor):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30561" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(solve({coeffs(co,y)}, indets(co) minus {omega,t,x,y,v})):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30562" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(%)</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30555" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Long equation </Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30547" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">last0:= convert(factor(series(subs(y=1/y,Dexp(n))*subs(x=y,coeff(Dexp(n),y,1)),t,n+1)),polynom)
:last0ser:= series(last0,y,2*n):
last:=add(coeff(last0ser,y,-i)*y^i,i=1..2*n):
res:=convert(factor(series((1-x)*(1-Dexp(n))+y*Dexp(n)*(Pexp(n)+t-t*v)+omega/y*(Dexp(n)-1-y*coeff(Dexp(n),y,1))+ last,t,n+1)),polynom):
collect(res,t,factor):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30550" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">co:=collect(numer(%),y,factor):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30554" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(solve({coeffs(co,y)}, indets(co) minus {omega,t,x,y,v})):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30563" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(%)</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30581" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">End of the part that we iterate: HERE</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30543" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">coeff(coeff(Dser(2),t,2),y,1);
coeff(coeff(Pser(2),t,2),y,1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsLCooSSZvbWVnYUc2IiIiIkkidkdGJkYnSSJ4R0YmRidGJyomRiVGJ0YoRichIiJGJUYrRilGJ0YrRidGJywmRitGJ0YpRichIiQ=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJ2RzYi</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30582" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30583" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n;indets(Dexp(n)); indets(Pexp(n))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIl</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCdJJm9tZWdhRzYiSSJ0R0YkSSJ2R0YkSSJ4R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCZJJm9tZWdhRzYiSSJ0R0YkSSJ2R0YkSSJ5R0Yk</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44871" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30542" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,series(Dexp(4)-Dser(4),t,5));
map(factor,series(Pexp(4)-Pser(4),t,5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30526" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30564" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30568" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30566" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30518" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L30522" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Group labelreference="L30537" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group><Presentation-Block>
<Group view="code" labelreference="L30587" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30591" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We can also check the equation expressing P in terms of P and D (Remark 3.8)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30588" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: last0:=subs(y=1/y,Pser(n))*convert(series(subs(x=y,D1ser(n)),y,2*n),polynom):
last:= convert(factor(series(add(coeff(last0,y,-i)*y^(i),i=1..n),t,n+1)),polynom):
factor(series(-Pser(n)+t*v+y*Pser(n)*(Pser(n)+t-t*v)+omega/y*(Pser(n)-t*v-y*coeff(Pser(n),y,1))+2*last,t,n+1));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIig=</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L30590" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L32826" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L30490" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30492" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Dser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyoqSSJ5RzYiRiMsNiooSSJ2R0YmRiNJInhHRiYiIiNGJUYjISIiKihJJm9tZWdhR0YmRiNGKUYjRipGI0YjKihGKUYjRipGI0YlRiNGKyomRi5GI0YpRiNGLComRilGI0YlRiNGLComRipGI0YlRiNGI0YuRixGKkYjRiVGLEYsRiNGIywmRixGI0YqRiMhIiRJInRHRiZGK0YjKihGJUYjRjVGI0YzRixGLA==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">A Dobrushin-like class of labelled maps (Section 3.4)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30597" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">A new set of patches, with Dobrushin boundary conditions (E-patches). The series here is the calligraphic version, that is, tE(tx,ty) if E is the original series</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30600" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eser:=proc(n) local i,produit:
produit:=subs(y=1/x,Pser(n))*convert(series(Dser(n),x,2*n),polynom):
convert(factor(series(add(coeff(produit,x,-i)*x^(i),i=0..n),t,n+1)),polynom):
map(factor,%):
end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30601" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJkkidEc2IiIiIkkidkdGJUYmRiYqKEYnRiYsJkkieEdGJUYmSSJ5R0YlRiZGJkYkIiIjRiYqKEYnRiYsOCooSSZvbWVnYUdGJUYmRidGJkYqRiZGJiooRjBGJkYnRiZGK0YmRiYqJkYnRiZGKkYsRiYqJkYnRiZGK0YsRiYqJkYwRiZGKkYmRiYqJkYwRiZGK0YmRiYqJEYqRixGJiomRipGJkYrRiZGJiokRitGLEYmRipGLEYrRixGJkYkIiIkRiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30599" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30602" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Symmetry property (Proposition 3.9</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30596" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: Eser(n)-subs({x=y,y=x},Eser(n))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30598" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Link with patches</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30594" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(subs(x=0,Eser(6))-Pser(6),t,6)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The alternative expression of P(y) as a constant term given at the end of Section 3.5</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=4: factor(series(coeff(convert(series(Dser(n),x,3*n),polynom)*subs(y=1/x,Pser(n+1)),x,0),t,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiJJInZHRiQiIiIqJkkieUdGJEYmRiVGJiIiIyooRiVGJkYoRiYsLComSSZvbWVnYUdGJEYmRiVGJkYmKiZGJUYmRihGJkYmRi1GJkYoRiZGKUYmRiYiIiQqKEYoRiZGJUYmLEAqJkYtRilGJUYpRikqKEYtRiZGJUYpRihGJkYpKiZGJUYpRihGKUYmKiZGLUYpRiVGJiIiJiooRi1GJkYlRiZGKEYmRjYqJkYlRiZGKEYpRi8qJEYtRilGKUYsIiIpKiZGLUYmRihGJkYpRi4iIiUqJEYoRilGJkYtRjpGJUYpRihGPEY6RiZGJkY8LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiZGNg==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L30607" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(Pser(n+1),t,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiJJInZHRiQiIiIqJkkieUdGJEYmRiVGJiIiIyooRiVGJkYoRiYsLComSSZvbWVnYUdGJEYmRiVGJkYmKiZGJUYmRihGJkYmRi1GJkYoRiZGKUYmRiYiIiQqKEYoRiZGJUYmLEAqJkYtRilGJUYpRikqKEYtRiZGJUYpRihGJkYpKiZGJUYpRihGKUYmKiZGLUYpRiVGJiIiJiooRi1GJkYlRiZGKEYmRjYqJkYlRiZGKEYpRi8qJEYtRilGKUYsIiIpKiZGLUYmRihGJkYpRi4iIiUqJEYoRilGJkYtRjpGJUYpRihGPEY6RiZGJkY8LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiZGNg==</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L44872" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%%-%,t))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L30584" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L34174" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L30674" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">A new characterisation of Q(t, omega, v) (Section 4)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30685" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The &quot;mixed&quot; series M(x)</Text-field>
</Input>
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<Group view="code" labelreference="L30694" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mser:=proc(n) 
collect(1/x*subs(y=1/x,Pser(n))+ D1ser(n),t,factor): 
end:</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30684" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"> map(convert,Mser(2),parfrac,x): collect(%,t)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiwoKiYsJiomSSZvbWVnYUc2IiIiIkkidkdGKUYqRipGKkYqRiosJiEiIkYqSSJ4R0YpRiohIiNGKiomRihGKkYsISIkRi0qJkYuRi9GK0YqRipGKkkidEdGKSIiI0YqKiYsJiomRi5GLUYrRipGKiokRixGLUYtRipGM0YqRio=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The ratio Z(x,y)</Text-field>
</Input>
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<Group hide-input="false" labelreference="L30709" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ratio:=(1-My/x)/(1-Mx/y)*(1-omega*y-x+t/y*(v-1)-My)/ (1-omega*x-y+t/x*(v-1)-Mx)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyYXRpb0dGKCoqLCYiIiJGMComSSNNeUdGKEYwSSJ4R0YoISIiRjRGMCwmRjBGMComSSNNeEdGKEYwSSJ5R0YoRjRGNEY0LCxGMEYwKiZJJm9tZWdhR0YoRjBGOEYwRjRGM0Y0KihJInRHRihGMEY4RjQsJkkidkdGKEYwRjRGMEYwRjBGMkY0RjAsLEYwRjAqJkY7RjBGM0YwRjRGOEY0KihGPUYwRjNGNEY+RjBGMEY3RjRGNDcjRi4=</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ratio:=factor(ratio)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyYXRpb0dGKCoqLCZJInhHRighIiJJI015R0YoIiIiRjMsLiomSSZvbWVnYUdGKEYzSSJ5R0YoIiIjRjMqJkYyRjNGN0YzRjMqJkkidEdGKEYzSSJ2R0YoRjNGMSomRjBGM0Y3RjNGM0Y7RjNGN0YxRjMsJkY3RjFJI014R0YoRjNGMSwuKiZGNkYzRjBGOEYzKiZGP0YzRjBGM0YzRjpGMUY9RjNGO0YzRjBGMUYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30710" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Proposition 4.1: no x nor y at the denominator</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30707" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=2: factor(series(subs(Mx=Mser(n),My=subs(x=y,Mser(n)),ratio),t,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44873" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Testing further, by specialising x=y=0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30713" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: factor(series(subs(Mx=Mser(n),My=subs(x=y,Mser(n)),ratio),t,n+1)): subs(x=0,y=0,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInRHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44874" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The case omega=0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30714" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: factor(series(subs(Mx=Mser(n),My=subs(x=y,Mser(n)),ratio),t,n+1)): subs(omega=0,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInRHNiIqJiwmISIiIiIiSSJ4R0YkRihGKCwmRidGKEkieUdGJEYoRiciIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44875" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The case omega=1</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30715" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=6: factor(series(subs(Mx=Mser(n),My=subs(x=y,Mser(n)),ratio),t,n+1)): subs(omega=1,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInRHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKA==</Equation></Text-field>
</Output>
</Group></Presentation-Block>
<Group labelreference="L30720" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series denoted F in the paper (Proposition 4.3): no negative power of x</Text-field>
</Input>
</Group>
<Group labelreference="L30721" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Fser:=proc(n) factor(series((1-omega*x-Mser(n))*(x*Mser(n)-t*(v-1)),t,n+1)): end:</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L30725" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Fser(3); indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYtLUkjbWlHRiQ2JVEoJm9tZWdhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYvNiVRInRGJy9GM0ZAL0Y2USdpdGFsaWNGJ0Y4LUYvNiVRInZGJ0ZURlVGOC1GLzYlUSJ4RidGVEZVLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGNUY1LyUlb3BlbkdRJyZsY3ViO0YnLyUmY2xvc2VHUScmcmN1YjtGJw==">PCZJJm9tZWdhRzYiSSJ0R0YkSSJ2R0YkSSJ4R0Yk</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30728" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(Pser(3),t)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqKEkidkc2IiIiIiwsKihJJm9tZWdhR0YlRiZGJEYmSSJ5R0YlRiZGJiomRiRGJkYqIiIjRiYqJkYpRiZGKkYmRiYqJEYqRixGJkYqRixGJkkidEdGJSIiJEYmKihGKkYmRiRGJkYvRixGJiomRi9GJkYkRiZGJg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35294" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqFM:=-F+(x*M-t*v+t)*(1-omega*x-M)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcUZNR0YoLCZJIkZHRighIiIqJiwoKiZJIk1HRigiIiJJInhHRihGNUY1KiZJInRHRihGNUkidkdGKEY1RjBGOEY1RjUsKComSSZvbWVnYUdGKEY1RjZGNUYwRjRGMEY1RjVGNUY1NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35293" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor([solve(eqFM,M)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyQsJComSSJ4RzYiISIiLCwqJkkmb21lZ2FHRiYiIiJGJSIiI0YnKiZJInRHRiZGK0kidkdGJkYrRitGLkYnRiVGKyokLDgqJkYqRixGJSIiJUYrKipGKkYrRi5GK0YvRitGJUYsRiwqKEYqRitGLkYrRiVGLCEiIyomRipGK0YlIiIkRjYqJkYuRixGL0YsRisqJkYuRixGL0YrRjYqKEYuRitGL0YrRiVGK0Y2KiZJIkZHRiZGK0YlRishIiUqJEYuRixGKyomRi5GK0YlRitGLCokRiVGLEYrI0YrRixGK0YrRkIsJComLCxGKUYrRi1GJ0YwRitGLkYrRiVGJ0YrRiVGJyNGJ0Ys</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44876" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The expression given in the paper</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L35292" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MFpap:=(x*(1-omega*x)+t*(v-1))/2/x- (x*(1-omega*x)-t*(v-1))/2/x*sqrt(1-4*x*F/(x*(1-omega*x)-t*(v-1))^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZNRnBhcEdGKCwmKiYsJiomSSJ4R0YoIiIiLCYqJkkmb21lZ2FHRihGM0YyRjMhIiJGM0YzRjNGMyomSSJ0R0YoRjMsJkkidkdGKEYzRjdGM0YzRjNGM0YyRjcjRjMiIiMqKCwmRjFGM0Y4RjdGM0YyRjcsJkYzRjMqKEYyRjNJIkZHRihGM0Y/ISIjISIlRjwjRjdGPTcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35296" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(subs(M=MFpap,eqFM)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35291" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35290" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30719" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check the expression of F(x) that proves that there are no negative powers of x (proof of Proposition 4.3)</Text-field>
</Input>
</Group></Presentation-Block>
<Group hide-input="false" labelreference="L30726" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=5: res:=convert(series(D1ser(n+1),x,3*n),polynom)*subs(y=1/x,Pser(n+1)):
add(coeff(res,x,i)*x^(i),i=-n-8..-1):
factor(series(t*(1-omega*x)-omega*coeff(Pser(n+1),y,1)+x*D1ser(n+1)*(1-omega*x+t/x*(v-1)-D1ser(n+1))-2*D1ser(n+2)*subs(y=1/x,Pser(n+1)) + 2* %,t,n+1)):</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L30722" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%-Fser(n+1),t))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35300" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Proving this formula</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L35299" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">FM:=solve(eqFM,F)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjRk1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZTLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2KC1GIzYmLUYsNiVRInhGJ0YvRjItRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZfby1GLDYlUSJNRidGL0YyRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZSRlQtRiM2Ji1GLDYlUSJ0RidGL0YyRltvLUYsNiVRInZGJ0YvRjJGOS1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkhGUkZURmlvRjlGOUZbby1GWDYkLUYjNigtRiM2Ji1GLDYlUSgmb21lZ2E7RicvRjBGPUY5RltvRmhuRjlGX3BGYW9GZG8tSSNtbkdGJDYkUSIxRidGOUY5RjlGOUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNGTUdGKCwkKiYsKComSSJNR0YoIiIiSSJ4R0YoRjNGMyomSSJ0R0YoRjNJInZHRihGMyEiIkY2RjNGMywoKiZJJm9tZWdhR0YoRjNGNEYzRjNGMkYzRjhGM0YzRjg3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35298" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">F_alt:=subs(M=1/x*P(1/x)+D1(x),FM);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZGX2FsdEdGKCwkKiYsKComSSJ4R0YoIiIiLCYqJkYyISIiLUkiUEdGKDYjKiRGMkY2RjNGMy1JI0QxR0YoNiNGMkYzRjNGMyomSSJ0R0YoRjNJInZHRihGM0Y2Rj9GM0YzLCoqJkkmb21lZ2FHRihGM0YyRjNGM0Y1RjNGO0YzRjZGM0YzRjY3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35297" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The equation that we use</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L30677" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=-P(1/x)+t*v+1/x*P(1/x)*(P(1/x)-t*v+t)+omega*x*(P(1/x)-P0-P1/x)+2*prod</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNlcUdGKCwsLUkiUEdGKDYjKiRJInhHRighIiJGNComSSJ0R0YoIiIiSSJ2R0YoRjdGNyooRjNGNEYvRjcsKEYvRjdGNUY0RjZGN0Y3RjcqKEkmb21lZ2FHRihGN0YzRjcsKEYvRjdJI1AwR0YoRjQqJkkjUDFHRihGN0YzRjRGNEY3RjdJJXByb2RHRigiIiM3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35288" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">F_alt1:=expand(F_alt+eq)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdGX2FsdDFHRigsOiomLUkiUEdGKDYjKiRJInhHRighIiIiIiItSSNEMUdGKDYjRjRGNiEiIyooRjQiIiNGN0Y2SSZvbWVnYUdGKEY2RjUqJkY0RjZGN0Y8RjUqJkY0RjZGN0Y2RjYqKkY9RjZJInRHRihGNkkidkdGKEY2RjRGNkY2KihGQUY2RkJGNkY3RjZGNiooRj1GNkZBRjZGNEY2RjUqJkZBRjZGN0Y2RjVGQUY2KihGPUY2RjRGNkkjUDBHRihGNkY1KiZGPUY2SSNQMUdGKEY2RjVJJXByb2RHRihGPDcjRi4=</Equation></Text-field>
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<Group hide-input="false" labelreference="L35303" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">F_pap:=t*(1-omega*x) -omega*P1+x*D1(x)*(1-omega*x-D1(x))+t*(v-1)*D1(x)-2*(P(1/x)*D1(x)-prod)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZGX3BhcEdGKCwuKiZJInRHRigiIiIsJiomSSZvbWVnYUdGKEYxSSJ4R0YoRjEhIiJGMUYxRjFGMSomRjRGMUkjUDFHRihGMUY2KihGNUYxLUkjRDFHRig2I0Y1RjEsKEYxRjFGM0Y2RjpGNkYxRjEqKEYwRjEsJkkidkdGKEYxRjZGMUYxRjpGMUYxKiYtSSJQR0YoNiMqJEY1RjZGMUY6RjEhIiNJJXByb2RHRigiIiM3I0Yu</Equation></Text-field>
</Output>
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<Group hide-input="false" labelreference="L35302" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand(F_alt1-F_pap)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKkkmb21lZ2FHNiIiIiJJInRHRiVGJkkidkdGJUYmSSJ4R0YlRiZGJiooSSNQMEdGJUYmRiRGJkYpRiYhIiI=</Equation></Text-field>
</Output>
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<Group hide-input="false" labelreference="L35301" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ratio</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiosJkkieEc2IiEiIkkjTXlHRiUiIiJGKCwuKiZJJm9tZWdhR0YlRihJInlHRiUiIiNGKComRidGKEYsRihGKComSSJ0R0YlRihJInZHRiVGKEYmKiZGJEYoRixGKEYoRjBGKEYsRiZGKCwmRixGJkkjTXhHRiVGKEYmLC4qJkYrRihGJEYtRigqJkY0RihGJEYoRihGL0YmRjJGKEYwRihGJEYmRiY=</Equation></Text-field>
</Output>
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<Group hide-input="false" labelreference="L35287" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numZ:=(1-My/x)*(1-omega*y-x+t/y*(v-1)-My)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVudW1aR0YoKiYsJiIiIkYwKiZJI015R0YoRjBJInhHRighIiJGNEYwLCxGMEYwKiZJJm9tZWdhR0YoRjBJInlHRihGMEY0RjNGNCooSSJ0R0YoRjBGOEY0LCZJInZHRihGMEY0RjBGMEYwRjJGNEYwNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" labelreference="L35312" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numZ_alt:=((x*y-t*(v-1))*(1-x-omega*y)-F)/x/y</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEpbnVtWl9hbHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1GIzYmLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2Ji1GIzYmLUYsNiVRInhGJ0YvRjItRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZeby1GLDYlUSJ5RidGL0YyRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZnby1GIzYmLUYsNiVRInRGJ0YvRjJGam4tRlc2JC1GIzYmLUYsNiVRInZGJ0YvRjJGY28tSSNtbkdGJDYkUSIxRidGOUY5RjlGOUY5RjlGam4tRlc2JC1GIzYpLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZmb0Zoby1GIzYmLUYsNiVRKCZvbWVnYTtGJy9GMEY9RjlGam5GYG9GOUZjb0Znbi1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkhGZm9GaG9GZXBGOUY5RjlGY28tRiw2JVEiRkYnRi9GMkY5RmVuLyUubGluZXRoaWNrbmVzc0dGaHAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYHIvJSliZXZlbGxlZEdGPUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSludW1aX2FsdEdGKCooLCYqJiwmKiZJInhHRigiIiJJInlHRihGNEY0KiZJInRHRihGNCwmSSJ2R0YoRjQhIiJGNEY0RjpGNCwoKiZJJm9tZWdhR0YoRjRGNUY0RjpGM0Y6RjRGNEY0RjRJIkZHRihGOkY0RjNGOkY1Rjo3I0Yu</Equation></Text-field>
</Output>
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<Group hide-input="false" labelreference="L35311" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(F=subs(x=y,FM),M=My,numZ_alt-numZ))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
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<Group labelreference="L35314" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L35313" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L30676" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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</Section><Presentation-Block>
<Group view="code" labelreference="L30673" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L30672" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L30755" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">When the ratio Z(x,y) reduces to its constant term: the cases omega=0, 1 (Sections 5, 8, 9).</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L30778" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This must be symmetric in x and y</Text-field>
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<Group view="code" hide-input="false" labelreference="L30730" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">esym:=(1-y-omega*x)*(1 - My/x)*(1 - y*omega - x - t*(1 - v)/y - My)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlc3ltR0YoKigsKComSSZvbWVnYUdGKCIiIkkieEdGKEYyISIiSSJ5R0YoRjRGMkYyRjIsJkYyRjIqJkkjTXlHRihGMkYzRjRGNEYyLCxGMkYyKiZGMUYyRjVGMkY0RjNGNCooSSJ0R0YoRjIsJkYyRjJJInZHRihGNEYyRjVGNEY0RjhGNEYyNyNGLg==</Equation></Text-field>
</Output>
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<Input><Text-field style="Text" layout="Normal">The variant mentioned in the paper</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30782" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">esym_paper:=(1-y-omega*x)*(y*My-t*(v-1))*(1-omega*y-My)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStlc3ltX3BhcGVyR0YoKigsKComSSZvbWVnYUdGKCIiIkkieEdGKEYyISIiSSJ5R0YoRjRGMkYyRjIsJiomSSNNeUdGKEYyRjVGMkYyKiZJInRHRihGMiwmSSJ2R0YoRjJGNEYyRjJGNEYyLCgqJkYxRjJGNUYyRjRGOEY0RjJGMkYyNyNGLg==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">This is x/y symmetric</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30781" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(x*y*esym+esym_paper)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCwoKiZJJm9tZWdhRzYiIiIiSSJ4R0YnRihGKEkieUdGJ0YoISIiRihGKCwoKiZJInRHRidGKEkidkdGJ0YoRigqJkYpRihGKkYoRitGLkYrRigsKComRiZGKEYqRihGKEYpRihGK0YoRihGKw==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">Indeed,</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30786" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(%/subs({x=y,y=x},%))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIi</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L30791" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L30788" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">Now omega=0 (Section 5.1, Section 8.2 for DA, Section 9.1 for trees)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L44878" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This is the series R, depending on t only</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30804" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">esym0:=subs(omega=0,esym_paper)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZlc3ltMEdGKCooLCZJInlHRighIiIiIiJGMkYyLCYqJkkjTXlHRihGMkYwRjJGMiomSSJ0R0YoRjIsJkkidkdGKEYyRjFGMkYyRjFGMiwmRjVGMUYyRjJGMjcjRi4=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">First terms in the series R (the first term is just t, written by Maple in a complicated form)</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L30797" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,series(subs(y=x, My=Mser(3),omega=0,esym0),t,4))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUYjNiYtRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW5HRiQ2JFEiMUYnRjMtRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQ0ZFRkgtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjRRJ2l0YWxpY0YnRjMtRiM2J0YvRk8tRjA2LVEnJnBsdXM7RidGM0Y2RjlGO0Y9Rj9GQUZDRkVGSEZWRjMvJS5saW5ldGhpY2tuZXNzR0ZSLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmJvLyUpYmV2ZWxsZWRHRjhGMy1GMDYtUTEmSW52aXNpYmxlVGltZXM7RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRltwLUZXNiVRInRGJ0ZaRmduRjNGW28tRiM2Ji1JKG1mZW5jZWRHRiQ2JC1GIzYnRi8tRlc2JVEidkYnRlpGZ25GU0ZPRjNGM0Znby1JJW1zdXBHRiQ2JUZdcC1GUDYkUSIyRidGMy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGM0Zbby1GIzYmLUZjcDYkLUYjNidGLy1GIzYmLUZQNiRRIjNGJ0YzRmdvRmdwRjNGU0ZPRjNGM0Znby1GW3E2JUZdcEZbckZgcUYzRltvLUYjNiYtRjA2LVEiT0YnRjNGNkY5RjtGPUY/RkFGQ0Zqb0ZccC1GMDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0YzRjZGOUY7Rj1GP0ZBRkNGam9GXHAtRmNwNiQtRiM2Jy1GW3E2JUZdcC1GUDYkUSI0RidGM0ZgcS8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y4RjNGM0YzRjM=">KytJInRHNiIsJComLCYiIiJGKEkieEdGJCEiIkYoLCZGKkYoRilGKEYqRipGKCwmSSJ2R0YkRipGKkYoIiIjLCZGLSEiJEYqRigiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJQ==</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L30801" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">esym0-R; factor([solve(%,My)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKCwmSSJ5RzYiISIiIiIiRihGKCwmKiZJI015R0YmRihGJUYoRigqJkkidEdGJkYoLCZJInZHRiZGKEYnRihGKEYnRigsJkYrRidGKEYoRihGKEkiUkdGJkYn</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyQsJCooLDAqKEkieUc2IiIiIkkidkdGKEYpSSJ0R0YoRilGKSomRitGKUYqRikhIiIqJkYrRilGJ0YpRi0qJEYnIiIjRilGK0YpRidGLSokKiYsJkYtRilGJ0YpRiksPCooRitGMEYqRjBGJ0YpRikqJkYrRjBGKkYwRi0qKEYrRjBGKkYpRidGKSEiIyooRitGKUYqRilGJ0YwRjgqJkYrRjBGKkYpRjAqJkYrRjBGJ0YpRikqKEYrRilGKkYpRidGKUYwKiZGK0YpRidGMEYwKiRGJyIiJEYpKiZJIlJHRihGKUYnRikiIiUqJEYrRjBGLUYuRjhGL0YtRikjRilGMEYpRilGM0YtRidGLUZELCQqKCwwRiZGLUYsRilGLkYpRi9GLUYxRilGK0YtRidGKUYpRjNGLUYnRi0jRi1GMA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L32828" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The expression of the paper</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30820" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR0:=(y+t*(v-1))/2/y - ((y-t*(v-1))/2/y)* sqrt(1-4*y*R/(1-y)/(y-t*(v-1))^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRNUjBHRigsJiomLCZJInlHRigiIiIqJkkidEdGKEYyLCZJInZHRihGMiEiIkYyRjJGMkYyRjFGNyNGMiIiIyooLCZGMUYyRjNGN0YyRjFGNywmRjJGMioqRjFGMkkiUkdGKEYyLCZGMUY3RjJGMkY3RjshIiMhIiVGOCNGN0Y5NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30819" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(subs(My=MR0,esym0)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJSRzYi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30861" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR01:=subs(v=1,MR0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVNUjAxR0YoLCYjIiIiIiIjRjAqJCwmRjBGMCooSSJ5R0YoISIiSSJSR0YoRjAsJkY1RjZGMEYwRjYhIiVGLyNGNkYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30812" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Checking the expression of M(y) in terms of R=R_0</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30807" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mexpr:=proc(N): local j,k,n: 
t*(v-1)/y+add(add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(n+j,n)*t^k*(v-1)^k*R^(n+1)*y^(j-n-k-1),j=0..N),k=0..N),n=0..N): end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L30815" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We expand (esym0-R) in t and R: a high lower degree confirms that Mexpr is a solution of the quadratic equation</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30813" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=4: factor(series(mtaylor(subs(My=Mexpr(n),esym0-R),[t,R],n),y,n))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInlHNiIsJComSSJSR0YkIiIjLCgqJkkidEdGJCIiIkkidkdGJEYsRihGJyIiKEYrISIjRiwhIiUiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGLCIiJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30803" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=8: factor(series(mtaylor(subs(My=Mexpr(n),esym0-R),[t,R],n),y,n)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30810" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ldegree(convert(%,polynom,[t,R,y]))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiM1</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30817" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=12: factor(series(mtaylor(subs(My=Mexpr(n),esym0-R),[t,R],n),y,n)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30818" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ldegree(convert(%,polynom,[t,R,y]))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjMTRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiM5</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L31100" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31099" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45003" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45131" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">Predicted singular point (Prediction 5.2)</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L45000" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR0</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiwmSSJ5RzYiIiIiKiZJInRHRiZGJywmSSJ2R0YmRichIiJGJ0YnRidGJ0YlRiwjRiciIiMqKCwmRiVGJ0YoRixGJ0YlRiwsJkYnRicqKkYlRidJIlJHRiZGJywmRiVGLEYnRidGLEYwISIjISIlRi0jRixGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45178" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series R0 computed when checking the theorems in the introduction</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45179" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R0ser</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45058" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"> We write u=t(v-1) in the discriminant of MR0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45056" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">disc:=subs(t=u/(v-1),1-4*y*R/(1-y)/(y-t*(v-1))^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVkaXNjR0YoLCYiIiJGLyoqSSJ5R0YoRi9JIlJHRihGLywmRjEhIiJGL0YvRjQsJkYxRi9JInVHRihGNCEiIyEiJTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L45060" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ndisc:=collect((1 - y)*(y - u)^2-4*y*R,y,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZuZGlzY0dGKCwqKiRJInlHRigiIiQhIiIqJiwmIiIiRjVJInVHRigiIiNGNUYwRjdGNSomLCgqJEY2RjdGMkkiUkdGKCEiJUY2ISIjRjVGMEY1RjVGOkY1NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45059" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The three roots</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L45057" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(allvalues,algeqtoseries(subs(u=t*(v-1), R=convert(R0ser,polynom), ndisc),t,y,2))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUrKUkidEc2IiIiIiIiISEiJUYmLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjRiYiIiMrKUYkLChJInZHRiVGJkYmRiYqJEYyI0YmRi9GL0YmLChGMkYvRi9GJkYzIiIlRi9GKSIiJCspRiQsKEYyRiZGJkYmRjMhIiNGJiwoRjJGL0YvRiZGM0YoRi9GKUY3</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L44992" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45067" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We want the discriminant to have a double root yc at the critical point tc</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45034" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dndisc:=diff(ndisc,y)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdkbmRpc2NHRigsLCokSSJ5R0YoIiIjISIkKiYsJiIiIkY1SSJ1R0YoRjFGNUYwRjVGMSokRjZGMSEiIkkiUkdGKCEiJUY2ISIjNyNGLg==</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L45033" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">By eliminating R or u, we can express u and R in terms of yc</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L45032" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(resultant(ndisc,dndisc,R))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiwmSSJ1RzYiIiIiSSJ5R0YmISIiRicsKCokRigiIiMhIiNGJUYnRihGJ0YnIiIl</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor([solve(%,u)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYpLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JkYuLUY5Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y8Rj4vRkJGQEZDRkVGR0ZJRktGTS9GUUZPLUYjNiQtRiw2Ji1GLDYmLUkjbW5HRiQ2JFEiMkYnRjxGVUYuRjwtRjk2LVEoJm1pbnVzO0YnRjxGPkZYRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZiby1GW282JFEiMUYnRjxGPEY8RjwvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGQEY8RjwvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0Yn">NyRJInlHNiIqJkYjIiIiLCZGIyIiIyEiIkYmRiY=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L45066" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">uc:=yc*(2*yc-1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1Y0dGKComSSN5Y0dGKCIiIiwmRi8iIiMhIiJGMEYwNyNGLg==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L45077" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(resultant(ndisc,dndisc,u))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJkkiUkc2IiIiIiwsKiRJInlHRiUiIiVGJiokRikiIiQhIiQqJEYpIiIjRixGJEYmRikhIiJGJiIjOw==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L45080" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rc:=subs(y=yc,factor(solve(op(3,%),R)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjUmNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZTLUYjNiYtRiw2JVEjeWNGJ0YvRjItRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZobi1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYnRk8tSSNtbkdGJDYkUSIxRidGOS1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkhGUkZURldGOUY5LUZjbzYkUSIzRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNSY0dGKCwkKiZJI3ljR0YoIiIiLCYhIiJGMUYwRjEiIiRGMzcjRi4=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L45023" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L45064" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font size="14" bold="true">The characterization of yc given in the paper, and a numerical check</Font></Text-field></Title><Presentation-Block>
<Group labelreference="L45052" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45096" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Numerics</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">fv:=2*Pi*v/(v-1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZnZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1GIzYoLUkjbW5HRiQ2JFEiMkYnRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZmbi1GLDYlUSUmcGk7RicvRjBGPUY5RlgtRiw2JVEidkYnRi9GMkY5LUYjNiZGXG8tRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZlby1GVTYkUSIxRidGOUY5LyUubGluZXRoaWNrbmVzc0dGaW8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnAvJSliZXZlbGxlZEdGPUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNmdkdGKCwkKioiIiMiIiJJI1BpR0YmRjFJInZHRihGMSwmRjNGMUYxISIiRjVGMTcjRi4=</Equation></Text-field>
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<Group view="code" labelreference="L45082" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(fv,v=0..20, y=-10..10)</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eval(subs(y=1,gy))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(factor(subs(vy,y*(2*y-1)/(v-1))),arctan,factor)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqLCIiJCIiIkkieUc2IkYlLCYqJiIiI0YlRiZGJUYlRiUhIiJGJUkjUGlHJSpwcm90ZWN0ZWRHRistSSdhcmN0YW5HNiRGLUkoX3N5c2xpYkdGJzYjKiQpLCYqJiIiJUYlRiZGJUYlRiVGKyNGJUYqRiVGJUYlKihGOEYlLCoqKEY3RiUpRiZGKkYlRixGJUYlKihGKkYlRiZGJUYsRiVGKyomRjRGJUYmRiVGJUYzRitGJUYsRitGKw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45152" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(y=1/2,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiMiIiIiIiVGJUkjUGlHJSpwcm90ZWN0ZWRHISIiRiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45107" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc:=proc(u) if u=1 then 1/2 else fsolve(subs(v=u,fv)-gy,y=1/4..1)fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45106" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc(2);yc(4);yc(0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC41NTgyNjMzOTMzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrTFJqI2UmISM1</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC42MjA4NDU2NTQ4RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrW2xYM2khIzU=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC4yNTAwMDAwMDAwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrKysrK0QhIzU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45129" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([seq([u,yc(u)],u=1..10)],style=point)</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [[[1, 1/2], [2, .5582633933], [3, .5945570270], [4, .6208456548], [5, .6413496308], [6, .6580769304], [7, .6721456535], [8, .6842435287], [9, .6948239327], [10, .7042014922]]], 3 = (style = point)]), &quot;originalview&quot; = [1. .. 10., .500000000000000000 .. .704201492199999945]])">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</Plot></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45133" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tc_val:=proc(u)
if u=1 then 1/4/Pi else yc(u)*(2*yc(u)-1)/(u-1):fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45124" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tc_val(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEuMC4wNjUwNTI2Mzk1MkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JCIrX1JFMGwhIzY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45104" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=plot([seq([i/10,tc_val(i/10)],i=0..100)],thickness=3,font=[helvetica,roman,16])</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [[[0, .1250000000], [1/10, .1119825072], [1/5, .1051783892], [3/10, .1000450210], [2/5, 0.9585134985e-1], [1/2, 0.9228320402e-1], [3/5, 0.8916920278e-1], [7/10, 0.8640323380e-1], [4/5, 0.8391410470e-1], [9/10, 0.8165130243e-1], [1, (1/4)/Pi], [11/10, 0.7766409118e-1], [6/5, 0.7588881465e-1], [13/10, 0.7423377833e-1], [7/5, 0.7268444108e-1], [3/2, 0.7122879286e-1], [8/5, 0.6985678965e-1], [17/10, 0.6855993846e-1], [9/5, 0.6733098769e-1], [19/10, 0.6616369435e-1], [2, 0.6505263952e-1], [21/10, 0.6399309035e-1], [11/5, 0.6298088609e-1], [23/10, 0.6201235036e-1], [12/5, 0.6108421529e-1], [5/2, 0.6019356418e-1], [13/5, 0.5933778291e-1], [27/10, 0.5851451889e-1], [14/5, 0.5772164633e-1], [29/10, 0.5695723879e-1], [3, 0.5621954485e-1], [31/10, 0.5550696695e-1], [16/5, 0.5481804368e-1], [33/10, 0.5415143630e-1], [17/5, 0.5350591321e-1], [7/2, 0.5288034024e-1], [18/5, 0.5227367042e-1], [37/10, 0.5168493470e-1], [19/5, 0.5111323493e-1], [39/10, 0.5055773759e-1], [4, 0.5001766653e-1], [41/10, 0.4949229871e-1], [21/5, 0.4898095934e-1], [43/10, 0.4848301767e-1], [22/5, 0.4799788341e-1], [9/2, 0.4752500286e-1], [23/5, 0.4706385644e-1], [47/10, 0.4661395592e-1], [24/5, 0.4617484205e-1], [49/10, 0.4574608172e-1], [5, 0.4532726682e-1], [51/10, 0.4491801183e-1], [26/5, 0.4451795257e-1], [53/10, 0.4412674430e-1], [27/5, 0.4374406100e-1], [11/2, 0.4336959291e-1], [28/5, 0.4300304700e-1], [57/10, 0.4264414430e-1], [29/5, 0.4229262017e-1], [59/10, 0.4194822280e-1], [6, 0.4161071248e-1], [61/10, 0.4127986076e-1], [31/5, 0.4095545033e-1], [63/10, 0.4063727332e-1], [32/5, 0.4032513172e-1], [13/2, 0.4001883611e-1], [33/5, 0.3971820564e-1], [67/10, 0.3942306739e-1], [34/5, 0.3913325567e-1], [69/10, 0.3884861191e-1], [7, 0.3856898425e-1], [71/10, 0.3829422711e-1], [36/5, 0.3802420068e-1], [73/10, 0.3775877116e-1], [37/5, 0.3749780948e-1], [15/2, 0.3724119243e-1], [38/5, 0.3698880082e-1], [77/10, 0.3674052058e-1], [39/5, 0.3649624182e-1], [79/10, 0.3625585868e-1], [8, 0.3601926917e-1], [81/10, 0.3578637539e-1], [41/5, 0.3555708263e-1], [83/10, 0.3533129977e-1], [42/5, 0.3510893891e-1], [17/2, 0.3488991515e-1], [43/5, 0.3467414657e-1], [87/10, 0.3446155422e-1], [44/5, 0.3425206153e-1], [89/10, 0.3404559489e-1], [9, 0.3384208274e-1], [91/10, 0.3364145630e-1], [46/5, 0.3344364873e-1], [93/10, 0.3324859539e-1], [47/5, 0.3305623391e-1], [19/2, 0.3286650363e-1], [48/5, 0.3267934602e-1], [97/10, 0.3249470432e-1], [49/5, 0.3231252343e-1], [99/10, 0.3213275002e-1], [10, 0.3195533231e-1]]], 3 = (thickness = 3), 4 = (font = [helvetica, roman, 16])]), &quot;originalview&quot; 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</Output>
</Group>
<Group labelreference="L45113" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">read(&quot;Q0.txt&quot;):</Text-field>
</Input>
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<Group view="code" labelreference="L45155" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q0pol:=convert(Q_0,polynom):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45116" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(Q_0,t)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiIsJComIiIjIiIiSSJ2R0YkRihGKEYoLCYqJkYnRigpRilGJ0YoRigqJiIiKUYoRilGKEYoRicsKComRidGKClGKSIiJEYoRigqJiIjQ0YoRixGKEYoKiYiI1NGKEYpRihGKEYyLCoqJkYnRigpRikiIiVGKEYoKiYiI1tGKEYxRihGKComIiRJI0YoRixGKEYoKiYiJEMjRihGKUYoRihGOiwsKiZGJ0YoKUYpIiImRihGKComIiMhKUYoRjlGKEYoKiYiJF0oRihGMUYoRigqJiIlUz9GKEYsRihGKComIiVXOEYoRilGKEYoRkQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJw==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L45158" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">nops(Q0pol); coeff(Q0pol,t,38)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjMzhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiNR</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45087" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot([seq(coeff(Q0pol,t,(5*n+7))/coeff(Q0pol,t,5*n+8),n=0..6)],v=0..10,colour=blue)</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [(2*v^7+168*v^6+3850*v^5+32788*v^4+112210*v^3+146160*v^2+54912*v)/(2*v^8+224*v^7+7140*v^6+89712*v^5+495180*v^4+1212768*v^3+1209414*v^2+366080*v), (2*v^12+528*v^11+43450*v^10+1582416*v^9+29526420*v^8+303693984*v^7+1781568600*v^6+5996984340*v^5+11339442400*v^4+11368065032*v^3+5330798876*v^2+852017152*v)/(2*v^13+624*v^12+61490*v^11+2723864*v^10+63002940*v^9+822444480*v^8+6310968924*v^7+28925828880*v^6+78791713286*v^5+123964474816*v^4+105807815750*v^3+43081573808*v^2+6085836800*v), 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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(subs(y=yc+epsilon,%),epsilon,3))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJKGVwc2lsb25HNiIsJCoqIyIiIiIiJUYoLCYqJkYpRihJI3ljR0YkRihGKEYoISIiRigpRiwiIiNGLSksJkYoRi1GLEYoRi9GLUYtRi8tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45008" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1 for the expression of M(y) to hold analytically</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L44997" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">mo:=factor(1-%%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNtb0dGKCwkKi4iIiUiIiJJInlHRihGMUkjeWNHRihGMSksJkYxISIiRjNGMSIiJEYxLCZGMUY2RjJGMUY2KSwoKiYiIiNGMSlGM0Y8RjFGNkYyRjFGM0YxRjxGNkYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45068" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Some special points</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45102" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(y=yc,mo)); factor(subs(y=(2*yc-1)^2,mo))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIi</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIi</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45173" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">A simple root of the discriminant: </Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45122" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(solve(-4*yc^2 + y + 4*yc - 1,y))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQpLCYqJiIiIyIiIkkjeWNHNiJGJ0YnRichIiJGJkYn</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45111" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font size="16" bold="true">Visualising the parts of the complex plane where the modulus is less than 1, for various values of yc</Font></Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L45174" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45176" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45016" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example: yc=1/4 (minimal value): three loops</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45004" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/4: (2*yc0-1)^2;factor(subs(yc=1/4,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JFEiNEYnRi8vJS5saW5ldGhpY2tuZXNzR0YuLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjkvJSliZXZlbGxlZEdRJmZhbHNlRic=">IyIiIiIiJQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKiIjRiIiIkkieUc2IkYlLCZGJSEiIkYmRiVGKSksJiomIiIpRiVGJkYlRiVGJUYlIiIjRilGKQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45114" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45168" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKiIkSCgiIiIsKiokKUkidUdGKCIiI0YxRjEqJClJInZHRihGNkYxRjEqJkY2RjFGNUYxISIiRjFGMUY7KSwqKiYiI2tGMUY0RjFGMSomRj9GMUY4RjFGMSomIiM7RjFGNUYxRjFGMUYxRjZGOywmRjNGMUY3RjFGMUYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45136" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained ,view=[-0.5..1.3,-0.4..0.4],labels=[a,b],font=[Helvetica,roman,12])</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(u=0,v=0,cond-1);subs(u=0.8,v=0,cond-1);;subs(u=-0.2,v=0,cond-1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFErJnVtaW51czA7MUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">ISIi</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsMi44ODk3NDA1MzBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JCIrSTB1KilHISIq</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEsMTU1LjI1MDAwMDBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JCIrKytdXzohIig=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L45020" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45078" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45112" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example: yc=1/4+1/20 (just above minimal value): three loops</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45117" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/4+1/20: (2*yc0-1)^2;factor(subs(yc=1/4+1/20,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JFEjMjVGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Y6LyUpYmV2ZWxsZWRHUSZmYWxzZUYn">IyIiJSIjRA==</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKiMiJUg1IiIlIiIiSSJ5RzYiRicsJkYnISIiRihGJ0YrKSwmKiYiI0RGJ0YoRidGJyIiJEYnIiIjRitGKw==</Equation></Text-field>
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<Group view="code" labelreference="L45051" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Group view="code" hide-input="false" labelreference="L45095" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKiMiKFQpZTUiIzsiIiIsKiokKUkidUdGKCIiI0YzRjMqJClJInZHRihGOEYzRjMqJkY4RjNGN0YzISIiRjNGM0Y9KSwqKiYiJEQnRjNGNkYzRjMqJkZBRjNGOkYzRjMqJiIkXSJGM0Y3RjNGMyIiKkYzRjhGPSwmRjVGM0Y5RjNGM0YzNyNGLg==</Equation></Text-field>
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<Group view="code" labelreference="L45053" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],numpoints=10000,labels=[a,b]):</Text-field>
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<Group view="code" labelreference="L45125" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot(0,a=(2*yc0-1)^2..1,thickness=6):display(P1,P2)</Text-field>
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<Group view="code" labelreference="L45091" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example, still below 1/2: yc=1/3 (again three loop)</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L45134" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/3: (2*yc0-1)^2;factor(subs(yc=1/3,mo))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JFEiOUYnRi8vJS5saW5ldGhpY2tuZXNzR0YuLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjkvJSliZXZlbGxlZEdRJmZhbHNlRic=">IyIiIiIiKg==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">implicitplot(cond-1,u=-1..1.5,v=-0.5..0.5,numpoints=10000,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],numpoints=10000)</Text-field>
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<Group view="code" labelreference="L45069" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example, just below 1/2</Text-field>
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<Group view="code" hide-input="false" labelreference="L45031" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2-1/10: (2*yc0-1)^2;factor(subs(yc=1/2-1/10,mo))</Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=a+I*b,1/%)*subs(y=a-I*b,1/%))))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">implicitplot(cond-1,a=-1..1.5,b=-0.5..0.5,numpoints=10000,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],numpoints=10000)</Text-field>
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<Input><Text-field style="Text" layout="Normal">Example: transition at yc=1/2: the inside loop reduces to a point</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2: (2*yc0-1)^2; factor(subs(yc=1/2,mo))</Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand((subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(%%-1,y)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JFEiMkYnRjIvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRjwvJSliZXZlbGxlZEdRJmZhbHNlRictSSNtb0dGJDYtUSgmY29tbWE7RidGMi8lJmZlbmNlR0ZBLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRkEvJSpzeW1tZXRyaWNHRkEvJShsYXJnZW9wR0ZBLyUubW92YWJsZWxpbWl0c0dGQS8lJ2FjY2VudEdGQS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRitGMg==">NiQjIiIiIiIjRiM=</Equation></Text-field>
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<Group view="code" labelreference="L45105" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-0.5..0.5,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],numpoints=10000,labels=[a,b]):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45100" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot(0,a=(2*yc0-1)^2..1,thickness=6):display(P1,P2)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2+1/22: (2*yc0-1)^2;factor(subs(yc=1/2+1/22,mo))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKiIoKysrKiIiIiwqKiQpSSJ1R0YoIiIjRjFGMSokKUkidkdGKEY2RjFGMSomRjZGMUY1RjEhIiJGMUYxRjspLCoqJiImVFkiRjFGNEYxRjEqJkY/RjFGOEYxRjEqJiIlXzlGMUY1RjFGOyIjT0YxRjZGOywmRjNGMUY3RjFGMUYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45001" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The inside loop is swalled by the outer curve</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45099" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..1.5,v=-0.5..0.5,numpoints=10000,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],numpoints=10000,labels=[a,b]):</Text-field>
</Input>
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<Group view="code" labelreference="L45074" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot(0,a=(2*yc0-1)^2..1,thickness=6):display(P1,P2)</Text-field>
</Input>
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<Group view="code" labelreference="L44993" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example, beyond 1/2: </Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L45015" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2+1/15: (2*yc0-1)^2;factor(subs(yc=1/2+1/15,mo))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjRGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JFEkMjI1RidGLy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGOi8lKWJldmVsbGVkR1EmZmFsc2VGJw==">IyIiJSIkRCM=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKiMiJlx0JCIiJSIiIkkieUc2IkYnLCZGJyEiIkYoRidGKyksJiomIiREI0YnRihGJ0YnIiM8RisiIiNGK0Yr</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Group view="code" hide-input="false" labelreference="L45012" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2+1/8: (2*yc0-1)^2;factor(subs(yc=1/2+1/8,mo))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiw2JFEjMTZGJ0YvLyUubGluZXRoaWNrbmVzc0dGLi8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Y5LyUpYmV2ZWxsZWRHUSZmYWxzZUYn">IyIiIiIjOw==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..1.5,v=-0.5..0.5,numpoints=10000,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],labels=[a,b]):</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot(0,a=(2*yc0-1)^2..1,thickness=6):display(P1,P2)</Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45175" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example: yc=9/10</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L45038" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=9/10,mo))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSZtZnJhY0dGJDYoLUYjNiYtSSNtbkdGJDYkUSI5RidGLy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRlMtSSNtaUdGJDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8tRiM2KC1GTDYkUSI0RidGL0ZPLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GTDYkUSIxRidGLy1GLDYtUScmcGx1cztGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERlVGL0YvRk8tSSVtc3VwR0YkNiUtRl5vNiQtRiM2Ji1GIzYmLUZMNiRRIzI1RidGL0ZPRlVGLy1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GTDYkUSMxOEYnRi9GL0YvLUZMNiRRIjJGJ0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YvLyUubGluZXRoaWNrbmVzc0dGZG8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZHEvJSliZXZlbGxlZEdGNEYv">LCQqKiMiIioiIiUiIiJJInlHNiJGJywmRichIiJGKEYnRispLCYqJiIjREYnRihGJ0YnIiM9RisiIiNGK0Yr</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L45138" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L45140" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=1/factor(expand(rationalize(subs(y=u+I*v,1/%)*subs(y=u-I*v,1/%))))</Text-field>
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<Input><Text-field style="Text" layout="Normal">The curve gets smaller and smaller</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">implicitplot(cond-1,u=-1..1.5,v=-0.5..0.5,numpoints=10000,scaling=constrained,view=[-0.5..1.3,-0.4..0.4],labels=[a,b])</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,subs(R=Rc, t=u/(v-1),u=uc,MR0))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKCMiIiIiIiNGJSwoKiZGJkYlKUkjeWNHNiJGJkYlRiVJInlHRitGJUYqISIiRiVGLEYtRiUqKkYkRiUsKEYoRi1GLEYlRipGJUYlKSoqLCoqJiIiJUYlRilGJUYtRixGJSomRjRGJUYqRiVGJUYlRi1GJSksJkYsRiVGKkYtRiZGJSwmRiVGLUYsRiVGLSlGL0YmRi1GJEYlRixGLUYt</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44999" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We assume y&gt;yc and y &gt;yc(2yc-1) (in fact the first condition implies the second)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45037" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mc:=(2*yc^2 + y - yc)/(2*y)-1/2/y*(y - yc)*sqrt((-4*yc^2 + y + 4*yc - 1)/((-1 + y)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNNY0dGKCwmKigjIiIiIiIjRjEsKComRjJGMSlJI3ljR0YoRjJGMUYxSSJ5R0YoRjFGNiEiIkYxRjdGOEYxKipGMEYxRjdGOCwmRjdGMUY2RjhGMSkqJiwqKiYiIiVGMUY1RjFGOEY3RjEqJkY/RjFGNkYxRjFGMUY4RjEsJkYxRjhGN0YxRjhGMEYxRjg3I0Yu</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L44996" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(Mc,y,1) assuming (yc&gt;1/4,yc&lt;1/2));
factor(series(Mc,y,1) assuming (yc&lt;1,yc&gt;1/2))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInlHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiE=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInlHNiIqJkkjeWNHRiQiIiIsJiomIiIjRidGJkYnRidGJyEiIkYnRistSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45043" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Anti-derivative</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45040" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mhat:=int(Mc,y):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45013" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45165" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Expression of the paper. The log is taken with a cut on the *positive* real axis</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45143" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mhat_pap := yc*(2*yc - 1)*ln((sqrt((-4*yc^2 + y + 4*yc - 1)/(-1 + y))*(y-1)  + y + 2*yc - 1)/(2*yc))-((-1 + y)*(sqrt((-4*yc^2 + y + 4*yc - 1)/(-1 + y))))/2+(y-1)/2</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlNaGF0X3BhcEdGKCwqKihJI3ljR0YoIiIiLCYqJiIiI0YxRjBGMUYxRjEhIiJGMS1JI2xuR0YlNiMsJCooI0YxRjRGMSwqKiYpKiYsKiomIiIlRjEpRjBGNEYxRjVJInlHRihGMSomRkJGMUYwRjFGMUYxRjVGMSwmRjFGNUZERjFGNUY7RjFGRkYxRjFGREYxRjNGMUYxRjVGMUYwRjVGMUYxRjEqKEY7RjFGPkYxRkZGMUY1RjtGNSomRjtGMUZERjFGMTcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45161" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(factor(expand(rationalize(diff(Mhat_pap,y))))); factor(%-Mc)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiIiIiIiNGJSwqKiYsJkkieUc2IiEiIkkjeWNHRitGJUYlKSomLCoqJiIiJUYlKUYtRiZGJUYsRipGJSomRjJGJUYtRiVGJUYlRixGJSwmRiVGLEYqRiVGLEYkRiVGJSomRiZGJUYzRiVGJUYqRiVGLUYsRiVGKkYsRiU=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L45098" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr:=(sqrt((-4*yc^2 + y + 4*yc - 1)/(-1 + y))*(-1 + y) + y + 2*yc - 1)/(2*yc)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoLCQqKCMiIiIiIiNGMSwqKiYpKiYsKiomIiIlRjEpSSN5Y0dGKEYyRjEhIiJJInlHRihGMSomRjlGMUY7RjFGMUYxRjxGMSwmRjFGPEY9RjFGPEYwRjFGP0YxRjFGPUYxKiZGMkYxRjtGMUYxRjFGPEYxRjtGPEYxNyNGLg==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">When is expr real and positive? Only for y real \134ge 0 (light blue below)</Font></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots): complexplot3d(subs(yc=1/2,expr),y=-2-2*I..2+2*I);</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJKGVwc2lsb25HNiIsJiomIiIlIiIiSSN5Y0dGJEYoISIiRihGKCIiISooKiZGJ0YoXiNGKEYoRihGKUYoLCZGKEYqRilGKEYqRigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiIw==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L45150" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">sqrt_p:=-I*sqrt(4*yc-1);sqrt_m:=I*sqrt(4*yc-1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdzcXJ0X3BHRigsJComLCReIyIiIkYyRjIpLCYqJiIiJUYySSN5Y0dGKEYyRjJGMiEiIiNGMiIiI0YyRjg3I0Yu</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdzcXJ0X21HRigqJl4jIiIiRjApLCYqJiIiJUYwSSN5Y0dGKEYwRjBGMCEiIiNGMCIiI0YwNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45177" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The part with the log</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45151" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr:=(sqrt((-4*yc^2 + y + 4*yc - 1)/(-1 + y))*(-1 + y) + y + 2*yc - 1)/(2*yc)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoLCQqKCMiIiIiIiNGMSwqKiYpKiYsKiomIiIlRjEpSSN5Y0dGKEYyRjEhIiJJInlHRihGMSomRjlGMUY7RjFGMUYxRjxGMSwmRjFGPEY9RjFGPEYwRjFGP0YxRjFGPUYxKiZGMkYxRjtGMUYxRjFGPEYxRjtGPEYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45149" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(sqrt((-4*yc^2 + y + 4*yc - 1)/(-1 + y))=sqrt_p,y=yc,expr);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2KS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZGLUYsNigtSSNtbkdGJDYkUS0mSW1hZ2luYXJ5STtGJ0YyLUYvNi1RMSZJbnZpc2libGVUaW1lcztGJ0YyRjVGOEY6RjxGPkZARkIvRkVRJjAuMGVtRicvRkhGUy1JJm1zcXJ0R0YkNiMtRiw2Ji1GLDYmLUZMNiRRIjRGJ0YyRk8tSSNtaUdGJDYlUSN5Y0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyLUYvNi1RKCZtaW51cztGJ0YyRjVGOEY6RjxGPkZARkJGREZHLUZMNiRRIjFGJ0YyRjJGTy1JKG1mZW5jZWRHRiQ2JC1GLDYnRi5GZW8tRi82LVEnJnBsdXM7RidGMkY1RjhGOkY8Rj5GQEZCRkRGR0ZpbkYyRjJGMkZdcC1GLDYmLUZMNiRRIjNGJ0YyRk9GaW5GMkZib0Zlb0YyLUYsNiYtRkw2JFEiMkYnRjJGT0ZpbkYyLyUubGluZXRoaWNrbmVzc0dGZ28vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnEvJSliZXZlbGxlZEdGNw==">LCQqKCMiIiIiIiNGJSwoKigsJF4jRiVGJUYlKSwmKiYiIiVGJUkjeWNHNiJGJUYlRiUhIiJGJEYlLCZGJUYxRi9GJUYlRjEqJiIiJEYlRi9GJUYlRiVGMUYlRi9GMUYl</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45119" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">squared modulus: very simple</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45120" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(%*subs(I=-I,%)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEjeWNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">SSN5Y0c2Ig==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45075" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" inline-output="false" labelreference="L45144" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L45147" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45145" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The simplified expression of M</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45142" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">di:=(-4*yc^2 + y + 4*yc - 1)/(-1 + y)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNkaUdGKComLCoqJiIiJSIiIilJI3ljR0YoIiIjRjIhIiJJInlHRihGMiomRjFGMkY0RjJGMkYyRjZGMiwmRjJGNkY3RjJGNjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L45169" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc0:=1/2: 1/factor(1/I*expand(factor(expand(rationalize(1/(subs(y=a+I*b,yc=yc0,di)- subs(y=a-I*b,yc=yc0,di)))))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCIiIyIiIkkiYkc2IkYlLCoqJClJImFHRidGJEYlRiUqJClGJkYkRiVGJSomRiRGJUYrRiUhIiJGJUYlRi9GJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45170" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The discriminant di is only negative when y is real</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L45171" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">1/factor(1/I*expand(factor(expand(rationalize(1/(subs(y=a+I*b,yc=yc,di)- subs(y=a-I*b,yc=yc,di)))))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLCIiKSIiIiwqKiQpSSJhRzYiIiIjRiVGJSokKUkiYkdGKkYrRiVGJSomRitGJUYpRiUhIiJGJUYlRjBGLkYlSSN5Y0dGKkYlLCZGJUYwRjFGJUYlRjA=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45167" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45166" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L45172" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" labelreference="L45045" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L31098" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31097" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31096" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30816" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">Explicit differential equations for R0 and Q0 (Section 8.2)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35562" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Our first objective is to study the vector space spanned by Omega and its derivatives in r  and u.
<Font encoding="UTF-8">We will first guess linear relations between these derivatives, using Hermite-Pad\303\251 approximants.
</Font>Since they handle power series in one variable only (possibly with polynomial coefficients), we do the guessing for Omega and its derivatives evaluated at r and u*r.</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35561" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series Omega</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31164" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(k+2* n, n)*u^k*
r^(n + 1)/(n + 1), k = 0 .. N-n-1), n = 0 .. N-1); end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31190" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjNyIiIilJInJHNiIiIiRGJUYlKigiIipGJSlGJyIiI0YlSSJ1R0YoRiVGJSomRidGJSlGLkYtRiVGJSomRi1GJUYsRiVGJSomRidGJUYuRiVGJUYnRiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L32829" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Redefining derivatives so that diff(F,x$0) is understood...</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31141" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">der:=proc(F,x,k)
if k=0 then F else diff(F,x$k): fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31146" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">der(u^2*r,r,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjwvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkcvJSlzdHJldGNoeUdGRy8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVi1GLzYlUSJyRidGMkY1Rjw=">KiYpSSJ1RzYiIiIjIiIiSSJyR0YlRic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L31191" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Derivatives of Omega w.r.t. r and u</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31188" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_d:=proc(N,d1,d2)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(k+2* n, n)*der(u^k,u,d2)*
der(r^(n + 1),r,d1)/(n + 1), k = 0 .. N-n+d2), n = 0 .. N-1+d1); end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31149" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_d(4,1,1); Omega_d(4,0,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LEAqJiImIVF6IiIiKUkickc2IiIiJUYlRiUqKCImP0YnRiUpRiciIiRGJUkidUdGKEYlRiUqKCImSUsiRiUpRiciIiNGJSlGLkYyRiVGJSooIiQ/KEYlRidGJSlGLkYtRiVGJSomIiImRiUpRi5GKUYlRiUqJiIlK1xGJUYsRiVGJSooIiUrRkYlRjFGJUYuRiVGJSooIiQrJEYlRidGJUYzRiVGJSomRilGJUY2RiVGJSomRj9GJUYxRiVGJSooIiMnKkYlRidGJUYuRiVGJSomRi1GJUYzRiVGJSomIiM9RiVGJ0YlRiUqJkYyRiVGLkYlRiVGJUYl</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LD4qKCIlRDciIiIpSSJyRzYiIiIlRiVJInVHRihGJUYlKigiJF0lRiUpRiciIiRGJSlGKiIiI0YlRiUqKCIjXUYlKUYnRjBGJSlGKkYuRiVGJSomRidGJSlGKkYpRiVGJSomIiQrIkYlRiZGJUYlKihGOEYlRi1GJUYqRiVGJSooIiNDRiVGM0YlRi9GJUYlKiZGJ0YlRjRGJUYlKiYiIzdGJUYtRiVGJSooIiIqRiVGM0YlRipGJUYlKiZGJ0YlRi9GJUYlKiZGMEYlRjNGJUYlKiZGJ0YlRipGJUYlRidGJQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L31192" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now, let's guess relations between these functions (evaluated at (r,ur) as said above). Moreover, it is often faster to specialise u, do the guessing and reconstruct.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35565" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(numapprox):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35568" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The vector space spanned by Omega and its derivatives</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35578" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The second derivative in r in terms of 3 other series, namely Omega and its first derivatives (in r and in u)</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35584" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=100*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIiYrKyQiIiJJInJHNiJGJiEiIiIkLyRGJiwkKigiJCsiRiZGJ0YmLCYqJiIkKylGJkYnRiZGJkYmRiZGJkYmLCQqKCIlKztGJkYnRiYsJiomIiV2PUYmRidGJkYmIiM+RilGJkYmKiZGJ0YmLCoqJiIqKysrKyJGJilGJyIiJEYmRiYqJiIoKysjSEYmKUYnIiIjRiZGKSomIiY7PyRGJkYnRiZGJiIkLCJGKUYm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35590" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=1000*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIigrKyskIiIiSSJyRzYiRiZGJiIlL0khIiIsJCooIiUrNUYmRidGJiwmKiYiJSshKUYmRidGJkYmRiZGJkYmRiosJCooIiUrU0YmRidGJiwmKiYiJysrdkYmRidGJkYmIiReKEYqRiZGKiwkKiZGJ0YmLCoqJiIuKysrKysrIkYmKUYnIiIkRiZGJiomIisrKysjKkhGJilGJyIiI0YmRioqJiIoOystJEYmRidGJkYmIiUsNUYqRiZGKg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35591" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The coefficients are not too hard to guess for a generic u. But on this example, things work quite efficiently with the parameter u.</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35583" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed1:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkMUdGKDcmLCgqKCIiJCIiIkkickdGKEYyKUkidUdGKCIiI0YyISIiKiZGMUYyRjVGMkYyIiIlRjIqKEY1RjJGM0YyLCYqKCIiKUYyRjNGMkY1RjJGMkYyRjJGMiooRjVGMkYzRjIsKEYwRjJGOEY3RjlGN0YyKiZGM0YyLDIqJilGM0YxRjIpRjVGOUYyRjIqKEYxRjIpRjNGNkYyKUY1RjFGMkY3KihGPUYyRkZGMkY0RjJGMkYwRjIqKCIjP0YyRjNGMkY1RjJGMiomIiM7RjJGM0YyRjJGNUY3RjJGN0YyNyNGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35587" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The second derivative in u in terms of the same 3 series</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35597" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=1000*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,0,2)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsKComIigrKysiIiIiKUkickc2IiIiI0YmRiYqJiIlNz9GJkYoRiYhIiJGJkYmLCQqJkYoRiYsKComIigrKyslRiZGJ0YmRiYqJiIlO11GJkYoRiZGLUYmRiZGJkYtLCQqKCIlKzVGJkYoRiZGI0YmRi0qJkYoRiYsKiomIi4rKysrKysiRiYpRigiIiRGJkYmKiYiKysrKyMqSEYmRidGJkYtKiYiKDsrLSRGJkYoRiZGJiIlLDVGLUYm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35598" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed2:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,0,2)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkMkdGKDcmLCoqJilJInJHRigiIiMiIiIpSSJ1R0YoRjNGNCEiIiooRjNGNEYyRjRGNkY0RjQqJiIjN0Y0RjJGNEY0RjRGNyomRjJGNCwqKigiIiVGNEYxRjRGNUY0RjQqKCIiJkY0RjJGNEY2RjRGNyomIiM7RjRGMkY0RjdGNEY0RjQqKEY2RjRGMkY0LCpGMEY0RjhGN0Y5RjdGNEY0RjQsJComRjJGNCwyKiYpRjIiIiRGNClGNkY+RjRGNCooRkpGNEYxRjQpRjZGSkY0RjcqKCIiKUY0RjFGNEY1RjRGNCooRkpGNEYyRjRGNUY0RjQqKCIjP0Y0RjJGNEY2RjRGNEZBRjRGNkY3RjRGN0Y0Rjc3I0Yu</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35579" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Finally, rhe mixed derivative in r,u</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35582" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=10*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,1,1)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIiMhKSIiIkkickc2IkYmISIiRiZGKSwkKigiIzVGJkYnRiYsKComIiQrIkYmKUYnIiIjRiZGJiomIiNLRiZGJ0YmRilGJkYmRiZGKSwkKihGLEYmRidGJiwmRiRGJkYmRiZGJkYmLCQqJkYnRiYsKiomIiYrKyJGJilGJyIiJEYmRiYqJiIlK0FGJkYwRiZGKSomIiQ7JkYmRidGJkYmIiM2RilGJkYp</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35589" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed3:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,1,1)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkM0dGKDcmLCYqKCIiKSIiIkkickdGKEYySSJ1R0YoRjJGMkYyRjIqKEY0RjJGM0YyLCoqJilGMyIiI0YyKUY0RjlGMkYyKihGOUYyRjNGMkY0RjIhIiIqJiIjN0YyRjNGMkY8RjJGMkYyLCQqKEY0RjJGM0YyRi9GMkY8KiZGM0YyLDIqJilGMyIiJEYyKUY0IiIlRjJGMiooRkVGMkY4RjIpRjRGRUYyRjwqKEYxRjJGOEYyRjpGMkYyKihGRUYyRjNGMkY6RjJGMiooIiM/RjJGM0YyRjRGMkYyKiYiIztGMkYzRjJGMkY0RjxGMkY8RjI3I0Yu</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35585" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">So it seems that we have a vector space of dimension 3. Let us reconstruct 3 equations, recalling that the above linear relations are for series avaluated at (r,ur)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35580" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1:=subs(u=u/r,coed1[1])*Om(r,u)+subs(u=u/r,coed1[2])*diff(Om(r,u),r)+subs(u=u/r,coed1[3])*diff(Om(r,u),u)+subs(u=u/r,coed1[4])*diff(Om(r,u),r$2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35570" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed2:=subs(u=u/r,coed2[1])*Om(r,u)+subs(u=u/r,coed2[2])*diff(Om(r,u),r)+subs(u=u/r,coed2[3])*diff(Om(r,u),u)+subs(u=u/r,coed2[4])*diff(Om(r,u),u$2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35602" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed3:=subs(u=u/r,coed3[1])*Om(r,u)+subs(u=u/r,coed3[2])*diff(Om(r,u),r)+subs(u=u/r,coed3[3])*diff(Om(r,u),u)+subs(u=u/r,coed3[4])*diff(diff(Om(r,u),r),u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35601" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Once these equations are guessed, they are easy to check by coefficient extraction, since Omega(r,u) is doubly hypergeometric.
Let us also check them numerically</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35661" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjNyIiIilJInJHNiIiIiRGJUYlKigiIipGJSlGJyIiI0YlSSJ1R0YoRiVGJSomRidGJSlGLkYtRiVGJSomRi1GJUYsRiVGJSomRidGJUYuRiVGJUYnRiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35600" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed1))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35603" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed2))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35605" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed3))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35604" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35569" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L35567" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" labelreference="L35566" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35564" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We can express all partial derivatives of Omega(r,u) in terms of 3 of them.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L31390" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1; ed2;ed3</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsKiomLCoqJClJInVHRigiIiMiIiIhIiIqJiIjN0YzSSJyR0YoRjNGMyomRjJGM0YxRjNGM0YzRjRGMy1JI09tR0YoNiRGN0YxRjNGMyooRjdGMywqKiYiIiVGM0YwRjNGMyomIiM7RjNGN0YzRjQqJiIiJkYzRjFGM0Y0RjNGM0YzLUklZGlmZkdGJjYkRjlGN0YzRjMqKEYxRjMsKkYvRjNGNUY0RjhGNEYzRjNGMy1GRTYkRjlGMUYzRjMqKEY3RjMsMiomRjdGNClGMUY/RjNGMyooIiIkRjNGN0Y0KUYxRlBGM0Y0KiYiIilGM0YwRjNGMyooRlBGM0Y3RjRGMEYzRjMqJiIjP0YzRjFGM0YzRkBGMyomRjFGM0Y3RjRGNEYzRjRGMy1GRTYkRjktSSIkR0YmNiRGMUYyRjNGNDcjLCpGLUYzRjxGM0ZHRjMqKEY3RjNGTEYzLUZFNiRGSUYxRjNGNA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L31313" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d11:=(convert(isolate(ed1,diff(Om(r, u),r$2 )),D))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkMTFHRigvLS0mSSJER0YlNiQiIiJGNDYjSSNPbUdGKDYkSSJyR0YoSSJ1R0YoKigsKComLCgqKCIiJEY0RjghIiIpRjkiIiNGNEZAKihGP0Y0RjlGNEY4RkBGNCIiJUY0RjQtRjZGN0Y0RkAqKEY5RjQsJiomIiIpRjRGOUY0RjRGNEY0RjQtLSZGMjYjRjRGNUY3RjRGQCooRjlGNCwoRj5GNEZDRkBGREZARjQtLSZGMjYjRkJGNUY3RjRGQEY0RjhGQCwyKiZGOEZAKUY5RkRGNEY0KihGP0Y0RjhGQClGOUY/RjRGQComRklGNEZBRjRGNEY+RjQqJiIjP0Y0RjlGNEY0KiYiIztGNEY4RjRGNComRjlGNEY4RkBGQEY0RkBGQDcjRi4=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L31310" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d22:=(convert(isolate(ed2,diff(Om(r, u),u$2 )),D))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31312" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d12:=convert(isolate(ed3,diff(diff(Om(r, u),r),u )),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkMTJHRigvLS0mSSJER0YlNiQiIiIiIiM2I0kjT21HRig2JEkickdGKEkidUdGKCooLCgqJiwmKiYiIilGNEY6RjRGNEY0RjRGNC1GN0Y4RjQhIiIqKEY6RjQsKiokKUY6RjVGNEY0KiYiIzdGNEY5RjRGQiomRjVGNEY6RjRGQkY0RjRGNC0tJkYyNiNGNEY2RjhGNEZCKihGOkY0Rj5GNC0tJkYyNiNGNUY2RjhGNEY0RjRGOUZCLDIqJkY5RkIpRjoiIiVGNEY0KigiIiRGNEY5RkIpRjpGWEY0RkIqJkZARjRGRkY0RjQqKEZYRjRGOUZCRkZGNEY0KiYiIz9GNEY6RjRGNComIiM7RjRGOUY0RjQqJkY6RjRGOUZCRkJGNEZCRkI3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31311" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We observe that the second order derivatives are in fact linear combinations of </Text-field><Text-field style="Text" layout="Normal">Om_r and the difference Phi:=(Om- u*Om_u).</Text-field><Text-field style="Text" layout="Normal">So we also have a 2D sub-space generated by these two series</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L31268" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi_ser:=proc(N)
Omega_d(N,0,0)-u*Omega_d(N,0,1): end:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35607" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check this</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35612" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef:=D[2](Om)(r, u)= (Om(r,u)-Phi(r,u))/u</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwaGlkZWZHRigvLS0mSSJER0YlNiMiIiM2I0kjT21HRig2JEkickdGKEkidUdGKComLCYtRjZGNyIiIi1JJFBoaUdGKEY3ISIiRj1GOUZANyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35606" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed11_phi:=collect(subs(phidef, d11),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDExX3BoaUdGKC8tLSZJIkRHRiU2JCIiIkY0NiNJI09tR0YoNiRJInJHRihJInVHRigsJiosRjlGNCwmKiYiIilGNEY5RjRGNEY0RjRGNEY4ISIiLDIqJkY4Rj8pRjkiIiVGNEY0KigiIiRGNEY4Rj8pRjlGRUY0Rj8qJkY+RjQpRjkiIiNGNEY0KihGRUY0RjhGP0ZIRjRGNComIiM/RjRGOUY0RjQqJiIjO0Y0RjhGNEY0KiZGOUY0RjhGP0Y/RjRGP0Y/LS0mRjI2I0Y0RjVGN0Y0Rj8qKiwoRkpGNCooRkVGNEY5RjRGOEY/Rj9GQ0Y/RjQtSSRQaGlHRihGN0Y0RjhGP0ZARj9GNDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35610" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed22_phi:=collect(subs(phidef, d22),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDIyX3BoaUdGKC8tLSZJIkRHRiU2JCIiI0Y0NiNJI09tR0YoNiRJInJHRihJInVHRigsJiooLCoqJiIiJSIiIilGOUY0Rj8hIiIqJiIjO0Y/RjhGP0Y/KiYiIiZGP0Y5Rj9GP0Y/RkFGPywyKiZGOEZBKUY5Rj5GP0Y/KigiIiRGP0Y4RkEpRjlGSkY/RkEqJiIiKUY/RkBGP0Y/KihGSkY/RjhGQUZARj9GPyomIiM/Rj9GOUY/Rj9GQkY/KiZGOUY/RjhGQUZBRj9GQUZBLS0mRjI2I0Y/RjVGN0Y/RkEqKiwqKiRGQEY/Rj8qJiIjN0Y/RjhGP0ZBKiZGNEY/RjlGP0ZBRj9GP0Y/LUkkUGhpR0YoRjdGP0Y4RkFGRkZBRkE3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35609" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed12_phi:=collect(subs(phidef, d12),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDEyX3BoaUdGKC8tLSZJIkRHRiU2JCIiIiIiIzYjSSNPbUdGKDYkSSJyR0YoSSJ1R0YoLCYqLEY6RjQsKiokKUY6RjVGNEY0KiYiIzdGNEY5RjQhIiIqJkY1RjRGOkY0RkJGNEY0RjRGOUZCLDIqJkY5RkIpRjoiIiVGNEY0KigiIiRGNEY5RkIpRjpGSUY0RkIqJiIiKUY0Rj9GNEY0KihGSUY0RjlGQkY/RjRGNComIiM/RjRGOkY0RjQqJiIjO0Y0RjlGNEY0KiZGOkY0RjlGQkZCRjRGQkZCLS0mRjI2I0Y0RjZGOEY0RkIqKiwmKiZGTEY0RjpGNEY0RjRGNEY0LUkkUGhpR0YoRjhGNEY5RkJGREZCRkI3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35608" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We will also need the derivatives of Phi</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35649" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
factor(hermite_pade(subs(u=u*r,[diff(Phi_ser(N),r), Omega_d(N,1,0),Phi_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUsMiomKUkickc2IiIiJCIiIilJInVHRiciIiVGKUYpKihGKEYpKUYmIiIjRikpRitGKEYpISIiKigiIilGKUYuRikpRitGL0YpRikqKEYoRilGJkYpRjRGKUYpKigiIz9GKUYmRilGK0YpRikqJiIjO0YpRiZGKUYpRitGMUYpRjEsMiooRi9GKUYlRilGKkYpRjEqKCIiJkYpRi5GKUYwRilGKSooRixGKUYuRilGNEYpRikqKEYsRilGJkYpRjRGKUYxRjZGMUY4RjFGK0YpRilGKSwkKiZGK0YpLCYqKEYzRilGJkYpRitGKUYpRilGKUYpRjE=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35655" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edPhi1:=subs(u=u/r,op(1,%))*diff(Phi(r,u),r)+ subs(u=u/r,op(2,%))*diff(Om(r,u),r)+subs(u=u/r,op(3,%))*Phi(r,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35663" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi_ser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUYjNigtSSNtbkdGJDYkUSI5RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1JI21pR0YkNiVRInVGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMlEnaXRhbGljRidGNC1JJW1zdXBHRiQ2JS1GTTYlUSJyRidGUEZTLUYuNiRRIjJGJ0YxLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YxLUY1Ni1RJyZwbHVzO0YnRjFGOEY7Rj1GP0ZBRkNGRS9GSFEsMC4yMjIyMjIyZW1GJy9GS0Zfby1GIzYmRlhGNC1GVjYlRkxGZW5GaG5GMUZbby1GIzYmRmVuRjRGVUYxRltvLUYjNiZGWEY0RkxGMUZbb0ZYLUY1Ni1RKCZtaW51cztGJ0YxRjhGO0Y9Rj9GQUZDRkVGXm9GYG8tRiM2JkZMRjQtSShtZmVuY2VkR0YkNiQtRiM2LC1GIzYoLUYuNiRRIzQ4RidGMUY0RkxGNEZVRjFGW28tRiM2KC1GLjYkUSIzRidGMUY0RlhGNEZjb0YxRltvLUYjNiZGLUY0RlVGMUZbby1GIzYoRmVuRjRGWEY0RkxGMUZbb0ZYRjFGMUYxRjE=">LC4qKCIiKiIiIkkidUc2IkYlKUkickdGJyIiI0YlRiUqJkYpRiUpRiZGKkYlRiUqJkYqRiVGKEYlRiUqJkYpRiVGJkYlRiVGKUYlKiZGJkYlLCwqKCIjW0YlRihGJUYmRiVGJSooIiIkRiVGKUYlRixGJUYlKiZGJEYlRihGJUYlKihGKkYlRilGJUYmRiVGJUYpRiVGJSEiIg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35654" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N),numer(edPhi1))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35647" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1_Phi:=convert(collect(isolate(edPhi1, diff(Phi(r, u), r)),[Om,Phi]),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35667" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
factor(hermite_pade(subs(u=u*r,[diff(Phi_ser(N),u), Omega_d(N,1,0),Phi_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUsMiomKUkickc2IiIiJCIiIilJInVHRiciIiVGKUYpKihGKEYpKUYmIiIjRikpRitGKEYpISIiKigiIilGKUYuRikpRitGL0YpRikqKEYoRilGJkYpRjRGKUYpKigiIz9GKUYmRilGK0YpRikqJiIjO0YpRiZGKUYpRitGMUYpRjEqKEYmRilGK0YpLCoqKEYsRilGLkYpRjRGKUYpKigiIiZGKUYmRilGK0YpRjFGOEYxRilGKUYpLCQqJkYrRiksKiomRi5GKUY0RilGKSooRi9GKUYmRilGK0YpRjEqJiIjN0YpRiZGKUYxRilGKUYpRjE=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35669" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edPhi2:=subs(u=u/r,op(1,%))*diff(Phi(r,u),u)+ subs(u=u/r,op(2,%))*diff(Om(r,u),r)+subs(u=u/r,op(3,%))*Phi(r,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdlZFBoaTJHRigsKComLDIqJkkickdGKCEiIilJInVHRigiIiUiIiJGNyooIiIkRjdGMkYzKUY1RjlGN0YzKiYiIilGNylGNSIiI0Y3RjcqKEY5RjdGMkYzRj1GN0Y3KiYiIz9GN0Y1RjdGNyomIiM7RjdGMkY3RjcqJkY1RjdGMkYzRjNGN0YzRjctSSVkaWZmR0YmNiQtSSRQaGlHRig2JEYyRjVGNUY3RjcqKEY1RjcsKiomRjZGN0Y9RjdGN0ZCRjMqJiIiJkY3RjVGN0YzRjdGN0Y3LUZGNiQtSSNPbUdGKEZKRjJGN0Y3KipGNUY3LCoqJEY9RjdGNyomIiM3RjdGMkY3RjMqJkY+RjdGNUY3RjNGN0Y3RjdGMkYzRkhGN0YzNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35665" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N),numer(edPhi2))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35668" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed2_Phi:=convert(collect(isolate(edPhi2, diff(Phi(r, u), u)),[Om,Phi]),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZDJfUGhpR0YoLy0tJkkiREdGJTYjIiIjNiNJJFBoaUdGKDYkSSJyR0YoSSJ1R0YoLCYqLEY5IiIiLCoqJClGOUY0RjxGPComIiM3RjxGOEY8ISIiKiZGNEY8RjlGPEZCRjxGPEY8RjhGQiwyKiZGOEZCKUY5IiIlRjxGPCooIiIkRjxGOEZCKUY5RklGPEZCKiYiIilGPEY/RjxGPCooRklGPEY4RkJGP0Y8RjwqJiIjP0Y8RjlGPEY8KiYiIztGPEY4RjxGPComRjlGPEY4RkJGQkY8RkJGQi1GNkY3RjxGPCoqRjlGPCwqKiZGR0Y8Rj9GPEY8RlBGQiomIiImRjxGOUY8RkJGPEY8RjwtLSZGMjYjRjw2I0kjT21HRihGN0Y8RkRGQkZCNyNGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35646" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31393" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L31267" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">t-Derivatives of R0</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L31274" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id[0]:=Om(R(t),t*(v-1))-t</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiISwmLUkjT21HRig2JC1JIlJHRig2I0kidEdGKComRjgiIiIsJkkidkdGKEY6RjohIiJGOkY6RjhGPTcjRjE=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35611" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Differentiate twice with respect to t</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31284" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 2 do id[i]:=diff(id[0],t$i) od</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiIiwoKiYtLSZJIkRHRiVGLzYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ0R0YoKiZGPUYwLCZJInZHRihGMEYwISIiRjBGMC1JJWRpZmZHRiY2JEY6Rj1GMEYwKiYtLSZGNjYjIiIjRjdGOUYwRj9GMEYwRjBGQTcjRjE=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiIywoKiYsJiomLS0mSSJER0YlNiQiIiJGOjYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ0R0YoKiZGQUY6LCZJInZHRihGOkY6ISIiRjpGOi1JJWRpZmZHRiY2JEY+RkFGOkY6KiYtLSZGODYkRjpGMEY7Rj1GOkZDRjpGOkY6RkZGOkY6KiYtLSZGODYjRjpGO0Y9RjotRkc2JEY+LUkiJEdGJjYkRkFGMEY6RjoqJiwmKiZGSkY6RkZGOkY6KiYtLSZGODYkRjBGMEY7Rj1GOkZDRjpGOkY6RkNGOkY6NyMsKEYyRjoqJkZPRjotRkc2JEZGRkFGOkY6RlhGOg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L32854" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Rewrite with Phi instead of Om_u</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35613" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_tv:=subs(r=R(t),u=t*(v-1),phidef)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpwaGlkZWZfdHZHRigvLS0mSSJER0YlNiMiIiM2I0kjT21HRig2JC1JIlJHRig2I0kidEdGKComRjsiIiIsJkkidkdGKEY9Rj0hIiJGPSooLCYtRjZGN0Y9LUkkUGhpR0YoRjdGQEY9RjtGQEY+RkA3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L32853" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id1_phi:=collect(subs(phidef_tv,Om(R(t), t*(v - 1))=t,id[1]),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShpZDFfcGhpR0YoLCYqJi0tJkkiREdGJTYjIiIiNiNJI09tR0YoNiQtSSJSR0YoNiNJInRHRigqJkY8RjUsJkkidkdGKEY1RjUhIiJGNUY1LUklZGlmZkdGJjYkRjlGPEY1RjUqJkY8RkAtSSRQaGlHRihGOEY1RkA3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35636" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed11_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIiRiw2I0kjT21HRio2JEkickdGKkkidUdGKiwmKixGMUYsLCYqJiIiKUYsRjFGLEYsRixGLEYsRjAhIiIsMiomRjBGNylGMSIiJUYsRiwqKCIiJEYsRjBGNylGMUY9RixGNyomRjZGLClGMSIiI0YsRiwqKEY9RixGMEY3RkBGLEYsKiYiIz9GLEYxRixGLComIiM7RixGMEYsRiwqJkYxRixGMEY3RjdGLEY3RjctLSZGJjYjRixGLUYvRixGNyoqLChGQkYsKihGPUYsRjFGLEYwRjdGN0Y7RjdGLC1JJFBoaUdGKkYvRixGMEY3RjhGN0Ys</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35638" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We check that the denominator does not vanish at (R,t(v-1)).</Text-field><Text-field style="Text" layout="Normal">The first coefficients of R0 are computed in the section (Checking...&quot;)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35767" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R0ser := t + (-v - 1)*t^2 + (-3*v - 1)*t^3 + (-3*v^2 - 14*v - 3)*t^4 + (-3*v^3 - 39*v^2 - 78*v - 12)*t^5 + (-3*v^4 - 76*v^3 - 399*v^2 - 474*v - 56)*t^6 + (-3*v^5 - 125*v^4 - 1245*v^3 - 3735*v^2 - 3036*v - 288)*t^7 + (-3*v^6 - 186*v^5 - 3000*v^4 - 16746*v^3 - 33429*v^2 - 20148*v - 1584)*t^8 + (-3*v^7 - 259*v^6 - 6153*v^5 - 54957*v^4 - 201103*v^3 - 291375*v^2 - 137178*v - 9152)*t^9 + (-3*v^8 - 344*v^7 - 11298*v^6 - 147420*v^5 - 854910*v^4 - 2243592*v^3 - 2496303*v^2 - 952258*v - 54912)*t^10 + O(t^11)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35639" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numer(u^4/r - 3*u^3/r + 8*u^2 + 3*u^2/r + 20*u + 16*r - u/r - 1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDIqJClJInVHNiIiIiUiIiJGKCooIiIpRihJInJHRiZGKClGJSIiI0YoRigqJiIiJEYoKUYlRi9GKCEiIiomIiM7RigpRitGLUYoRigqKCIjP0YoRitGKEYlRihGKComRi9GKEYsRihGKEYrRjFGJUYx</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35637" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(subs(r=R0ser,u=t*(v-1),%),t,5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUYjNiYtRiM2JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0YzLUYwNi1RMSZJbnZpc2libGVUaW1lcztGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGVy1GSzYlUSJ0RidGTkZRRjMtRjA2LVEnJnBsdXM7RidGM0Y2RjlGO0Y9Rj9GQUZDRkVGSC1GIzYoLUkjbW5HRiQ2JFEiM0YnRjNGUy1GIzYmRkpGUy1JKG1mZW5jZWRHRiQ2JC1GIzYmRkpGZm4tRlxvNiRRIjVGJ0YzRjNGM0YzRlMtSSVtc3VwR0YkNiVGWS1GXG82JFEiMkYnRjMvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjMtRjA2LVEoJm1pbnVzO0YnRjNGNkY5RjtGPUY/RkFGQ0ZFRkgtRiM2KEZbb0ZTLUYjNiZGSkZTLUZibzYkLUYjNigtRmpvNiVGSkZccEZfcEZmbkZKRmZuLUZcbzYkUSMxOEYnRjNGM0YzRjNGUy1Gam82JUZZRltvRl9wRjNGZm4tRiM2Ji1GIzYmRkpGUy1GYm82JC1GIzYqLUZqbzYlRkpGW29GX3BGYnAtRiM2Ji1GXG82JFEjMTJGJ0YzRlNGXXFGM0ZicC1GIzYmLUZcbzYkUSMyN0YnRjNGU0ZKRjNGYnAtRlxvNiRRIjZGJ0YzRjNGM0YzRlMtRmpvNiVGWS1GXG82JFEiNEYnRjNGX3BGM0Zmbi1GIzYmLUYwNi1RIk9GJ0YzRjZGOUY7Rj1GP0ZBRkNGVkZYLUYwNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjNGNkY5RjtGPUY/RkFGQ0ZWRlgtRmJvNiQtRiM2Jy1Gam82JUZZRmZvRl9wLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjhGM0YzRjNGMw==">Ky1JInRHNiIsJEkidkdGJCEiIiIiIiwkKigiIiRGKEYmRigsJkYmRigiIiZGKEYoRigiIiMsJCooRitGKEYmRigsKCokKUYmRi5GKEYoRiZGKCIjPUYoRihGJ0YrKiZGJkYoLCoqJClGJkYrRihGKComIiM3RihGM0YoRicqJiIjRkYoRiZGKEYnIiInRidGKCIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRi0=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35616" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id2_phi:=collect(subs(phidef_tv,Om(R(t), t*(v - 1))=t,subs(r=R(t),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}),id[2]),
[Om,Phi],factor): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi0qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLS1GOjYkRjItSSIkR0YmNiRGLSIiIy0tJkkiREdGJTYjRjY2I0kjT21HRihGMTcjPClGLUYuRi9GMkY5LUY6NiRGOUYtRkI=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35635" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(coeff(id2_phi,D[1](Om)(R(t), t*(v - 1))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35615" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Compare both equations between Phi and Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35614" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(id1_phi, Phi(R(t), t*(v - 1))),id2_phi))): nops(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35618" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(1,res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMiIiI2I0kjT21HRik2JC1JIlJHRik2I0kidEdGKSomRjJGKywmSSJ2R0YpRitGKyEiIkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35620" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">A second order DE for R</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35619" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt:=collect(convert(op(2,res),D),R, factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35621" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Rewrite in terms of t and u=t(v-1)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35622" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numer(factor(subs(v=1+u/t,edRt)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31302" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt_u:=collect(%,R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(edRt_u,[(D@@2)(R)(t),D(R)(t),R],factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35623" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The case v=1, that is, u=0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31291" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(op(3,factor(subs(u=0,edRt_u))),[(D@@2)(R)(t)],factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKC1JIlJHNiI2I0kidEdGJiIiIiwmKiYiIztGKUYkRilGKUYpISIiRiktLS1JI0BARzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiRJIkRHRjIiIiM2I0YlRidGKUYpKigiIiVGKSktLUY2RjhGJyIiJEYpRihGKUYt</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L31280" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check with the coefficients of R0 computed in the section (Checking...&quot;)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L31278" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R0ser</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L31298" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(eval(subs(R(t)=R0ser,u=t*(v-1),convert(edRt,diff))),t,14))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiT0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSShtZmVuY2VkR0YkNiQtRiM2Jy1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictSSNtbkdGJDYkUSMxMUYnRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGL0YvRi8=">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L31272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L31271" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
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</Section><Presentation-Block>
<Group view="code" labelreference="L31320" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33133" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33116" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">v-Derivatives of R0</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L33111" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now an equation in v</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33117" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv[0]:=subs(R(t)=R(v),id[0])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkkaWR2R0YoNiMiIiEsJi1JI09tR0YoNiQtSSJSR0YoNiNJInZHRigqJkkidEdGKCIiIiwmRjhGO0Y7ISIiRjtGO0Y6Rj03I0Yx</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33140" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 3 do idv[i]:=diff(idv[0],v$i) od:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L33139" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv_list:=[seq(idv[i],i=0..3)]:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33123" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv[1];</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidkdGKComSSJ0R0YoRjMsJkY6RjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomLS0mRjE2IyIiI0Y0RjZGM0Y8RjNGM0Yr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35625" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Again, we rewrite these equations in terms of Om_r and Phi, but they are no longer homogeneous</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35629" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_v:=subs(r=R(v),u=t*(v-1),phidef)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlwaGlkZWZfdkdGKC8tLSZJIkRHRiU2IyIiIzYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ2R0YoKiZJInRHRigiIiIsJkY7Rj5GPiEiIkY+KigsJi1GNkY3Rj4tSSRQaGlHRihGN0ZARj5GPUZARj9GQDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35628" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv1_phi:=collect(subs(phidef_v,Om(R(v), t*(v - 1))=t,idv[1]),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlpZHYxX3BoaUdGKCwoKiYtLSZJIkRHRiU2IyIiIjYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ2R0YoKiZJInRHRihGNSwmRjxGNUY1ISIiRjVGNS1JJWRpZmZHRiY2JEY5RjxGNUY1KiZGP0ZALUkkUGhpR0YoRjhGNUZAKiZGPkY1Rj9GQEY1NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35626" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv2_phi:=collect(subs(phidef_v,Om(R(t), t*(v - 1))=t,subs(r=R(v),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}),idv[2]),
[Om,Phi],factor): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy0tJkkiREdGJTYjRjY2I0kjT21HRihGMTcjPClGLUYuRi9GMkY5LUY6NiRGOUYuRkI=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35631" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Compare both equations between Phi and Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35632" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(idv1_phi, Phi(R(v), t*(v - 1))),idv2_phi))): nops(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjNjlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiNw</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35630" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KEkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy0tJkkiREdGJTYjIiIiNiNJI09tR0YoNiRGLyomRi1GQCwmRi5GQEZAISIiRkA3IzwoRi1GLkYvRjItRjM2JEYyRi5GOw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35624" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(coeff(res,D[1](Om)(R(v), t*(v - 1)))):
factor(series(subs(R(v)=R0ser,%),t,7))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiIiIiIiIiUsJiIjOyEiIiomRiZGJUkidkdGJEYlRikiIiYsKComIiInRiUpRisiIiNGJUYlKiYiI0NGJUYrRiVGJSIjb0YlRi8tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35641" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This is non-zero. So we need to use the third derivative as well.</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33118" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(idv[3])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8L0kidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JEYvKiZGLUZFLCZGLkZFRkUhIiJGRS0tJkZDNiRGRUZFRkZGSC0tJkZDNiRGRUY6RkZGSC0tJkZDNiVGRUZFRkVGRkZILS0mRkM2JUZFRkVGOkZGRkgtLSZGQzYlRkVGOkY6RkZGSC0tJkZDNiVGOkY6RjpGRkZINyM8L0YtRi5GL0YyLUYzNiRGMkYuLUYzNiRGYG9GLkZARkxGUEZURlhGZm5Gam4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35642" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">It is faster to differentiate idv2_phi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35644" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">diff(idv2_phi,v): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDY9LUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JVEidkYnRjJGNUY4LUYsNiYtRi82JVEmJlBoaTtGJy9GM0ZARjwtRjk2LVEwJkFwcGx5RnVuY3Rpb247RidGPEY+L0ZCRkBGQ0ZFRkdGSUZLRk0vRlFGTy1GIzYkLUYsNiktRiw2Ji1GLzYlUSJSRidGMkY1RmZuLUYjNiQtRiw2J0ZTLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkBGPEY8RjxGOC1GLDYmRi4tRjk2LVExJkludmlzaWJsZVRpbWVzO0YnRjxGPkZpbkZDRkVGR0ZJRktGTUZqbi1GIzYkLUYsNiZGUy1GOTYtUSgmbWludXM7RidGPEY+RmluRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZdcS1JI21uR0YkNiRRIjFGJ0Y8RjxGPEY8RmhvRltwRl5wRjxGPEY8RjhGX29GOC1GLDYmLUkmbWZyYWNHRiQ2KC1GOTYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y8Rj5GaW5GQ0ZFRkdGSUZLRk1Gam4tRiw2JUZocUZTRjwvJS5saW5ldGhpY2tuZXNzR0ZicS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zhci8lKWJldmVsbGVkR0ZALUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRltzLyUqbGluZWJyZWFrR1ElYXV0b0YnRl9vRjxGOC1GLDYmLUZmcTYoLUklbXN1cEdGJDYlRmhxLUZgcTYkUSIyRidGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiw2JUZocS1GaXM2JUZTRlt0Rl50RjxGXXJGX3JGYnJGZHJGZnJGX29GPEY4LUYsNiYtRmZxNigtRmlzNiVGaHEtRmBxNiRRIjNGJ0Y8Rl50LUYsNiVGaHEtRmlzNiVGU0ZbdUZedEY8Rl1yRl9yRmJyRmRyRmZyRl9vRjxGOC1GLDYmLUYsNiYtSSVtc3ViR0YkNiUtRi82JVEiREYnRmVuRjxGX3EvJS9zdWJzY3JpcHRzaGlmdEdGYHRGZm4tRiM2JC1GLDYnLUYvNiVRI09tRidGMkY1RmhvRltwRl5wRjxGPEY8RmZuRltvRjxGOC1GLDYmLUYsNiZGZnVGZm4tRiM2JC1GLDYnRlhGaG9GW3BGXnBGPEY8RjxGZm5GW29GPEY4LUYsNiYtRiw2Ji1GZ3U2JUZpdUZbdEZcdkZmbkZpdkY8RmZuRltvRjxGOC1GLDYmLUYsNiYtRmd1NiVGaXUtRiw2JkZfcS1GOTYtUSgmY29tbWE7RidGPEY+RkFGQ0ZFRkdGSUZLRk1GUEZfcUY8Rlx2RmZuRl52RjxGZm5GW29GPEY4LUYsNiYtRiw2Ji1GZ3U2JUZpdS1GLDYmRl9xRlt4Rlt0RjxGXHZGZm5GXnZGPEZmbkZbb0Y8RmhvRltwRl5wRjxGPC8lJW9wZW5HUScmbGN1YjtGJy8lJmNsb3NlR1EnJnJjdWI7Ric=">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8LkkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy1GOjYkRjItRj82JEYuIiIkLS0mSSJER0YlNiNGNjYjSSNPbUdGKEYxLS1GSTYjRjBGMS0tJkZKNiNGQUZQRjEtLSZGSjYkRjZGNkZMRjEtLSZGSjYkRjZGQUZMRjE3IzwuRi1GLkYvRjJGOS1GOjYkRjlGLi1GOjYkRmluRi5GR0ZORlFGVUZZ</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35643" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv3_phi:=collect(subs(phidef_v,Om(R(t), t*(v - 1))=t,subs(r=R(v),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}), diff(idv2_phi,v)),[Om,Phi],factor):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35645" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDY5LUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JVEidkYnRjJGNUY4LUYsNiYtRi82JVEmJlBoaTtGJy9GM0ZARjwtRjk2LVEwJkFwcGx5RnVuY3Rpb247RidGPEY+L0ZCRkBGQ0ZFRkdGSUZLRk0vRlFGTy1GIzYkLUYsNiktRiw2Ji1GLzYlUSJSRidGMkY1RmZuLUYjNiQtRiw2J0ZTLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkBGPEY8RjxGOC1GLDYmRi4tRjk2LVExJkludmlzaWJsZVRpbWVzO0YnRjxGPkZpbkZDRkVGR0ZJRktGTUZqbi1GIzYkLUYsNiZGUy1GOTYtUSgmbWludXM7RidGPEY+RmluRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZdcS1JI21uR0YkNiRRIjFGJ0Y8RjxGPEY8RmhvRltwRl5wRjxGPEY8RjhGX29GOC1GLDYmLUkmbWZyYWNHRiQ2KC1GOTYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y8Rj5GaW5GQ0ZFRkdGSUZLRk1Gam4tRiw2JUZocUZTRjwvJS5saW5ldGhpY2tuZXNzR0ZicS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zhci8lKWJldmVsbGVkR0ZALUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRltzLyUqbGluZWJyZWFrR1ElYXV0b0YnRl9vRjxGOC1GLDYmLUZmcTYoLUklbXN1cEdGJDYlRmhxLUZgcTYkUSIyRidGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRiw2JUZocS1GaXM2JUZTRlt0Rl50RjxGXXJGX3JGYnJGZHJGZnJGX29GPEY4LUYsNiYtRmZxNigtRmlzNiVGaHEtRmBxNiRRIjNGJ0Y8Rl50LUYsNiVGaHEtRmlzNiVGU0ZbdUZedEY8Rl1yRl9yRmJyRmRyRmZyRl9vRjxGOC1GLDYmLUYsNiYtSSVtc3ViR0YkNiUtRi82JVEiREYnRmVuRjxGX3EvJS9zdWJzY3JpcHRzaGlmdEdGYHRGZm4tRiM2JC1GLDYnLUYvNiVRI09tRidGMkY1RmhvRltwRl5wRjxGPEY8RmZuRltvRjxGOC1GLDYmLUYsNiZGZnVGZm4tRiM2JC1GLDYnRlhGaG9GW3BGXnBGPEY8RjxGZm5GW29GPEY4LUYsNiYtRiw2Ji1GZ3U2JUZpdUZbdEZcdkZmbkZpdkY8RmZuRltvRjxGaG9GW3BGXnBGPEY8LyUlb3BlbkdRJyZsY3ViO0YnLyUmY2xvc2VHUScmcmN1YjtGJw==">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8LEkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy1GOjYkRjItRj82JEYuIiIkLS0mSSJER0YlNiNGNjYjSSNPbUdGKEYxLS1GSTYjRjBGMS0tJkZKNiNGQUZQRjE3IzwsRi1GLkYvRjJGOS1GOjYkRjlGLi1GOjYkRldGLkZHRk5GUQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35675" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_v</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIjNiNJI09tR0YqNiQtSSJSR0YqNiNJInZHRioqJkkidEdGKiIiIiwmRjNGNkY2ISIiRjYqKCwmLUYuRi9GNi1JJFBoaUdGKkYvRjhGNkY1RjhGN0Y4</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35674" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res_bis:=numer(factor(subs(subs(r=R(v),u=t*(v-1),{ed1_Phi, ed2_Phi}),isolate(idv1_phi, Phi(R(v), t*(v - 1))),idv3_phi))):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35673" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JEYvKiZGLUZFLCZGLkZFRkUhIiJGRTcjPClGLUYuRi9GMi1GMzYkRjJGLi1GMzYkRk5GLkZA</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35678" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we have two expressions for Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35677" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eda:=numer(factor(subs(isolate(res,D[1](Om)(R(v), t*(v - 1))),res_bis))): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiNUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35676" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eda)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KEkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkNyM8KEYtRi5GL0YyLUYzNiRGMkYuLUYzNiRGQkYu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35672" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,eda),i=1..5)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM3JzwiPCNJInRHRig8JEkidkdGKC1JIlJHRig2I0YxPCVGL0YxRjI8KEYvRjFGMi1JJWRpZmZHRiY2JEYyRjEtRjg2JEYyLUkiJEdGJjYkRjEiIiMtRjg2JEYyLUY9NiRGMSIiJDcjNydGLUYuRjBGNTwoRi9GMUYyRjctRjg2JEY3RjEtRjg2JEZIRjE=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35681" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edb:=op(5,eda):nops(%);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNDUzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiRgJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35680" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRv:=collect(convert(edb,D),R,factor):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33144" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33142" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(eval(subs(R(v)=R0ser,convert(edRv,diff))),t,15))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33120" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L33125" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33110" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L33266" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">t-Derivatives of Q0</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L33282" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write (Q0+v)t^2=Lambda(R,t(v-1)). 
Note that Maple claims that binomial(-1,0)=1 (this term is obtained for k=n=0), hence the term -r below</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35682" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">binomial(-1,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33280" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambda_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(2*n + k-1, n)*u^k*r^(n + 1)/(n + 1), k = 0 .. N - n - 1), n = 0 .. N - 1) -r
;end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33284" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambda_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJiIiJyIiIilJInJHNiIiIiRGJUYlKihGJEYlKUYnIiIjRiVJInVHRihGJUYlKiZGJ0YlKUYtRixGJUYlKiRGK0YlRiUqJkYnRiVGLUYlRiU=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35704" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font bold="true">The series Lambda and Lambda_hat</Font></Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35724" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Link with our series Omega: now we are in the 4D vector space spanned by 1, Om, Om_r, Om_u</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35707" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=100*r,[1, Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Lambda_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NycsJComIiIlIiIiSSJyRzYiRiZGJiwmKiYiJCskRiZGJ0YmRiYiIiQhIiIsJComRidGJiwmKiYiJCspRiZGJ0YmRiZGJkYmRiZGLSwkKigiIztGJkYnRiYsJiomIiV2PUYmRidGJkYmIiM+Ri1GJkYtIiIn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35718" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=u*r,[1, Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Lambda_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NycsJComIiIlIiIiSSJyRzYiRiYhIiIsJiooIiIkRiZGJ0YmSSJ1R0YoRiZGKUYsRiYqJkYnRiYsJiooIiIpRiZGJ0YmRi1GJkYmRiZGJkYmKiZGJ0YmLCgqKEYsRiZGJ0YmKUYtIiIjRiZGJiomRixGJkYtRiZGKUYlRilGJiEiJw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35712" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We prefer to work in 2 dimensions: here's a new Lambda, called Lambda_hat</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35709" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambdah_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(2*n + k-1, n)*u^k*r^(n + 1)/(n + 1), k = 0 .. N - n - 1), n = 0 .. N - 1) -r
+2*r/3*(1+Omega_ser(N+1)/u)
;end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35714" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambdah_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIiJyIiIilJInJHNiIiIiRGJUYlKihGJEYlSSJ1R0YoRiUpRiciIiNGJUYlKiZGJ0YlKUYrRi1GJUYlKiRGLEYlRiUqJkYnRiVGK0YlRiUqKCNGLUYpRiVGJ0YlLCZGJUYlKiYsNiomIiQrIkYlKUYnIiIlRiVGJSooRjhGJUYmRiVGK0YlRiUqKCIjQ0YlRixGJUYvRiVGJSomRidGJSlGK0YpRiVGJSomIiM3RiVGJkYlRiUqKCIiKkYlRixGJUYrRiVGJUYuRiUqJkYtRiVGLEYlRiVGMUYlRidGJUYlRishIiJGJUYlRiU=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35721" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we can work in the 2D space generated by Phi and Om_r.</Text-field><Text-field style="Text" layout="Normal">Here are equations for Lambda_hat and its first derivatives</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35725" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed5:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),u*Lambdah_ser(N)])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkNUdGKDclLCQqJkkickdGKCIiIiwoKigiIiRGMkYxRjIpSSJ1R0YoIiIjRjJGMiomRjVGMkY3RjIhIiIiIiVGOkYyRjoqKEY3RjIpRjFGOEYyLCYqKCIiKUYyRjFGMkY3RjJGMkYyRjJGMiEiJzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35715" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed5:=convert(map(factor,subs(u=u/r,coed5[1])*Phi(r,u) + subs(u=u/r,coed5[2])*diff(Om(r,u),r) +subs(u=u/r,coed5[3])*u*Lah(r,u) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDVHRigsKComLCgqJiIiJCIiIilJInVHRigiIiNGMyEiIiomIiIlRjNJInJHRihGM0YzKiZGMkYzRjVGM0YzRjMtSSRQaGlHRig2JEY6RjVGM0YzKipGNUYzRjpGMywmKiYiIilGM0Y1RjNGM0YzRjNGMy0tJkkiREdGJTYjRjM2I0kjT21HRihGPkYzRjMqKCIiJ0YzRjVGMy1JJExhaEdGKEY+RjNGNzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35710" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35719" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed5,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35711" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_0:=collect(isolate(ed5,Lah(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF8wR0YoLy1JJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKiMiIiIiIidGN0YyRjcsJiomIiIpRjdGM0Y3RjdGN0Y3RjctLSZJIkRHRiU2I0Y3NiNJI09tR0YoRjFGN0Y3KipGNkY3LCgqJiIiJEY3KUYzIiIjRjchIiIqJiIiJUY3RjJGN0Y3KiZGRkY3RjNGN0Y3RjctSSRQaGlHRihGMUY3RjNGSUY3NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35717" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed6:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),normal(u*diff(Lambdah_ser(N+2),r))])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkNkdGKDclISIjLCQqJkkickdGKCIiIiwoKiZGMkYzKUkidUdGKCIiI0YzRjMqJkY4RjNGN0YzRjNGOEYzRjMhIiIiIiQ3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35728" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed6:=convert(map(factor,subs(u=u/r,coed6[1])*Phi(r,u) + subs(u=u/r,coed6[2])*diff(Om(r,u),r) +subs(u=u/r,coed6[3])*u*diff(Lah(r,u),r) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDZHRigsKComIiIjIiIiLUkkUGhpR0YoNiRJInJHRihJInVHRihGMSEiIiomLCgqJClGNkYwRjFGMSomRjBGMUY1RjFGMSomRjBGMUY2RjFGMUYxLS0mSSJER0YlNiNGMTYjSSNPbUdGKEY0RjFGNyooIiIkRjFGNkYxLS1GQDYjSSRMYWhHRihGNEYxRjE3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35713" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed7:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),normal(u^2*diff(Lambdah_ser(N+2),u))])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkN0dGKDclKiZJInJHRigiIiIsJiooIiIkRjFGMEYxKUkidUdGKCIiI0YxRjFGN0YxRjEsJCooIiInRjFGNUYxKUYwRjRGMSEiIkY0NyNGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35708" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed7:=convert(map(factor,subs(u=u/r,coed7[1])*Phi(r,u) + subs(u=u/r,coed7[2])*diff(Om(r,u),r) +subs(u=u/r,coed7[3])*u^2*diff(Lah(r,u),u) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDdHRigsKComLCYqJiIiJCIiIilJInVHRigiIiNGM0YzKiZGNkYzSSJyR0YoRjNGM0YzLUkkUGhpR0YoNiRGOEY1RjNGMyoqIiInRjNGOEYzRjRGMy0tJkkiREdGJTYjRjM2I0kjT21HRihGO0YzISIiKihGMkYzRjRGMy0tJkZBNiNGNjYjSSRMYWhHRihGO0YzRjM3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35727" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35716" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed6,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35723" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed7,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35722" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_r:=collect(isolate(ed6,D[1](Lah)(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF9yR0YoLy0tJkkiREdGJTYjIiIiNiNJJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKiNGNCIiJEY0LCgqJClGOSIiI0Y0RjQqJkZBRjRGOEY0RjQqJkZBRjRGOUY0RjRGNEY5ISIiLS1GMTYjSSNPbUdGKEY3RjRGNCooI0ZBRj1GNC1JJFBoaUdGKEY3RjRGOUZERjQ3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35720" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_u:=collect(isolate(ed7,D[2](Lah)(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF91R0YoLy0tJkkiREdGJTYjIiIjNiNJJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKEY0IiIiRjhGPC0tJkYyNiNGPDYjSSNPbUdGKEY3RjxGPCoqI0Y8IiIkRjwsJiomRkVGPClGOUY0RjxGPComRjRGPEY4RjxGPEY8LUkkUGhpR0YoRjdGPEZIISIiRkw3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35726" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35706" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35705" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L35702" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" labelreference="L35703" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35697" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_0;edLah_r;edLah_u</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJExhaEc2IjYkSSJyR0YlSSJ1R0YlLCYqKiMiIiIiIidGLEYnRiwsJiomIiIpRixGKEYsRixGLEYsRiwtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YsNiNJI09tR0YlRiZGLEYsKipGK0YsLCgqJiIiJEYsKUYoIiIjRiwhIiIqJiIiJUYsRidGLEYsKiZGPkYsRihGLEYsRiwtSSRQaGlHRiVGJkYsRihGQUYs</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIiNiNJJExhaEdGKjYkSSJyR0YqSSJ1R0YqLCYqKiNGLCIiJEYsLCgqJClGMSIiI0YsRiwqJkY5RixGMEYsRiwqJkY5RixGMUYsRixGLEYxISIiLS1GJTYjSSNPbUdGKkYvRixGLCooI0Y5RjVGLC1JJFBoaUdGKkYvRixGMUY8Riw=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIjNiNJJExhaEdGKjYkSSJyR0YqSSJ1R0YqLCYqKEYsIiIiRjBGNC0tJkYmNiNGNDYjSSNPbUdGKkYvRjRGNCoqI0Y0IiIkRjQsJiomRj1GNClGMUYsRjRGNComRixGNEYwRjRGNEY0LUkkUGhpR0YqRi9GNEZAISIiRkQ=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35696" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now let's get back to the variables t and v</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35695" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh_def:=Lh(t)=Lah(R(t),t*(v-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdMaF9kZWZHRigvLUkjTGhHRig2I0kidEdGKC1JJExhaEdGKDYkLUkiUkdGKEYxKiZGMiIiIiwmSSJ2R0YoRjlGOSEiIkY5NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35732" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id1_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidEdGKComRjpGMywmSSJ2R0YoRjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomRjpGPi1JJFBoaUdGKEY2RjNGPkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35731" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh_phi:=collect(subs(subs(r=R(t),u=t*(v-1),edLah_0),isolate(id1_phi, D[1](Om)(R(t), t*(v - 1))),Lh_def),Phi)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdMaF9waGlHRigvLUkjTGhHRig2I0kidEdGKComLCYqLCMiIiIiIidGNy1JIlJHRihGMUY3LCYqKCIiKUY3RjJGNywmSSJ2R0YoRjdGNyEiIkY3RjdGN0Y3RjdGMkZALUklZGlmZkdGJjYkRjlGMkZARjcqKkY2RjcsKCooIiIkRjcpRjIiIiNGNylGPkZJRjdGQComIiIlRjdGOUY3RjcqKEZHRjdGMkY3Rj5GN0Y3RjdGMkZARj5GQEY3RjctSSRQaGlHRig2JEY5KiZGMkY3Rj5GN0Y3NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35730" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dLh_phi:=collect(subs(subs(r=R(t),u=t*(v-1),{edLah_r,edLah_u}),isolate(id1_phi, D[1](Om)(R(t), t*(v - 1))),diff(Lh_def,t)),Phi)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShkTGhfcGhpR0YoLy1JJWRpZmZHRiY2JC1JI0xoR0YoNiNJInRHRihGNSomLCYqJiwmKiwjIiIiIiIkRjwsKComKUY1IiIjRjwpLCZJInZHRihGPEY8ISIiRkFGPEY8KiZGQUY8LUkiUkdGKEY0RjxGPCooRkFGPEY1RjxGQ0Y8RjxGPEZARkVGQ0ZFLUYwNiRGR0Y1RkVGPCooI0ZBRj1GPEY1RkVGQ0ZFRjxGPEZKRjxGPComLCYqKkZBRjxGR0Y8RjVGRUZKRkVGPCoqRjtGPCwmKihGPUY8RkBGPEZCRjxGPEZGRjxGPEZARkVGQkZFRkVGPEZDRjxGPEY8LUkkUGhpR0YoNiRGRyomRjVGPEZDRjxGPDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L33308" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The log derivative of L_hat</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35735" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dlog_Lh:=convert(factor(op(2,dLh_phi)/op(2,Lh_phi)),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35737" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dloh_Lh_u:=factor(subs(v=1+u/t,%));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpkbG9oX0xoX3VHRigsJCoqIiIlIiIiLCoqJiktLUkiREdGJTYjSSJSR0YoNiNJInRHRigiIiNGMSlGO0Y8RjFGMSooKUkidUdGKEY8RjFGNUYxRjtGMSEiIiooIiIkRjEtRjlGOkYxRj9GMUYxKihGO0YxRjVGMUZARjFGMUYxRjtGQSwsKipGQ0YxRj9GMUY1RjFGO0YxRkEqKkYwRjFGREYxRjVGMUY7RjFGMSooIiIpRjFGREYxRj9GMUYxKipGQ0YxRjtGMUY1RjFGQEYxRjEqJkZERjFGQEYxRjFGQUYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35734" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(numer(%/4),R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqKCIiJCIiIi1JIlJHNiI2I0kidEdGKEYlKUkidUdGKCIiI0YlRiUqJiktLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKDYjRidGKUYtRiUpRipGLUYlRiUqKkYqRiVGLEYlLCZGLEYlRiUhIiJGJUYwRiVGOg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35733" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(denom(%%*t),R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiwmKigiIiUiIiJJInRHNiJGJy0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiNJIlJHRik2I0YoRidGJyomSSJ1R0YpRicsJiomIiIpRidGNEYnRidGJ0YnRidGJ0YnLUYxRjJGJ0YnKiwiIiRGJ0YoRidGNEYnLCZGNEYnRichIiJGJ0YqRidGPA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35741" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we can write 3 equations between L, L', L'' and L''' and R and R' (using the second order DE for R)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35740" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35739" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e1:=collect(convert(numer(eval(subs(Lh(t)=L(t)+2*v*R(t)/3/(v-1),diff(Lh(t),t)/Lh(t))-dlog_Lh)),D),L,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35738" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(e1); e1:=collect(op(3,%),L,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35744" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(e1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PChJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35745" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35743" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e2:=numer(factor(subs(isolate(edRt,(D@@2)(R)(t)),factor(convert(diff(e1,t),D))))): nops(%); indets(e2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNDA2RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQxJQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKA==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35749" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e3:=numer(factor(subs(isolate(edRt,(D@@2)(R)(t)),factor(convert(diff(e2,t),D))))): nops(%); indets(e3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFElMjUwMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiUrRA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCpJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tLUY4NiRGLSIiJEYxRig=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35748" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we eliminate R and R' between these three equations to obtain a DE of third order for L</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35747" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(D(R)(t)=dR,R(t)=R,(D@@3)(L)(t)=L3, (D@@2)(L)(t)=L2,D(L)(t)=L1, L(t)=L,[e1,e2,e3]):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35742" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eqs)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCpJIkxHNiJJI0wxR0YkSSNMMkdGJEkjTDNHRiRJIlJHRiRJI2RSR0YkSSJ0R0YkSSJ2R0Yk</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35751" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(degree,eqs,R); map(degree,eqs,dR); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUiIiMiIiUiIig=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUiIiMiIiUiIic=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35753" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res1:=factor(resultant(eqs[1],eqs[2],dR)): nops(res1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiN0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIo</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35752" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,res1),i=1..nops(res1))])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Nyk8IjwjSSJSRzYiPCNJInZHRiY8JUYlSSJ0R0YmRig8JUkiTEdGJkYqRig8JUYsRiVGKDwoRixJI0wxR0YmSSNMMkdGJkYlRipGKA==</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35750" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser:=proc(N) factor(series(t^2*(v+subs(omega=0,Qser(N))),t,N+1)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35760" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser(6)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiJJInZHRiQiIiMsJComRiYiIiJGJUYpRikiIiQsJCooRiZGKUYlRiksJkYlRikiIiVGKUYpRilGLiwkKipGJkYpRiVGKSwmRiVGKSIjNUYpRiksJkYlRilGJkYpRilGKSIiJiwkKihGJkYpRiVGKSwqKiQpRiVGKkYpRikqJiIjQ0YpKUYlRiZGKUYpKiYiJDoiRilGJUYpRikiJDciRilGKUYpIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35759" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=3:factor(series(subs(R=R0ser, L=Lser(N),op(4,res1)),t,N+1));
factor(series(subs(R=R0ser, L=Lser(N),op(5,res1)),t,N+1));
factor(series(subs(R=R0ser, L=Lser(N),op(6,res1)),t,N+1));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInRHNiIqJClJInZHRiQiIiMiIiJGKCwkKigiIidGKUYmRiksJkYnRikiIiZGKUYpISIiIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIiU=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiIsJEkidkdGJCEiIiIiIiomRiZGKCwmRiZGKEYoRihGKCIiIywkKiYiIiVGKEYmRihGKCIiJC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRi4=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUYjNiYtRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGMy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZLLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0YzRjYtRk82JVEidEYnRlJGVUYzLUY3Ni1RJyZwbHVzO0YnRjNGOkY9Rj9GQUZDRkVGRy9GSlEsMC4yMjIyMjIyZW1GJy9GTUZobi1GIzYmLUYjNiZGTkY2LUkobWZlbmNlZEdGJDYkLUYjNiZGTi1GNzYtUSgmbWludXM7RidGM0Y6Rj1GP0ZBRkNGRUZHRmduRmluLUYwNiRRIjVGJ0YzRjNGM0YzRjYtSSVtc3VwR0YkNiVGV0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YzRmNvLUYjNigtRjA2JFEiOEYnRjNGNkZORjYtRmpvNiVGVy1GMDYkUSIzRidGM0ZccEYzRlotRiM2Ji1GNzYtUSJPRidGM0Y6Rj1GP0ZBRkNGRUZHRklGTC1GNzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0YzRjpGPUY/RkFGQ0ZFRkdGSUZMLUZfbzYkLUYjNictRmpvNiVGVy1GMDYkUSI0RidGM0ZccC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y8RjNGM0YzRjM=">KytJInRHNiIsJComIiIjIiIiSSJ2R0YkRihGKEYoKiZGKUYoLCZGKUYoIiImISIiRihGJywkKiYiIilGKEYpRihGLSIiJC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIl</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35766" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:factor(series(subs(R=R0ser, L=Lser(N),L1=diff(Lser(N+1),t),L2=diff(Lser(N+2),t$2),L3=diff(Lser(N+3),t$3),op(7,res1)),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35758" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res2:=op(7,res1): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkODEwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQ1KQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35763" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res3:=factor(resultant(eqs[1],eqs[3],dR)): nops(res3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiNkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35762" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,res3),i=1..nops(res3))])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYxLUkjbWlHRiQ2JVEoJmVtcHR5O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiM2Ji1GLDYrLUYvNiVRIkxGJ0YyRjVGOC1GLzYlUSJ0RidGMkY1RjgtRi82JVEidkYnRjJGNS8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZARjxGPC8lJW9wZW5HUScmbGN1YjtGJy8lJmNsb3NlR1EnJnJjdWI7RidGOC1GIzYmLUYsNictRi82JVEiUkYnRjJGNUZqbkZdb0Zgb0Y8RjxGYm9GZW9GOC1GIzYmLUYsNidGZ25Gam5GXW9GYG9GPEY8RmJvRmVvRjgtRiM2Ji1GLDYrRlxwRjhGWkY4RmduRmpuRl1vRmBvRjxGPEZib0Zlb0Y4LUYjNiYtRiw2M0ZXRjgtRi82JVEjTDFGJ0YyRjVGOC1GLzYlUSNMMkYnRjJGNUY4LUYvNiVRI0wzRidGMkY1RjhGXHBGOEZaRjhGZ25Gam5GXW9GYG9GPEY8RmJvRmVvRmpuRl1vRmBvRjxGPC9GY29RJyZsc3FiO0YnL0Zmb1EnJnJzcWI7Ric=">Nyg8IjwlSSJMRzYiSSJ0R0YmSSJ2R0YmPCNJIlJHRiY8I0YoPCVGKkYnRig8KUYlSSNMMUdGJkkjTDJHRiZJI0wzR0YmRipGJ0Yo</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35761" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res4:=op(6,res3): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEmMzA3MTZGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiY7MiQ=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35770" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:factor(series(subs(R=R0ser, L=Lser(N),L1=diff(Lser(N+1),t),L2=diff(Lser(N+2),t$2),L3=diff(Lser(N+3),t$3),res4),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiT0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSShtZmVuY2VkR0YkNiQtRiM2Jy1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictSSNtbkdGJDYkUSI5RidGLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGNEYvRi9GLw==">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35769" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35765" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">It remains to eliminate R between res2 and res4 - but this is too big.</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35764" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res5:=factor(resultant(res2,res4,R)): nops(res5):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35757" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Let us try with Gr\303\266bner bases ; or for specific values of v. But later!</Font></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L33254" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35827" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33271" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L33276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
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</Section><Presentation-Block>
<Group view="code" labelreference="L33194" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L33192" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L33420" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L33414" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">v-Derivatives of Q0</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L33430" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write (Q0+v)t^2=Lambda(R,t(v-1)). </Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35779" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lhv_def:=Lh(v)=Lah(R(v),t*(v-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShMaHZfZGVmR0YoLy1JI0xoR0YoNiNJInZHRigtSSRMYWhHRig2JC1JIlJHRihGMSomSSJ0R0YoIiIiLCZGMkY6RjohIiJGOjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35780" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv1_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsKComLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidkdGKComSSJ0R0YoRjMsJkY6RjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomRj1GPi1JJFBoaUdGKEY2RjNGPiomRjxGM0Y9Rj5GM0Yr</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35777" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lhv_phi:=convert(collect(subs(subs(r=R(v),u=t*(v-1),edLah_0),isolate(idv1_phi, D[1](Om)(R(v), t*(v - 1))),Lhv_def),Phi),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShMaHZfcGhpR0YoLy1JI0xoR0YoNiNJInZHRigsJiomLCYqLCMiIiIiIidGOC1JIlJHRihGMUY4LCYqKCIiKUY4SSJ0R0YoRjgsJkYyRjhGOCEiIkY4RjhGOEY4RjhGQEZBLS1JIkRHRiU2I0Y7RjFGQUY4KipGN0Y4LCgqKCIiJEY4KUY/IiIjRjgpRkBGS0Y4RkEqJiIiJUY4RjpGOEY4KihGSUY4Rj9GOEZARjhGOEY4Rj9GQUZARkFGOEY4LUkkUGhpR0YoNiRGOiomRj9GOEZARjhGOEY4Ki5GN0Y4RjpGOEY8RjhGP0Y4RkBGQUZCRkFGQTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35785" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35784" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh1v_phi:=convert(map(Z-&gt;map(factor,Z),collect(subs(subs(u=t*(v-1),r=R(v),{ed1_Phi,ed2_Phi}),isolate(idv1_phi, D[1](Om)(R(v), t*(v - 1))), diff(Lhv_phi,v)),Phi)),D): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYzLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JVEidkYnRjJGNUY4LUYsNiYtRi82JVEmJlBoaTtGJy9GM0ZARjwtRjk2LVEwJkFwcGx5RnVuY3Rpb247RidGPEY+L0ZCRkBGQ0ZFRkdGSUZLRk0vRlFGTy1GIzYkLUYsNiktRiw2Ji1GLzYlUSJSRidGMkY1RmZuLUYjNiQtRiw2J0ZTLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkBGPEY8RjxGOC1GLDYmRi4tRjk2LVExJkludmlzaWJsZVRpbWVzO0YnRjxGPkZpbkZDRkVGR0ZJRktGTUZqbi1GIzYkLUYsNiZGUy1GOTYtUSgmbWludXM7RidGPEY+RmluRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZdcS1JI21uR0YkNiRRIjFGJ0Y8RjxGPEY8RmhvRltwRl5wRjxGPEY8RjhGX29GOC1GLDYmLUYsNiYtRi82JVEiREYnRmVuRjxGZm4tRiM2JC1GLDYnLUYvNiVRI0xoRidGMkY1RmhvRltwRl5wRjxGPEY8RmZuRmRvRjxGOC1GLDYmLUYsNiZGZ3FGZm4tRiM2JC1GLDYnRmFvRmhvRltwRl5wRjxGPEY8RmZuRmRvRjxGOC1GLDYmLUYsNiYtSSVtc3VwR0YkNiZGZ3EtRiM2JC1GLDYnLUZgcTYkUSIyRidGPEZob0ZbcEZecEY8RjwvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEjQEBGJ0ZmbkZlckY8RmZuRmRvRjxGaG9GW3BGXnBGPEY8LyUlb3BlbkdRJyZsY3ViO0YnLyUmY2xvc2VHUScmcmN1YjtGJw==">PClJInRHNiJJInZHRiQtSSRQaGlHRiQ2JC1JIlJHRiQ2I0YlKiZGIyIiIiwmRiVGLUYtISIiRi1GKS0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJI0xoR0YkRistLUYyNiNGKkYrLS0tSSNAQEdGMzYkRjIiIiNGOkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35781" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">An equation without Phi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35788" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(Lhv_phi,Phi(R(v), t*(v - 1))),op(2,Lh1v_phi)-D(Lh)(v)))): nops(%) ; indets(%%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNjA0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQvJw==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSNMaEdGJDYjRiUtSSJSR0YkRigtLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRidGKC0tRi02I0YqRigtLS1JI0BAR0YuNiRGLSIiI0Y0Rig=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35816" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35810" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev1:=factor(convert(numer(eval(subs(Lh(v)=L(v)+2*v*R(v)/3/(v-1),convert(res,diff)))),D)): nops(factor(ev1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35818" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(1,ev1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUklbXJvd0dGJDYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGUi1JI21uR0YkNiRRIjFGJ0Y/Rj9GPy1GVjYkUSI0RidGPy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=">KiQpLCZJInZHNiIiIiJGJyEiIiIiJUYn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35817" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev1:=op(2,ev1): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNDEzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQ4JQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35800" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(ev1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjRGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35799" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(edRv)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PChJInRHNiJJInZHRiQtSSJSR0YkNiNGJS0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS0tSSNAQEdGLDYkRisiIiNGL0YoLS0tRjM2JEYrIiIkRi9GKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35802" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev2:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev1,v),D))))): nops(%); indets(ev2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFElMjYzOEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiVRRQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCpJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYo</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35820" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev3:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev2,v),D))))): nops(%); indets(ev3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEmMjczOTVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiYmUkY=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCtJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYoLS0tRjg2JEYtIiIkRjFGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35819" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev4:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev3,v),D))))): nops(%); indets(ev4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEnMTM5MzI5RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IidIJFIi</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCxJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYoLS0tRjg2JEYtIiIkRjFGKC0tLUY4NiRGLSIiJUYxRig=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35796" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now if we could eliminate R , R' and R'' between these four equations we would obtain a DE of fourth order for L</Text-field>
</Input>
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<Group view="code" labelreference="L35797" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqsv:=subs((D@@2)(R)(v)=d2R, D(R)(v)=dR,R(v)=R,(D@@4)(L)(v)=L4,(D@@3)(L)(v)=L3, (D@@2)(L)(v)=L2,D(L)(v)=L1, L(v)=L,[ev1,ev2,ev3,ev4]):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35789" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eqsv)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCxJIkxHNiJJI0wxR0YkSSNMMkdGJEkjTDNHRiRJI0w0R0YkSSJSR0YkSSRkMlJHRiRJI2RSR0YkSSJ0R0YkSSJ2R0Yk</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35806" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(degree,eqsv,R); map(degree,eqsv,dR);  map(degree,eqsv,d2R); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYiIiUiIiciIzUiIzo=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYtLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYvNiRRIjZGJ0YyRjUtRi82JFEiOUYnRjJGNS1GLzYkUSMxMkYnRjIvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGO0YyRjIvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0Yn">NyYiIiQiIiciIioiIzc=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYiIiIiIiMiIiQiIiU=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35794" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser(6)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUYjNiYtSSNtaUdGJDYlUSJ2RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnL0Y1USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUklbXN1cEdGJDYlLUYuNiVRInRGJ0YxRjQtSSNtbkdGJDYkUSIyRidGOy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOy1GODYtUScmcGx1cztGJ0Y7Rj1GQEZCRkRGRkZIRkovRk1RLDAuMjIyMjIyMmVtRicvRlBGXG8tRiM2KEZXRjdGLUY3LUZSNiVGVC1GWDYkUSIzRidGO0ZlbkY7RmhuLUYjNihGV0Y3LUYjNiZGLUY3LUkobWZlbmNlZEdGJDYkLUYjNiZGLUZobi1GWDYkUSI0RidGO0Y7RjtGO0Y3LUZSNiVGVEZecEZlbkY7RmhuLUYjNihGV0Y3LUYjNihGLUY3LUZqbzYkLUYjNiZGLUZobi1GWDYkUSMxMEYnRjtGO0Y7RjctRmpvNiQtRiM2JkYtRmhuRldGO0Y7RjtGNy1GUjYlRlQtRlg2JFEiNUYnRjtGZW5GO0Zobi1GIzYoRldGNy1GIzYmRi1GNy1Gam82JC1GIzYqLUZSNiVGLUZib0ZlbkZobi1GIzYmLUZYNiRRIzI0RidGO0Y3LUZSNiVGLUZXRmVuRjtGaG4tRiM2Ji1GWDYkUSQxMTVGJ0Y7RjdGLUY7RmhuLUZYNiRRJDExMkYnRjtGO0Y7RjtGNy1GUjYlRlQtRlg2JFEiNkYnRjtGZW5GO0Zobi1GIzYmLUY4Ni1RIk9GJ0Y7Rj1GQEZCRkRGRkZIRkpGTEZPLUY4Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjtGPUZARkJGREZGRkhGSkZMRk8tRmpvNiQtRiM2Jy1GUjYlRlQtRlg2JFEiN0YnRjtGZW4vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGP0Y7RjtGO0Y7">Ky9JInRHNiJJInZHRiQiIiMsJComRiYiIiJGJUYpRikiIiQsJCooRiZGKUYlRiksJkYlRikiIiVGKUYpRilGLiwkKipGJkYpRiVGKSwmRiVGKSIjNUYpRiksJkYlRilGJkYpRilGKSIiJiwkKihGJkYpRiVGKSwqKiQpRiVGKkYpRikqJiIjQ0YpKUYlRiZGKUYpKiYiJDoiRilGJUYpRikiJDciRilGKUYpIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35809" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R0ser, dR=diff(R0ser,v), d2R=diff(R0ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[1]),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35822" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R0ser, dR=diff(R0ser,v), d2R=diff(R0ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[2]),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiT0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSShtZmVuY2VkR0YkNiQtRiM2Jy1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictSSNtbkdGJDYkUSMxM0YnRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGL0YvRi8=">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35821" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R0ser, dR=diff(R0ser,v), d2R=diff(R0ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[3]),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzs=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35824" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R0ser, dR=diff(R0ser,v), d2R=diff(R0ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[4]),t,N+1))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(%+U0-t)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCwmSSJ5RzYiIiIiRichIiJGJywmSSJNR0YmRidGJ0YoRicsKComRipGJ0YlRidGJyomSSJ0R0YmRidJInZHRiZGJ0YoRi5GJ0YnRig=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L34333" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
<Group view="code" labelreference="L34353" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L34354" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L34355" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L34356" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=3:M01:=map(factor,subs(omega=0,v=1,Mser(N)))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRNMDFHRigsKCosIiIjIiIiKUkidEdGKCIiJEYxLCoqJkYwRjEpSSJ4R0YoIiIlRjFGMSomRjlGMSlGOEY0RjEhIiIqJkYwRjFGOEYxRjFGMUY8RjEpLCZGMUY8RjhGMUY0RjxGO0Y8RjEqKilGM0YwRjEsKComRjBGMSlGOEYwRjFGMUY9RjxGMUYxRjEpRj9GMEY8RkRGPEYxKihGOEY8Rj9GPEYzRjFGPDcjRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(M01-M01^2,t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiIsJComSSJ4R0YkISIiLCYiIiJGKEYnRipGKEYoRiosJCooIiIjRipGJ0YoRilGKEYqRi0sJCooIiIlRipGJ0YoRilGKEYqIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRipGMA==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34351" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsJiomSSJ0RzYiIiIiSSJ5R0YmRidGJ0YnRidGJ0YlRidJInZHRiZGJw==</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L34900" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L35024" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L34902" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L30826" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">Now omega=1 (Section 5.2, Section 8.3 for DA, Section 9.2 for trees)</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L30841" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(omega=1,esym_paper)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsKEkieEc2IiEiIkkieUdGJUYmIiIiRihGKCwmKiZGJ0YoSSNNeUdGJUYoRigqJkkidEdGJUYoLCZJInZHRiVGKEYoRiZGKEYmRigsKEYrRiZGJ0YmRihGKEYo</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr:=(-My - y + 1)*(My*y - t*(v - 1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVElZXhwckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKSZBc3NpZ247RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiQtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GWC1GLDYlUSNNeUYnRi9GMi1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRldGWS1GLDYlUSJ5RidGL0YyLUY2Ni1RJyZwbHVzO0YnRjlGO0Y+RkBGQkZERkZGSEZXRlktSSNtbkdGJDYkUSIxRidGOUY5RjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZoby1GUDYkLUYjNiYtRiM2JkZaRmRvRmpuRjlGZ24tRiM2Ji1GLDYlUSJ0RidGL0YyRmRvLUZQNiQtRiM2Ji1GLDYlUSJ2RidGL0YyRmduRmBvRjlGOUY5RjlGOUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoKiYsKEkjTXlHRighIiJJInlHRihGMSIiIkYzRjMsJiomRjBGM0YyRjNGMyomSSJ0R0YoRjMsJkkidkdGKEYzRjNGMUYzRjFGMzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30844" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">First terms in the series R</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30831" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,series(subs(My=Mser(3),y=x,omega=1,expr),t,4))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInRHNiIsJCooLCgtSSVNc2VyR0YkNiMiIiQiIiJJInhHRiRGLEYsISIiRixGLUYsRihGLEYuIiIhKiZGJ0YsLCZJInZHRiRGLEYsRi5GLEYs</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30839" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr-R</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiwoSSNNeUc2IiEiIkkieUdGJkYnIiIiRilGKSwmKiZGKEYpRiVGKUYpKiZJInRHRiZGKSwmSSJ2R0YmRilGKUYnRilGJ0YpRilJIlJHRiZGJw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L39042" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR1:=(y*(1-y)+t*(v-1))/2/y -(y*(1-y)-t*(v-1))/2/y*sqrt(1- 4*y*R/(y*(1-y)-t*(v-1))^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRNUjFHRigsJiooIyIiIiIiI0YxLCYqJkkieUdGKEYxLCZGMUYxRjUhIiJGMUYxKiZJInRHRihGMSwmSSJ2R0YoRjFGMUY3RjFGMUYxRjVGN0YxKipGMEYxLCZGNEYxRjhGN0YxRjVGNyksJkYxRjEqKiIiJUYxRjVGMUkiUkdGKEYxKUY9RjJGN0Y3RjBGMUY3NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L30850" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(subs(My=MR1,expr)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJSRzYi</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L30840" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mexpr:=proc(N): local j,k,n: 
t*(v-1)/y+add(add(add(1/(n+1)*binomial(2*n,n)*binomial(2*n+k,k)*binomial(2*n+k+j,j)*t^k*(v-1)^k*R^(n+1)*y^(j-n-k-1),j=0..N),k=0..N),n=0..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30832" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=8: factor(series(mtaylor(subs(My=Mexpr(n),expr-R),[t,R],n),y,n)):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L30849" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ldegree(convert(%,polynom,[t,R,y]))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiM1</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L33794" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36074" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35909" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">Explicit differential equations for R1 and Q1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L36052" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Our first objective is to study the vector space spanned by Omega and its derivatives in r  and u.
<Font encoding="UTF-8">We will first guess linear relations between these derivatives, using Hermite-Pad\303\251 approximants.
</Font>Since they handle power series in one variable only (possibly with polynomial coefficients), we do the guessing for Omega and its derivatives evaluated at r and u*r.</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36053" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series Omega</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35881" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(2*k+3* n, n+k)*u^k*
r^(n + 1)/(n + 1), k = 0 .. N-n-1), n = 0 .. N-1); end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36012" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjSSIiIilJInJHNiIiIiRGJUYlKihGJEYlKUYnIiIjRiVJInVHRihGJUYlKigiIidGJUYnRiUpRi1GLEYlRiUqJkYpRiVGK0YlRiUqKEYsRiVGJ0YlRi1GJUYlRidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35896" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Redefining derivatives so that diff(F,x$0) is understood...</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35833" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">der:=proc(F,x,k)
if k=0 then F else diff(F,x$k): fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35848" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">der(u^2*r,r,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdXBHRiQ2JS1GLDYlUSJ1RidGL0YyLUkjbW5HRiQ2JFEiMkYnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjk=">KiZJInJHNiIiIiIpSSJ1R0YkIiIjRiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L36013" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Derivatives of Omega w.r.t. r and u</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36016" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_d:=proc(N,d1,d2)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(2*k+3* n, n+k)*der(u^k,u,d2)*
der(r^(n + 1),r,d1)/(n + 1), k = 0 .. N-n+d2), n = 0 .. N-1+d1); end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35838" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_d(4,1,1); Omega_d(4,0,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZALUYjNiYtSSNtbkdGJDYkUSgxMjYxMjYwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSS1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMlEnaXRhbGljRictRi42JFEiNEYnRjEvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjEtRjU2LVEnJnBsdXM7RidGMUY4RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLRlxvLUYjNigtRi42JFEoMTQ0MTQ0MEYnRjFGNC1GUDYlUSJ1RidGU0ZWRjQtRk02JUZPLUYuNiRRIjNGJ0YxRmVuRjFGaG4tRiM2KC1GLjYkUSc0OTg5NjBGJ0YxRjQtRk02JUZjby1GLjYkUSIyRidGMUZlbkY0LUZNNiVGT0ZicEZlbkYxRmhuLUYjNigtRi42JFEmNTU0NDBGJ0YxRjQtRk02JUZjb0Zob0ZlbkY0Rk9GMUZobi1GIzYmLUYuNiRRJTEyNjBGJ0YxRjQtRk02JUZjb0ZYRmVuRjFGaG4tRiM2Ji1GLjYkUSY0NjIwMEYnRjFGNEZmb0YxRmhuLUYjNigtRi42JFEmMzc4MDBGJ0YxRjRGY29GNEZlcEYxRmhuLUYjNigtRi42JFElNzU2MEYnRjFGNEZPRjRGYHBGMUZobi1GIzYmLUYuNiRRJDI4MEYnRjFGNEZccUYxRmhuLUYjNiYtRi42JFElMTY4MEYnRjFGNEZlcEYxRmhuLUYjNigtRi42JFEkODQwRidGMUY0Rk9GNEZjb0YxRmhuLUYjNiYtRi42JFEjNjBGJ0YxRjRGYHBGMUZobi1GIzYmRmVzRjRGT0YxRmhuLUYjNiYtRi42JFEjMTJGJ0YxRjRGY29GMUZobkZicEYx">LEAqJiIoZzdFIiIiIilJInJHNiIiIiVGJUYlKigiKFM5VyJGJSlGJyIiJEYlSSJ1R0YoRiVGJSooIidnKilcRiUpRiciIiNGJSlGLkYyRiVGJSooIiZTYSZGJUYnRiUpRi5GLUYlRiUqJiIlZzdGJSlGLkYpRiVGJSomIiYraSVGJUYsRiVGJSooIiYreSRGJUYxRiVGLkYlRiUqKCIlZ3ZGJUYnRiVGM0YlRiUqJiIkIUdGJUY2RiVGJSomIiUhbyJGJUYxRiVGJSooIiRTKUYlRidGJUYuRiVGJSomIiNnRiVGM0YlRiUqJkZHRiVGJ0YlRiUqJiIjN0YlRi5GJUYlRjJGJQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LD4qKCImXToiIiIiKUkickc2IiIiJUYlSSJ1R0YoRiVGJSooIiUrakYlKUYnIiIkRiUpRioiIiNGJUYlKigiJWc3RiUpRidGMEYlKUYqRi5GJUYlKigiI3FGJUYnRiUpRipGKUYlRiUqJiIkPyVGJUYmRiVGJSooIiRnJkYlRi1GJUYqRiVGJSooIiQ1I0YlRjNGJUYvRiVGJSooIiM/RiVGJ0YlRjRGJUYlKiYiI0lGJUYtRiVGJSooRkFGJUYzRiVGKkYlRiUqKCIiJ0YlRidGJUYvRiVGJSomRi5GJUYzRiVGJSooRjBGJUYnRiVGKkYlRiVGJ0Yl</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36040" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now, let's guess relations between these functions (evaluated at (r,ur) as said above). Moreover, it is often faster to specialise u, do the guessing and reconstruct.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36049" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(numapprox):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36062" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2">The vector space spanned by Omega and its derivatives</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L36079" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The second derivative in r in terms of 3 other series, namely Omega and its first derivatives (in r and in u)</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35986" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=100*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIicrKzsiIiJJInJHNiJGJkYmIiQxJSEiIiwkKigiJCsjRiZGJ0YmLCYqJiIlKzdGJkYnRiZGJkYmRiZGJkYqLCQqKEYtRiZGJ0YmLCYqJiImKyspRiZGJ0YmRiYiJC4jRipGJkYqKiZGJ0YmLCgqJiIpKysrO0YmKUYnIiIjRiZGJiomIiZGTylGJkYnRiZGKiIkLCJGJkYm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35983" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=1000*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIikrKys7IiIiSSJyRzYiRiZGJiIlMVMhIiIsJCooIiUrP0YmRidGJiwmKiYiJis/IkYmRidGJkYmRiZGJkYmRiosJCooRi1GJkYnRiYsJiomIigrKyspRiZGJ0YmRiYiJS4/RipGJkYqKiZGJ0YmLCgqJiIsKysrK2ciRiYpRiciIiNGJkYmKiYiKEZnLilGJkYnRiZGKiIlLDVGJkYm</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35982" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The coefficients are not too hard to guess for a generic u. But on this example, things work quite efficiently with the parameter u.</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35988" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed1:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,2,0)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkMUdGKDcmLCgqKCIjOyIiIkkickdGKEYyKUkidUdGKCIiI0YyRjIqJiIiJUYyRjVGMiEiIiIiJ0Y5LCQqKkY2RjJGM0YyRjVGMiwmKigiIzdGMkYzRjJGNUYyRjJGMkYyRjJGOSwkKipGNkYyRjNGMkY1RjIsKCooIiIpRjJGM0YyRjRGMkYyKiZGNkYyRjVGMkY5IiIkRjlGMkY5KiZGM0YyLC4qKEYxRjIpRjNGNkYyKUY1RkZGMkYyRkNGOSooIiNPRjJGM0YyRjVGMkY5KiYiI0ZGMkYzRjJGOUY1RjJGMkYyRjI3I0Yu</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35984" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The second derivative in u in terms of the same 3 series</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35994" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=1000*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,0,2)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIiVPISkiIiJJInJHNiJGJkYmIiIjISIiLCQqKEYpRiZGJ0YmLCYqJiImRj8iRiZGJ0YmRiZGJkYqRiZGKiwkKigiJSs/RiZGJ0YmLCYqJiIlPVNGJkYnRiZGJkYmRipGJkYqKiZGJ0YmLCgqJiIsKysrK2ciRiYpRidGKUYmRiYqJiIoRmcuKUYmRidGJkYqIiUsNUYmRiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35993" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed2:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,0,2)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkMkdGKDcmLCgqKCIiKSIiIkkickdGKEYySSJ1R0YoRjJGMiomIiNPRjJGM0YyRjIiIiMhIiIsJCooRjdGMkYzRjIsKCooIiM3RjJGM0YyRjRGMkYyKiYiI0ZGMkYzRjJGMkYyRjhGMkY4LCQqKkY3RjJGM0YyRjRGMiwoKigiIiVGMkYzRjJGNEYyRjIqJiIjPUYyRjNGMkYyRjJGOEYyRjgqJkYzRjIsLiooIiM7RjIpRjNGN0YyKUY0IiIkRjJGMiooRjFGMkYzRjIpRjRGN0YyRjgqKEY2RjJGM0YyRjRGMkY4Rj5GOEY0RjJGMkYyRjI3I0Yu</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36078" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Finally, rhe mixed derivative in r,u</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35989" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=10*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,1,1)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsJiomIiRTIyIiIkkickc2IkYmRiYiIiNGJiwkKigiIz9GJkYnRiYsJiomIiNlRiZGJ0YmRiZGJiEiIkYmRjAsJCooRixGJkYnRiYsJiomIiQ/IkYmRidGJkYmRiZGJkYmRjAsJComRidGJiwoKiYiJitnIkYmKUYnRilGJkYmKiYiJSg9IkYmRidGJkYwIiM2RiZGJkYw</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35992" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
coed3:=factor(hermite_pade(subs(u=u*r,[Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Omega_d(N,1,1)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkM0dGKDcmLCYqKCIjQyIiIkkickdGKEYySSJ1R0YoRjJGMiIiI0YyLCQqKkY1RjJGM0YyRjRGMiwoKigiIiVGMkYzRjJGNEYyRjIqJiIjPUYyRjNGMkYyRjIhIiJGMkY9LCQqKkY1RjJGM0YyRjRGMiwmKigiIzdGMkYzRjJGNEYyRjJGMkYyRjJGPSwkKiZGM0YyLC4qKCIjO0YyKUYzRjVGMilGNCIiJEYyRjIqKCIiKUYyRjNGMilGNEY1RjJGPSooIiNPRjJGM0YyRjRGMkY9KiYiI0ZGMkYzRjJGPUY0RjJGMkYyRjJGPTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35985" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">So it seems that we have a vector space of dimension 3. Let us reconstruct 3 equations, recalling that the above linear relations are for series avaluated at (r,ur)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36064" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1:=subs(u=u/r,coed1[1])*Om(r,u)+subs(u=u/r,coed1[2])*diff(Om(r,u),r)+subs(u=u/r,coed1[3])*diff(Om(r,u),u)+subs(u=u/r,coed1[4])*diff(Om(r,u),r$2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36076" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed2:=subs(u=u/r,coed2[1])*Om(r,u)+subs(u=u/r,coed2[2])*diff(Om(r,u),r)+subs(u=u/r,coed2[3])*diff(Om(r,u),u)+subs(u=u/r,coed2[4])*diff(Om(r,u),u$2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35955" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed3:=subs(u=u/r,coed3[1])*Om(r,u)+subs(u=u/r,coed3[2])*diff(Om(r,u),r)+subs(u=u/r,coed3[3])*diff(Om(r,u),u)+subs(u=u/r,coed3[4])*diff(diff(Om(r,u),r),u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEkZWQzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYmLUkobWZlbmNlZEdGJDYkLUYjNiYtRiM2Ji1JI21uR0YkNiRRIzI0RidGOS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmpuLUYsNiVRInVGJ0YvRjJGOS1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GY28tRlk2JFEiMkYnRjlGOUY5RmZuLUYjNiYtRiw2JVEjT21GJ0YvRjItRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmluRltvLUZSNiQtRiM2KS1GLDYlUSJyRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGaW4vRk5RLDAuMzMzMzMzM2VtRidGXG8vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RjlGOUY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGYm9GZG8tRiM2KkZlb0ZmbkZcb0Zmbi1GUjYkLUYjNigtRiM2Ji1GWTYkUSMxOEYnRjlGZm5GZHBGOUZfby1GIzYmLUZZNiRRIjRGJ0Y5RmZuRlxvRjlGZXEtRlk2JFEiMUYnRjlGOUY5RmZuLUZSNiQtRiM2KC1JJm1mcmFjR0YkNigtRjY2LVErJlBhcnRpYWxEO0YnRjlGO0Y+RkBGQkZERkZGSEZpbkZbby1GIzYlRmJzRmRwRjkvJS5saW5ldGhpY2tuZXNzR0Zqci8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbdC8lKWJldmVsbGVkR0Y9LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRmV0LyUqbGluZWJyZWFrR1ElYXV0b0YnRmpvRl1wRmBwRjlGOUY5RmVxLUYjNipGZW9GZm5GXG9GZm4tRlI2JC1GIzYmLUYjNiYtRlk2JFEjMTJGJ0Y5RmZuRlxvRjlGX29GaHJGOUY5RmZuLUZSNiQtRiM2KC1GYHM2KEZicy1GIzYlRmJzRlxvRjlGZ3NGaXNGXHRGXnRGYHRGam9GXXBGYHBGOUY5RjlGZXEtRiM2KEZkcEZmbi1GUjYkLUYjNi4tRmBzNigtRiM2Ji1GWTYkUSMxNkYnRjlGZm4tSSVtc3VwR0YkNiVGXG8tRlk2JFEiM0YnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjlGZHBGZ3NGaXNGXHRGXnRGZXEtRmBzNigtRiM2Ji1GWTYkUSI4RidGOUZmbi1GX3c2JUZcb0Zlb0Zkd0Y5RmRwRmdzRmlzRlx0Rl50RmVxLUYjNiYtRlk2JFEjMzZGJ0Y5RmZuRlxvRjlGZXEtRiM2Ji1GWTYkUSMyN0YnRjlGZm5GZHBGOUZfby1GYHM2KEZcb0ZkcEZnc0Zpc0ZcdEZedEZfb0ZockY5RjlGZm4tRlI2JC1GIzYoLUZgczYoLUZfdzYlRmJzRmVvRmR3LUYjNidGYnNGZHBGYnNGXG9GOUZnc0Zpc0ZcdEZedEZgdEZqb0ZdcEZgcEY5RjlGOUY5">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35957" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Once these equations are guessed, they are easy to check by coefficient extraction, since Omega(r,u) is doubly hypergeometric.
Let us also check them numerically</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36020" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Omega_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjSSIiIilJInJHNiIiIiRGJUYlKihGJEYlKUYnIiIjRiVJInVHRihGJUYlKigiIidGJUYnRiUpRi1GLEYlRiUqJkYpRiVGK0YlRiUqKEYsRiVGJ0YlRi1GJUYlRidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35959" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed1))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35952" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed2))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),numer(ed3))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L36050" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We can express all partial derivatives of Omega(r,u) in terms of 3 of them.</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1; ed2;ed3</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsKiomLCYqJiIjQyIiIkkidUdGKEYxRjEiIiNGMUYxLUkjT21HRig2JEkickdGKEYyRjFGMSoqRjNGMUYyRjEsKComIiM9RjFGN0YxRjEqJiIiJUYxRjJGMUYxRjEhIiJGMS1JJWRpZmZHRiY2JEY0RjdGMUY+KipGM0YxRjJGMSwmKiYiIzdGMUYyRjFGMUYxRjFGMS1GQDYkRjRGMkYxRj4qKEY3RjEsLiooIiM7RjFGN0Y+KUYyIiIkRjFGMSooIiIpRjFGN0Y+KUYyRjNGMUY+KiYiI09GMUYyRjFGPiomIiNGRjFGN0YxRj4qJkYyRjFGN0Y+RjFGMUYxRjEtRkA2JUY0RjdGMkYxRj43IywqRi1GMUY4Rj5GQkY+KihGN0YxRklGMS1GQDYkRj9GMkYxRj4=</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L35996" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d11:=(convert(isolate(ed1,diff(Om(r, u),r$2 )),D))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkMTFHRigvLS0mSSJER0YlNiQiIiJGNDYjSSNPbUdGKDYkSSJyR0YoSSJ1R0YoKigsKComLCgqKCIjO0Y0RjghIiIpRjkiIiNGNEY0KigiIiVGNEY5RjRGOEZARkAiIidGQEY0LUY2RjdGNEZAKipGQkY0RjlGNCwmKiYiIzdGNEY5RjRGNEY0RjRGNC0tJkYyNiNGNEY1RjdGNEY0KipGQkY0RjlGNCwoKigiIilGNEY4RkBGQUY0RjQqKEZCRjRGOUY0RjhGQEZAIiIkRkBGNC0tJkYyNiNGQkY1RjdGNEY0RjRGOEZALC4qKEY/RjRGOEZAKUY5RlRGNEY0RlFGQComIiNPRjRGOUY0RkAqJiIjRkY0RjhGNEZAKiZGOUY0RjhGQEY0RjRGNEZANyNGLg==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35997" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d22:=(convert(isolate(ed2,diff(Om(r, u),u$2 )),D))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkMjJHRigvLS0mSSJER0YlNiQiIiNGNDYjSSNPbUdGKDYkSSJyR0YoSSJ1R0YoKigsKComLCgqJiIjTyIiIkY4RkBGQComIiIpRkBGOUZARkBGNCEiIkZALUY2RjdGQEZDKipGNEZARjhGQCwoKiYiI0ZGQEY4RkBGQComIiM3RkBGOUZARkBGQEZDRkAtLSZGMjYjRkBGNUY3RkBGQCoqRjRGQEY5RkAsKComIiM9RkBGOEZARkAqJiIiJUZARjlGQEZARkBGQ0ZALS0mRjI2I0Y0RjVGN0ZARkBGQEY4RkMsLiooIiM7RkBGOEZDKUY5IiIkRkBGQCooRkJGQEY4RkMpRjlGNEZARkMqJkY/RkBGOUZARkNGR0ZDKiZGOUZARjhGQ0ZARkBGQEZDNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35995" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">d12:=convert(isolate(ed3,diff(diff(Om(r, u),r),u )),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkMTJHRigvLS0mSSJER0YlNiQiIiIiIiM2I0kjT21HRig2JEkickdGKEkidUdGKCwkKigsKComLCYqJiIjQ0Y0RjpGNEY0RjVGNEY0LUY3RjhGNCEiIioqRjVGNEY6RjQsKComIiM9RjRGOUY0RjQqJiIiJUY0RjpGNEY0RjRGQ0Y0LS0mRjI2I0Y0RjZGOEY0RjQqKkY1RjRGOkY0LCYqJiIjN0Y0RjpGNEY0RjRGNEY0LS0mRjI2I0Y1RjZGOEY0RjRGNEY5RkMsLiooIiM7RjRGOUZDKUY6IiIkRjRGNCooIiIpRjRGOUZDKUY6RjVGNEZDKiYiI09GNEY6RjRGQyomIiNGRjRGOUY0RkMqJkY6RjRGOUZDRjRGNEY0RkNGQzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35998" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We observe that the second order derivatives are in fact linear combinations of </Text-field><Text-field style="Text" layout="Normal">Om_r and the difference Phi:=(Om- u*Om_u).</Text-field><Text-field style="Text" layout="Normal">So we also have a 2D sub-space generated by these two series</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35842" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi_ser:=proc(N)
Omega_d(N,0,0)-u*Omega_d(N,0,1): end:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35943" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check this</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35978" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef:=D[2](Om)(r, u)= (Om(r,u)-Phi(r,u))/u</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwaGlkZWZHRigvLS0mSSJER0YlNiMiIiM2I0kjT21HRig2JEkickdGKEkidUdGKComLCYtRjZGNyIiIi1JJFBoaUdGKEY3ISIiRj1GOUZANyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35945" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed11_phi:=collect(subs(phidef, d11),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDExX3BoaUdGKC8tLSZJIkRHRiU2JCIiIkY0NiNJI09tR0YoNiRJInJHRihJInVHRigsJiouIiIjRjRGOUY0LCYqJiIjN0Y0RjlGNEY0RjRGNEY0RjghIiIsLiooIiM7RjRGOEZAKUY5IiIkRjRGNCooIiIpRjRGOEZAKUY5RjxGNEZAKiYiI09GNEY5RjRGQComIiNGRjRGOEY0RkAqJkY5RjRGOEZARjRGNEY0RkAtLSZGMjYjRjRGNUY3RjRGNCosRjxGNCwoRkZGNCooRjxGNEY5RjRGOEZARkBGRUZARjQtSSRQaGlHRihGN0Y0RjhGQEZBRkBGQDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35962" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed22_phi:=collect(subs(phidef, d22),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDIyX3BoaUdGKC8tLSZJIkRHRiU2JCIiI0Y0NiNJI09tR0YoNiRJInJHRihJInVHRigsJiooLCgqJiIjYSIiIkY4Rj9GPyomIiNDRj9GOUY/Rj9GNCEiIkY/LC4qKCIjO0Y/RjhGQilGOSIiJEY/Rj8qKCIiKUY/RjhGQilGOUY0Rj9GQiomIiNPRj9GOUY/RkIqJiIjRkY/RjhGP0ZCKiZGOUY/RjhGQkY/Rj9GP0ZCLS0mRjI2I0Y/RjVGN0Y/Rj8qLEY0Rj8sKComIiM9Rj9GOEY/Rj8qJiIiJUY/RjlGP0Y/Rj9GQkY/LUkkUGhpR0YoRjdGP0Y4RkJGQ0ZCRkI3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35939" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed12_phi:=collect(subs(phidef, d12),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSllZDEyX3BoaUdGKC8tLSZJIkRHRiU2JCIiIiIiIzYjSSNPbUdGKDYkSSJyR0YoSSJ1R0YoLCYqLkY1RjRGOkY0LCgqJiIjPUY0RjlGNEY0KiYiIiVGNEY6RjRGNEY0ISIiRjRGOUZCLC4qKCIjO0Y0RjlGQilGOiIiJEY0RjQqKCIiKUY0RjlGQilGOkY1RjRGQiomIiNPRjRGOkY0RkIqJiIjRkY0RjlGNEZCKiZGOkY0RjlGQkY0RjRGNEZCLS0mRjI2I0Y0RjZGOEY0RkIqLEY1RjQsJiomIiM3RjRGOkY0RjRGNEY0RjQtSSRQaGlHRihGOEY0RjlGQkZDRkJGNDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35940" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We will also need the derivatives of Phi</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35887" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
factor(hermite_pade(subs(u=u*r,[diff(Phi_ser(N),r), Omega_d(N,1,0),Phi_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUsLiooIiM7IiIiKUkickc2IiIiI0YmKUkidUdGKSIiJEYmRiYqKCIiKUYmRihGJilGLEYqRiYhIiIqKCIjT0YmRihGJkYsRiZGMSomIiNGRiZGKEYmRjFGLEYmRiZGJiwwKigiI0NGJkYnRiZGK0YmRjEqKEYzRiZGJ0YmRjBGJkYxKigiIzVGJkYoRiZGMEYmRiZGMkYmRjRGJkYsRjFGJkYxLCQqKEYqRiZGLEYmLCYqKCIjN0YmRihGJkYsRiZGJkYmRiZGJkYm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35908" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edPhi1:=subs(u=u/r,op(1,%))*diff(Phi(r,u),r)+ subs(u=u/r,op(2,%))*diff(Om(r,u),r)+subs(u=u/r,op(3,%))*Phi(r,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdlZFBoaTFHRigsKComLC4qKCIjOyIiIkkickdGKCEiIilJInVHRigiIiRGM0YzKigiIilGM0Y0RjUpRjciIiNGM0Y1KiYiI09GM0Y3RjNGNSomIiNGRjNGNEYzRjUqJkY3RjNGNEY1RjNGM0YzRjMtSSVkaWZmR0YmNiQtSSRQaGlHRig2JEY0RjdGNEYzRjMqJiwwKigiI0NGM0Y0RjVGNkYzRjUqJkY+RjNGO0YzRjUqKCIjNUYzRjRGNUY7RjNGM0Y9RjNGP0YzRkFGNUYzRjVGMy1GQzYkLUkjT21HRihGR0Y0RjNGMyosRjxGM0Y3RjMsJiomIiM3RjNGN0YzRjNGM0YzRjNGNEY1RkVGM0YzNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36018" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi_ser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qKCIjSSIiIkkidUc2IkYlKUkickdGJyIiI0YlRiUqKCIiJ0YlRilGJSlGJkYqRiVGJSomIiIkRiVGKEYlRiUqKEYqRiVGKUYlRiZGJUYlRilGJSomRiZGJSwsKigiJD8lRiVGKEYlRiZGJUYlKigiI2dGJUYpRiVGLUYlRiUqJkYkRiVGKEYlRiUqKCIjN0YlRilGJUYmRiVGJSomRipGJUYpRiVGJUYlISIi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35897" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N),numer(edPhi1))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35889" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed1_Phi:=convert(collect(isolate(edPhi1, diff(Phi(r, u), r)),[Om,Phi]),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZDFfUGhpR0YoLy0tJkkiREdGJTYjIiIiNiNJJFBoaUdGKDYkSSJyR0YoSSJ1R0YoLCYqLiIiI0Y0RjlGNCwmKiYiIzdGNEY5RjRGNEY0RjRGNEY4ISIiLC4qKCIjO0Y0RjhGQClGOSIiJEY0RjQqKCIiKUY0RjhGQClGOUY8RjRGQComIiNPRjRGOUY0RkAqJiIjRkY0RjhGNEZAKiZGOUY0RjhGQEY0RjRGNEZALUY2RjdGNEZAKigsMCooIiNDRjRGOEZARkRGNEZAKiZGSkY0RkhGNEZAKigiIzVGNEY4RkBGSEY0RjRGSUY0RktGNEZNRkBGNEZARjQtLUYxNiNJI09tR0YoRjdGNEZBRkBGQDcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36027" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=25:
factor(hermite_pade(subs(u=u*r,[diff(Phi_ser(N),u), Omega_d(N,1,0),Phi_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUsLiooIiM7IiIiKUkickc2IiIiI0YmKUkidUdGKSIiJEYmISIiKigiIilGJkYoRiYpRixGKkYmRiYqKCIjT0YmRihGJkYsRiZGJiomIiNGRiZGKEYmRiZGLEYuRiZGLiwkKipGKkYmRihGJkYsRiYsKCooIiM3RiZGKEYmRixGJkYmRjRGJkYmRi5GJkYuLCQqKEYqRiZGLEYmLCgqKCIiJUYmRihGJkYsRiZGJiomIiM9RiZGKEYmRiZGJkYuRiZGJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36024" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edPhi2:=subs(u=u/r,op(1,%))*diff(Phi(r,u),u)+ subs(u=u/r,op(2,%))*diff(Om(r,u),r)+subs(u=u/r,op(3,%))*Phi(r,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdlZFBoaTJHRigsKComLC4qKCIjOyIiIkkickdGKCEiIilJInVHRigiIiRGM0Y1KigiIilGM0Y0RjUpRjciIiNGM0YzKiYiI09GM0Y3RjNGMyomIiNGRjNGNEYzRjMqJkY3RjNGNEY1RjVGM0Y1RjMtSSVkaWZmR0YmNiQtSSRQaGlHRig2JEY0RjdGN0YzRjMqKkY8RjNGN0YzLChGP0YzKiYiIzdGM0Y3RjNGM0YzRjVGMy1GQzYkLUkjT21HRihGR0Y0RjNGNSosRjxGM0Y3RjMsKComIiM9RjNGNEYzRjMqJiIiJUYzRjdGM0YzRjNGNUYzRjRGNUZFRjNGMzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36014" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: mtaylor(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N),numer(edPhi2))),[u,r],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36025" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed2_Phi:=convert(collect(isolate(edPhi2, diff(Phi(r, u), u)),[Om,Phi]),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZDJfUGhpR0YoLy0tJkkiREdGJTYjIiIjNiNJJFBoaUdGKDYkSSJyR0YoSSJ1R0YoLCYqLkY0IiIiRjlGPCwoKiYiIz1GPEY4RjxGPComIiIlRjxGOUY8RjxGPCEiIkY8RjhGQiwuKigiIztGPEY4RkIpRjkiIiRGPEZCKigiIilGPEY4RkIpRjlGNEY8RjwqJiIjT0Y8RjlGPEY8KiYiI0ZGPEY4RjxGPComRjlGPEY4RkJGQkY8RkJGQi1GNkY3RjxGQiosRjRGPEY5RjwsKEZNRjwqJiIjN0Y8RjlGPEY8RjxGQkY8LS0mRjI2I0Y8NiNJI09tR0YoRjdGPEZDRkJGPDcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35890" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35862" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35849" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">t-Derivatives of R1</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35859" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id[0]:=Om(R(t),t*(v-1))-t</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiISwmLUkjT21HRig2JC1JIlJHRig2I0kidEdGKComRjgiIiIsJkkidkdGKEY6RjohIiJGOkY6RjhGPTcjRjE=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35980" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Differentiate twice with respect to t</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35878" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 2 do id[i]:=diff(id[0],t$i) od</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiIiwoKiYtLSZJIkRHRiVGLzYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ0R0YoKiZGPUYwLCZJInZHRihGMEYwISIiRjBGMC1JJWRpZmZHRiY2JEY6Rj1GMEYwKiYtLSZGNjYjIiIjRjdGOUYwRj9GMEYwRjBGQTcjRjE=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjaWRHRig2IyIiIywoKiYsJiomLS0mSSJER0YlNiQiIiJGOjYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ0R0YoKiZGQUY6LCZJInZHRihGOkY6ISIiRjpGOi1JJWRpZmZHRiY2JEY+RkFGOkY6KiYtLSZGODYkRjpGMEY7Rj1GOkZDRjpGOkY6RkZGOkY6KiYtLSZGODYjRjpGO0Y9RjotRkc2JEY+LUkiJEdGJjYkRkFGMEY6RjoqJiwmKiZGSkY6RkZGOkY6KiYtLSZGODYkRjBGMEY7Rj1GOkZDRjpGOkY6RkNGOkY6NyMsKEYyRjoqJkZPRjotRkc2JEZGRkFGOkY6RlhGOg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L36059" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Rewrite with Phi instead of Om_u</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35975" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_tv:=subs(r=R(t),u=t*(v-1),phidef)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpwaGlkZWZfdHZHRigvLS0mSSJER0YlNiMiIiM2I0kjT21HRig2JC1JIlJHRig2I0kidEdGKComRjsiIiIsJkkidkdGKEY9Rj0hIiJGPSooLCYtRjZGN0Y9LUkkUGhpR0YoRjdGQEY9RjtGQEY+RkA3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36061" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id1_phi:=collect(subs(phidef_tv,Om(R(t), t*(v - 1))=t,id[1]),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShpZDFfcGhpR0YoLCYqJi0tJkkiREdGJTYjIiIiNiNJI09tR0YoNiQtSSJSR0YoNiNJInRHRigqJkY8RjUsJkkidkdGKEY1RjUhIiJGNUY1LUklZGlmZkdGJjYkRjlGPEY1RjUqJkY8RkAtSSRQaGlHRihGOEY1RkA3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35870" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed11_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIiRiw2I0kjT21HRio2JEkickdGKkkidUdGKiwmKi4iIiNGLEYxRiwsJiomIiM3RixGMUYsRixGLEYsRixGMCEiIiwuKigiIztGLEYwRjgpRjEiIiRGLEYsKigiIilGLEYwRjgpRjFGNEYsRjgqJiIjT0YsRjFGLEY4KiYiI0ZGLEYwRixGOComRjFGLEYwRjhGLEYsRixGOC0tJkYmNiNGLEYtRi9GLEYsKixGNEYsLChGPkYsKihGNEYsRjFGLEYwRjhGOEY9RjhGLC1JJFBoaUdGKkYvRixGMEY4RjlGOEY4</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35866" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We check that the denominator does not vanish at (R,t(v-1)).</Text-field><Text-field style="Text" layout="Normal">The first coefficients of R1 are computed in the section (Checking...&quot;)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36081" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R1ser := t + (-2*v - 1)*t^2 + (-2*v^2 - 8*v - 2)*t^3 + (-4*v^3 - 36*v^2 - 56*v - 9)*t^4 + (-10*v^4 - 152*v^3 - 524*v^2 - 466*v - 54)*t^5 + (-28*v^5 - 628*v^4 - 3648*v^3 - 7088*v^2 - 4232*v - 378)*t^6 + (-84*v^6 - 2568*v^5 - 22020*v^4 - 71760*v^3 - 92532*v^2 - 40536*v - 2916)*t^7 + (-264*v^7 - 10440*v^6 - 122160*v^5 - 586560*v^4 - 1262856*v^3 - 1183536*v^2 - 402504*v - 24057)*t^8 + (-858*v^8 - 42288*v^7 - 640920*v^6 - 4196304*v^5 - 13281912*v^4 - 20698944*v^3 - 14941320*v^2 - 4101960*v - 208494)*t^9 + (-2860*v^9 - 170868*v^8 - 3231936*v^7 - 27402144*v^6 - 118123488*v^5 - 270037152*v^4 - 322959168*v^3 - 186934344*v^2 - 42634280*v - 1876446)*t^10 + O(t^11)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35865" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numer(16*u^3/r - 8*u^2/r - 36*u - 27*r + u/r + 1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjOyIiIilJInVHNiIiIiRGJUYlKiYiI0ZGJSlJInJHRigiIiNGJSEiIiooIiNPRiVGLUYlRidGJUYvKiYiIilGJSlGJ0YuRiVGL0YtRiVGJ0Yl</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35868" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(subs(r=R1ser,u=t*(v-1),%),t,5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiJJInZHRiQiIiIsJCooIiIjRiZGJUYmLCYqJiIiJUYmRiVGJkYmIiM2RiZGJiEiIkYpLCQqKEYpRiZGJUYmLCgqJiIiKUYmKUYlRilGJkYmKiZGLUYmRiVGJkYmIiNjRiZGJkYmIiIkLCQqKEYsRiZGJUYmLCgqJiIjPEYmRjRGJkYmKiYiI1hGJkYlRiZGJiIjOEYmRiZGJkYsLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35969" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id2_phi:=collect(subs(phidef_tv,Om(R(t), t*(v - 1))=t,subs(r=R(t),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}),id[2]),
[Om,Phi],factor): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi0qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLS1GOjYkRjItSSIkR0YmNiRGLSIiIy0tJkkiREdGJTYjRjY2I0kjT21HRihGMTcjPClGLUYuRi9GMkY5LUY6NiRGOUYtRkI=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35872" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(coeff(id2_phi,D[1](Om)(R(t), t*(v - 1))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35971" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Compare both equations between Phi and Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35973" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(id1_phi, Phi(R(t), t*(v - 1))),id2_phi))): nops(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35966" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(1,res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LS0mSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMiIiI2I0kjT21HRik2JC1JIlJHRik2I0kidEdGKSomRjJGKywmSSJ2R0YpRitGKyEiIkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35831" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">A second order DE for R</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35961" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt:=collect(convert(op(2,res),D),R, factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35829" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Rewrite in terms of t and u=t(v-1)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35850" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numer(factor(subs(v=1+u/t,edRt)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35991" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt_u:=collect(%,R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35854" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(edRt_u,[(D@@2)(R)(t),D(R)(t),R],factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35846" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The case v=1, that is, u=0</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35902" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(op(3,factor(subs(u=0,edRt_u))),[(D@@2)(R)(t)],factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKC1JIlJHNiI2I0kidEdGJiIiIiwmKiYiI0ZGKUYkRilGKUYpISIiRiktLS1JI0BARzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiRJIkRHRjIiIiM2I0YlRidGKUYpKigiIidGKSktLUY2RjhGJyIiJEYpRihGKUYt</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35886" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check with the coefficients of R1 computed in the section (Checking...&quot;)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35873" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R1ser</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35898" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(eval(subs(R(t)=R1ser,u=t*(v-1),convert(edRt,diff))),t,14))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiT0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSShtZmVuY2VkR0YkNiQtRiM2Jy1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictSSNtbkdGJDYkUSMxMUYnRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGL0YvRi8=">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35863" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L35861" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" labelreference="L36002" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36035" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35904" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">v-Derivatives of R1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35900" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now an equation in v</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35906" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv[0]:=subs(R(t)=R(v),id[0])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkkaWR2R0YoNiMiIiEsJi1JI09tR0YoNiQtSSJSR0YoNiNJInZHRigqJkkidEdGKCIiIiwmRjhGO0Y7ISIiRjtGO0Y6Rj03I0Yx</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36057" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to 3 do idv[i]:=diff(idv[0],v$i) od:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36042" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv_list:=[seq(idv[i],i=0..3)]:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36015" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv[1];</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidkdGKComSSJ0R0YoRjMsJkY6RjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomLS0mRjE2IyIiI0Y0RjZGM0Y8RjNGM0Yr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35843" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Again, we rewrite these equations in terms of Om_r and Phi, but they are no longer homogeneous</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35835" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_v:=subs(r=R(v),u=t*(v-1),phidef)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEpcGhpZGVmX3ZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNiYtRiM2Ji1JJW1zdWJHRiQ2JS1GLDYlUSJERicvRjBGPUY5LUkjbW5HRiQ2JFEiMkYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GX28tSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYlUSNPbUYnRi9GMi8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjlGOUY5RltvLUZibzYkLUYjNiktRiM2Ji1GLDYlUSJSRidGL0YyRltvLUZibzYkLUYjNictRiw2JVEidkYnRi9GMkZpb0ZccEZfcEY5RjlGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRl5vL0ZOUSwwLjMzMzMzMzNlbUYnLUYjNiYtRiw2JVEidEYnRi9GMi1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRl5vRmBvLUZibzYkLUYjNiZGXnEtRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZnci1GZW42JFEiMUYnRjlGOUY5RjlGaW9GXHBGX3BGOUY5RjktRjY2LVEpJmVxdWFscztGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkmbWZyYWNHRiQ2KC1GIzYmLUYjNiZGZm9GW29GYXBGOUZjci1GIzYmLUYsNiVRJiZQaGk7RidGWUY5RltvRmFwRjlGOUZncS8lLmxpbmV0aGlja25lc3NHRltzLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl90LyUpYmV2ZWxsZWRHRj1GOQ==">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlwaGlkZWZfdkdGKC8tLSZJIkRHRiU2IyIiIzYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ2R0YoKiZJInRHRigiIiIsJkY7Rj5GPiEiIkY+KigsJi1GNkY3Rj4tSSRQaGlHRihGN0ZARj5GPUZARj9GQDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35836" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv1_phi:=collect(subs(phidef_v,Om(R(v), t*(v - 1))=t,idv[1]),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlpZHYxX3BoaUdGKCwoKiYtLSZJIkRHRiU2IyIiIjYjSSNPbUdGKDYkLUkiUkdGKDYjSSJ2R0YoKiZJInRHRihGNSwmRjxGNUY1ISIiRjVGNS1JJWRpZmZHRiY2JEY5RjxGNUY1KiZGP0ZALUkkUGhpR0YoRjhGNUZAKiZGPkY1Rj9GQEY1NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35840" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv2_phi:=collect(subs(phidef_v,Om(R(t), t*(v - 1))=t,subs(r=R(v),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}),idv[2]),
[Om,Phi],factor): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy0tJkkiREdGJTYjRjY2I0kjT21HRihGMTcjPClGLUYuRi9GMkY5LUY6NiRGOUYuRkI=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35855" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Compare both equations between Phi and Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35852" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(idv1_phi, Phi(R(v), t*(v - 1))),idv2_phi))): nops(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjNTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiNe</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35857" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(res)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KEkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy0tJkkiREdGJTYjIiIiNiNJI09tR0YoNiRGLyomRi1GQCwmRi5GQEZAISIiRkA3IzwoRi1GLkYvRjItRjM2JEYyRi5GOw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35844" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(coeff(res,D[1](Om)(R(v), t*(v - 1)))):
factor(series(subs(R(v)=R0ser,%),t,7))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiIiIiMiIiUsJiomIiNBIiIiSSJ2R0YkRiohIiIiI1NGLCIiJiwoKiYiIz9GKilGK0YlRipGKiomIiQ3IkYqRitGKkYqIiQhPkYqIiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35879" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">This is non-zero. So we need to use the third derivative as well.</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35903" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(idv[3])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8L0kidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JEYvKiZGLUZFLCZGLkZFRkUhIiJGRS0tJkZDNiRGRUZFRkZGSC0tJkZDNiRGRUY6RkZGSC0tJkZDNiVGRUZFRkVGRkZILS0mRkM2JUZFRkVGOkZGRkgtLSZGQzYlRkVGOkY6RkZGSC0tJkZDNiVGOkY6RjpGRkZINyM8L0YtRi5GL0YyLUYzNiRGMkYuLUYzNiRGYG9GLkZARkxGUEZURlhGZm5Gam4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35876" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">It is faster to differentiate idv2_phi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35894" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">diff(idv2_phi,v): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8LkkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy1GOjYkRjItRj82JEYuIiIkLS0mSSJER0YlNiNGNjYjSSNPbUdGKEYxLS1GSTYjRjBGMS0tJkZKNiNGQUZQRjEtLSZGSjYkRjZGNkZMRjEtLSZGSjYkRjZGQUZMRjE3IzwuRi1GLkYvRjJGOS1GOjYkRjlGLi1GOjYkRmluRi5GR0ZORlFGVUZZ</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35874" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv3_phi:=collect(subs(phidef_v,Om(R(t), t*(v - 1))=t,subs(r=R(v),u=t*(v-1),{ed11_phi, ed22_phi,ed12_phi}), diff(idv2_phi,v)),[Om,Phi],factor):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35892" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8LEkidEdGKEkidkdGKC1JJFBoaUdGKDYkLUkiUkdGKDYjRi4qJkYtIiIiLCZGLkY2RjYhIiJGNkYyLUklZGlmZkdGJjYkRjJGLi1GOjYkRjItSSIkR0YmNiRGLiIiIy1GOjYkRjItRj82JEYuIiIkLS0mSSJER0YlNiNGNjYjSSNPbUdGKEYxLS1GSTYjRjBGMS0tJkZKNiNGQUZQRjE3IzwsRi1GLkYvRjJGOS1GOjYkRjlGLi1GOjYkRldGLkZHRk5GUQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36032" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">phidef_v</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIjNiNJI09tR0YqNiQtSSJSR0YqNiNJInZHRioqJkkidEdGKiIiIiwmRjNGNkY2ISIiRjYqKCwmLUYuRi9GNi1JJFBoaUdGKkYvRjhGNkY1RjhGN0Y4</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L36034" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res_bis:=numer(factor(subs(subs(r=R(v),u=t*(v-1),{ed1_Phi, ed2_Phi}),isolate(idv1_phi, Phi(R(v), t*(v - 1))),idv3_phi))):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36036" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KUkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JEYvKiZGLUZFLCZGLkZFRkUhIiJGRTcjPClGLUYuRi9GMi1GMzYkRjJGLi1GMzYkRk5GLkZA</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L36043" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we have two expressions for Om_r</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36045" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eda:=numer(factor(subs(isolate(res,D[1](Om)(R(v), t*(v - 1))),res_bis))): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiNUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36030" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eda)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8KEkidEdGKEkidkdGKC1JIlJHRig2I0YuLUklZGlmZkdGJjYkRi9GLi1GMzYkRi8tSSIkR0YmNiRGLiIiIy1GMzYkRi8tRjg2JEYuIiIkNyM8KEYtRi5GL0YyLUYzNiRGMkYuLUYzNiRGQkYu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36039" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,eda),i=1..5)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM3JzwiPCNJInRHRig8JEkidkdGKC1JIlJHRig2I0YxPCVGL0YxRjI8KEYvRjFGMi1JJWRpZmZHRiY2JEYyRjEtRjg2JEYyLUkiJEdGJjYkRjEiIiMtRjg2JEYyLUY9NiRGMSIiJDcjNydGLUYuRjBGNTwoRi9GMUYyRjctRjg2JEY3RjEtRjg2JEZIRjE=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36056" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edb:=op(5,eda):nops(%);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkMjg2RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQnRw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36058" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRv:=collect(convert(edb,D),R,factor):</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36051" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36054" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(eval(subs(R(v)=R1ser,convert(edRv,diff))),t,15))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36021" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L36028" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35899" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L36077" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36048" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">t-Derivatives of Q1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35990" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write (Q1+v)t^2=Lambda(R,t(v-1)). 
Note that Maple claims that binomial(-1,0)=1 (this term is obtained for k=n=0), hence the term -r below</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36055" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">binomial(-1,0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36065" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambda_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(3*n +2* k-1, 2*n+k)*u^k*r^(n + 1)/(n + 1), k = 0 .. N - n - 1), n = 0 .. N - 1) -r
;end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35987" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambda_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJiIjNSIiIilJInJHNiIiIiRGJUYlKigiIzdGJSlGJyIiI0YlSSJ1R0YoRiVGJSooRilGJUYnRiUpRi5GLUYlRiUqJEYsRiVGJSomRidGJUYuRiVGJQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35917" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font bold="true">The series Lambda and Lambda_hat</Font></Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35953" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Link with our series Omega: now we are in the 4D vector space spanned by 1, Om, Om_r, Om_u</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35912" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=100*r,[1, Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Lambda_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NycsJComIiIkIiIiSSJyRzYiRiZGJiwmKiYiJCspRiZGJ0YmRiYiIiMhIiIsJComRidGJiwmKiYiJSs3RiZGJ0YmRiZGJkYmRiZGLSwkKiZGJ0YmLCYqJiImKyspRiZGJ0YmRiYiJC4jRi1GJkYtIiIn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35928" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:
factor(hermite_pade(subs(u=u*r,[1, Omega_d(N,0,0), Omega_d(N,1,0),Omega_d(N,0,1),Lambda_ser(N)]),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NycsJComIiIkIiIiSSJyRzYiRiZGJiwmKigiIilGJkYnRiZJInVHRihGJkYmIiIjISIiLCQqJkYnRiYsJiooIiM3RiZGJ0YmRixGJkYmRiZGJkYmRi4sJComRidGJiwoKihGK0YmRidGJilGLEYtRiZGJiomRi1GJkYsRiZGLkYlRi5GJkYuIiIn</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35935" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We prefer to work in 2 dimensions: here's a new Lambda, called Lambda_hat, living in a 2D space</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35910" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambdah_ser:=proc(N)
local k, n;
add(add(binomial(2*n, n)*binomial(2*n + k, k)*binomial(3*n + 2*k-1, 2*n+k)*u^k*r^(n + 1)/(n + 1), k = 0 .. N - n - 1), n = 0 .. N - 1) -r
+r/2*(1+Omega_ser(N+1)/u)
;end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35932" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lambdah_ser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJiIjNSIiIilJInJHNiIiIiRGJUYlKigiIzdGJUkidUdGKEYlKUYnIiIjRiVGJSooRilGJUYnRiUpRixGLkYlRiUqJEYtRiVGJSomRidGJUYsRiVGJSooI0YlRi5GJUYnRiUsJkYlRiUqJiw2KiYiJD8lRiUpRiciIiVGJUYlKigiJGcmRiVGJkYlRixGJUYlKigiJDUjRiVGLUYlRjBGJUYlKigiIz9GJUYnRiUpRixGKUYlRiUqJiIjSUYlRiZGJUYlKihGREYlRi1GJUYsRiVGJSooIiInRiVGJ0YlRjBGJUYlKiZGKUYlRi1GJUYlKihGLkYlRidGJUYsRiVGJUYnRiVGJUYsISIiRiVGJUYl</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35960" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we can work in the 2D space generated by Phi and Om_r.</Text-field><Text-field style="Text" layout="Normal">Here are equations for Lambda_hat and its first derivatives</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35951" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed5:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),u*Lambdah_ser(N)])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkNUdGKDclLCQqJkkickdGKCIiIiwoKigiIilGMkYxRjIpSSJ1R0YoIiIjRjJGMiomRjhGMkY3RjIhIiIiIiRGOkYyRjoqKEY3RjIpRjFGOEYyLCYqKCIjN0YyRjFGMkY3RjJGMkYyRjJGMiEiJzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35931" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed5:=convert(map(factor,subs(u=u/r,coed5[1])*Phi(r,u) + subs(u=u/r,coed5[2])*diff(Om(r,u),r) +subs(u=u/r,coed5[3])*u*Lah(r,u) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDVHRigsKComLCgqJiIiKSIiIilJInVHRigiIiNGMyEiIiomIiIkRjNJInJHRihGM0YzKiZGNkYzRjVGM0YzRjMtSSRQaGlHRig2JEY6RjVGM0YzKipGNUYzRjpGMywmKiYiIzdGM0Y1RjNGM0YzRjNGMy0tJkkiREdGJTYjRjM2I0kjT21HRihGPkYzRjMqKCIiJ0YzRjVGMy1JJExhaEdGKEY+RjNGNzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35938" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35926" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed5,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35937" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_0:=collect(isolate(ed5,Lah(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF8wR0YoLy1JJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKiMiIiIiIidGN0YyRjcsJiomIiM3RjdGM0Y3RjdGN0Y3RjctLSZJIkRHRiU2I0Y3NiNJI09tR0YoRjFGN0Y3KipGNkY3LCgqJiIiKUY3KUYzIiIjRjchIiIqJiIiJEY3RjJGN0Y3KiZGSEY3RjNGN0Y3RjctSSRQaGlHRihGMUY3RjNGSUY3NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35929" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed6:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),normal(u*diff(Lambdah_ser(N+2),r))])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkNkdGKDclISIiLCQqJkkickdGKCIiIiwmSSJ1R0YoRjNGM0YzRjNGLyIiIzcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35944" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed6:=convert(map(factor,subs(u=u/r,coed6[1])*Phi(r,u) + subs(u=u/r,coed6[2])*diff(Om(r,u),r) +subs(u=u/r,coed6[3])*u*diff(Lah(r,u),r) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDZHRigsKC1JJFBoaUdGKDYkSSJyR0YoSSJ1R0YoISIiKiYsJkYzIiIiRjJGN0Y3LS0mSSJER0YlNiNGNzYjSSNPbUdGKEYxRjdGNCooIiIjRjdGM0Y3LS1GOjYjSSRMYWhHRihGMUY3Rjc3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35933" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=30:
coed7:=factor(hermite_pade(normal(subs(u=u*r,[Phi_ser(N), Omega_d(N,1,0),normal(u^2*diff(Lambdah_ser(N+2),u))])),r,N-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZjb2VkN0dGKDclKiZJInJHRigiIiIsJiooIiIlRjFGMEYxKUkidUdGKCIiI0YxRjFGMUYxRjEsJCooIiInRjFGNUYxKUYwIiIkRjEhIiJGNzcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35911" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ed7:=convert(map(factor,subs(u=u/r,coed7[1])*Phi(r,u) + subs(u=u/r,coed7[2])*diff(Om(r,u),r) +subs(u=u/r,coed7[3])*u^2*diff(Lah(r,u),u) ),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlZDdHRigsKComLCYqJiIiJSIiIilJInVHRigiIiNGM0YzSSJyR0YoRjNGMy1JJFBoaUdGKDYkRjdGNUYzRjMqKiIiJ0YzRjdGM0Y0RjMtLSZJIkRHRiU2I0YzNiNJI09tR0YoRjpGMyEiIiooRjZGM0Y0RjMtLSZGQDYjRjY2I0kkTGFoR0YoRjpGM0YzNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35946" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35930" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed6,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35956" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: factor(mtaylor(numer(eval(subs(Om(r,u)=Omega_ser(N),Phi(r,u)=Phi_ser(N), Lah(r,u)=Lambdah_ser(N),convert(ed7,diff)))),[r,u],N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35958" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_r:=collect(isolate(ed6,D[1](Lah)(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF9yR0YoLy0tJkkiREdGJTYjIiIiNiNJJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKiNGNCIiI0Y0LCZGOUY0RjhGNEY0RjkhIiItLUYxNiNJI09tR0YoRjdGNEY0KihGPEY0LUkkUGhpR0YoRjdGNEY5Rj9GNDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35941" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_u:=collect(isolate(ed7,D[2](Lah)(r, u)),[Om,Phi])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlZExhaF91R0YoLy0tJkkiREdGJTYjIiIjNiNJJExhaEdGKDYkSSJyR0YoSSJ1R0YoLCYqKCIiJCIiIkY4Rj0tLSZGMjYjRj02I0kjT21HRihGN0Y9Rj0qKiNGPUY0Rj0sJiomIiIlRj0pRjlGNEY9Rj1GOEY9Rj0tSSRQaGlHRihGN0Y9RkkhIiJGTDcjRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L35921" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edLah_0;edLah_r;edLah_u</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJExhaEc2IjYkSSJyR0YlSSJ1R0YlLCYqKiMiIiIiIidGLEYnRiwsJiomIiM3RixGKEYsRixGLEYsRiwtLSZJIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YsNiNJI09tR0YlRiZGLEYsKipGK0YsLCgqJiIiKUYsKUYoIiIjRiwhIiIqJiIiJEYsRidGLEYsKiZGQEYsRihGLEYsRiwtSSRQaGlHRiVGJkYsRihGQUYs</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUYjNiYtRiM2Ji1JJW1zdWJHRiQ2JS1JI21pR0YkNiVRIkRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW5HRiQ2JFEiMUYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjkvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXLUkobWZlbmNlZEdGJDYkLUYjNictRjM2JVEkTGFoRicvRjdRJXRydWVGJy9GOlEnaXRhbGljRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGOEY5RjlGOUZDLUZlbjYkLUYjNiktRjM2JVEickYnRlxvRl5vLUZENi1RIixGJ0Y5RkcvRkpGXW9GS0ZNRk9GUUZTRlUvRllRLDAuMzMzMzMzM2VtRictRjM2JVEidUYnRlxvRl5vRmBvRmNvRmZvRjlGOUY5LUZENi1RKSZlcXVhbHM7RidGOUZHRklGS0ZNRk9GUUZTL0ZWUSwwLjI3Nzc3NzhlbUYnL0ZZRlxxLUYjNiYtSSZtZnJhY0dGJDYoLUYjNiYtRmVuNiQtRiM2JkZlcC1GRDYtUScmcGx1cztGJ0Y5RkdGSUZLRk1GT0ZRRlMvRlZRLDAuMjIyMjIyMmVtRicvRllGXXJGXHBGOUY5LUZENi1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RkdGSUZLRk1GT0ZRRlNGVUZYLUYjNiYtRiM2JkYvRkMtRmVuNiQtRiM2Jy1GMzYlUSNPbUYnRlxvRl5vRmBvRmNvRmZvRjlGOUY5RkNGaG9GOUY5LUYjNiYtRj02JFEiMkYnRjlGX3JGZXBGOS8lLmxpbmV0aGlja25lc3NHRj8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZnMvJSliZXZlbGxlZEdGOEZpcS1GYXE2KC1GIzYmLUYzNiVRJiZQaGk7RidGNkY5RkNGaG9GOUZdc0Zic0Zkc0Znc0Zpc0Y5Rjk=">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIiNiNJJExhaEdGKjYkSSJyR0YqSSJ1R0YqLCYqKiNGLCIiI0YsLCZGMUYsRjBGLEYsRjEhIiItLUYlNiNJI09tR0YqRi9GLEYsKihGNEYsLUkkUGhpR0YqRi9GLEYxRjdGLA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUYjNiYtRiM2Ji1JJW1zdWJHRiQ2JS1JI21pR0YkNiVRIkRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW5HRiQ2JFEiMkYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjkvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXLUkobWZlbmNlZEdGJDYkLUYjNictRjM2JVEkTGFoRicvRjdRJXRydWVGJy9GOlEnaXRhbGljRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGOEY5RjlGOUZDLUZlbjYkLUYjNiktRjM2JVEickYnRlxvRl5vLUZENi1RIixGJ0Y5RkcvRkpGXW9GS0ZNRk9GUUZTRlUvRllRLDAuMzMzMzMzM2VtRictRjM2JVEidUYnRlxvRl5vRmBvRmNvRmZvRjlGOUY5LUZENi1RKSZlcXVhbHM7RidGOUZHRklGS0ZNRk9GUUZTL0ZWUSwwLjI3Nzc3NzhlbUYnL0ZZRlxxLUYjNiYtRiM2KC1GPTYkUSIzRidGOS1GRDYtUTEmSW52aXNpYmxlVGltZXM7RidGOUZHRklGS0ZNRk9GUUZTRlVGWEZccEZlcS1GIzYmLUYjNiYtRjA2JUYyLUY9NiRRIjFGJ0Y5RkBGQy1GZW42JC1GIzYnLUYzNiVRI09tRidGXG9GXm9GYG9GY29GZm9GOUY5RjlGQ0Zob0Y5RjktRkQ2LVEoJm1pbnVzO0YnRjlGR0ZJRktGTUZPRlFGUy9GVlEsMC4yMjIyMjIyZW1GJy9GWUZccy1JJm1mcmFjR0YkNigtRiM2Ji1GZW42JC1GIzYmLUYjNiYtRj02JFEiNEYnRjlGZXEtSSVtc3VwR0YkNiVGZXBGPC8lMXN1cGVyc2NyaXB0c2hpZnRHRkJGOS1GRDYtUScmcGx1cztGJ0Y5RkdGSUZLRk1GT0ZRRlNGW3NGXXNGXHBGOUY5RmVxLUYjNiYtRjM2JVEmJlBoaTtGJ0Y2RjlGQ0Zob0Y5RjktRiM2JkY8RmVxRlx0RjkvJS5saW5ldGhpY2tuZXNzR0Zgci8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZfdS8lKWJldmVsbGVkR0Y4RjlGOQ==">Ly0tJkkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIjNiNJJExhaEdGKjYkSSJyR0YqSSJ1R0YqLCYqKCIiJCIiIkYwRjUtLSZGJjYjRjU2I0kjT21HRipGL0Y1RjUqKiNGNUYsRjUsJiomIiIlRjUpRjFGLEY1RjVGMEY1RjUtSSRQaGlHRipGL0Y1RkEhIiJGRA==</Equation></Text-field>
</Output>
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<Input><Text-field style="Text" layout="Normal">Now let's get back to the variables t and v</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L36071" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh_def:=Lh(t)=Lah(R(t),t*(v-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdMaF9kZWZHRigvLUkjTGhHRig2I0kidEdGKC1JJExhaEdGKDYkLUkiUkdGKEYxKiZGMiIiIiwmSSJ2R0YoRjlGOSEiIkY5NyNGLg==</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">id1_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJiomLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidEdGKComRjpGMywmSSJ2R0YoRjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomRjpGPi1JJFBoaUdGKEY2RjNGPkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35963" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh_phi:=collect(subs(subs(r=R(t),u=t*(v-1),edLah_0),isolate(id1_phi, D[1](Om)(R(t), t*(v - 1))),Lh_def),Phi)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdMaF9waGlHRigvLUkjTGhHRig2I0kidEdGKComLCYqLCMiIiIiIidGNy1JIlJHRihGMUY3LCYqKCIjN0Y3RjJGNywmSSJ2R0YoRjdGNyEiIkY3RjdGN0Y3RjdGMkZALUklZGlmZkdGJjYkRjlGMkZARjcqKkY2RjcsKCooIiIpRjcpRjIiIiNGNylGPkZJRjdGQComIiIkRjdGOUY3RjcqKEZJRjdGMkY3Rj5GN0Y3RjdGMkZARj5GQEY3RjctSSRQaGlHRig2JEY5KiZGMkY3Rj5GN0Y3NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35964" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dLh_phi:=collect(subs(subs(r=R(t),u=t*(v-1),{edLah_r,edLah_u}),isolate(id1_phi, D[1](Om)(R(t), t*(v - 1))),diff(Lh_def,t)),Phi)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShkTGhfcGhpR0YoLy1JJWRpZmZHRiY2JC1JI0xoR0YoNiNJInRHRihGNSomLCYqJiwmKiwjIiIiIiIjRjwsJiomRjVGPCwmSSJ2R0YoRjxGPCEiIkY8RjwtSSJSR0YoRjRGPEY8KUY1Rj1GQkZARkItRjA2JEZDRjVGQkY8KihGO0Y8RjVGQkZARkJGPEY8RkZGPEY8KiYsJioqIiIkRjxGQ0Y8RjVGQkZGRkJGPCoqRjtGPCwmKigiIiVGPEZFRjwpRkBGPUY8RjxGQ0Y8RjxGRUZCRlFGQkZCRjxGQEY8RjxGPC1JJFBoaUdGKDYkRkNGP0Y8NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35947" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The log derivative of L_hat</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35974" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dlog_Lh:=convert(factor(op(2,dLh_phi)/op(2,Lh_phi)),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35970" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dloh_Lh_u:=factor(subs(v=1+u/t,%));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpkbG9oX0xoX3VHRigsJCoqIiIkIiIiLCoqJiktLUkiREdGJTYjSSJSR0YoNiNJInRHRigiIiNGMSlGO0Y8RjFGMSoqIiIlRjEpSSJ1R0YoRjxGMUY1RjFGO0YxISIiKihGO0YxRjVGMUZBRjFGMSooIiInRjEtRjlGOkYxRkBGMUYxRjFGO0ZCLCwqKiIiKUYxRkBGMUY1RjFGO0YxRkIqKkYwRjFGRkYxRjVGMUY7RjFGMSoqRjxGMUY7RjFGNUYxRkFGMUYxKigiIzdGMUZGRjFGQEYxRjEqJkZGRjFGQUYxRjFGQkYxNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35976" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(numer(%/3),R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqKCIiJyIiIi1JIlJHNiI2I0kidEdGKEYlKUkidUdGKCIiI0YlRiUqJiktLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKDYjRidGKUYtRiUpRipGLUYlRiUqKkYqRiVGLEYlLCYqJiIiJUYlRixGJUYlRiUhIiJGJUYwRiVGPA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35979" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">collect(denom(%%*t),R,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiwmKigiIiQiIiJJInRHNiJGJy0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiNJIlJHRik2I0YoRidGJyomSSJ1R0YpRicsJiomIiM3RidGNEYnRidGJ0YnRidGJ0YnLUYxRjJGJ0YnKiwiIiNGJ0YoRidGNEYnLCYqJiIiJUYnRjRGJ0YnRichIiJGJ0YqRidGPg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35832" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we can write 3 equations between L, L', L'' and L''' and R and R' (using the second order DE for R)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35834" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35967" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e1:=collect(convert(numer(eval(subs(Lh(t)=L(t)+v*R(t)/2/(v-1),diff(Lh(t),t)/Lh(t))-dlog_Lh)),D),L,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35968" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(e1); e1:=collect(op(3,%),L,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2KC1JI21uR0YkNiRRIjJGJ0YvLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVGUC1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GSTYkUSIxRidGL0YvRi9GSC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGTC1GVjYkLUYjNlotRiM2Ki1GSTYkUSI4RidGL0ZMLUYjNiYtRiM2Ji1GZW42JVEiREYnL0ZpbkY0Ri8tRiw2LVEwJkFwcGx5RnVuY3Rpb247RidGL0YyRjVGN0Y5RjtGPUY/Rk9GUS1GVjYkLUYjNictRmVuNiVRIlJGJ0ZobkZbby8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y0Ri9GL0YvRmdwLUZWNiQtRiM2Jy1GZW42JVEidEYnRmhuRltvRmFxRmRxRmdxRi9GL0YvRkwtRiM2Ji1GIzYmRmNwRmdwLUZWNiQtRiM2Jy1GZW42JVEiTEYnRmhuRltvRmFxRmRxRmdxRi9GL0YvRmdwRmlxRi9GTC1GUzYlRl1yRkhGY29GL0Zdby1GIzYqLUZJNiRRIjNGJ0YvRkxGX3BGTC1GIzYmRl5xRmdwRmlxRi9GTEZgckYvLUYsNi1RJyZwbHVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRiM2KkZIRkxGX3BGTEZgckZMRl1yRi9GXW8tRiM2Ki1GSTYkUSMxMkYnRi9GTEZic0ZMRmByRkxGXXJGL0Zdby1GIzYoRmJzRkxGYHJGTEZaRi9GZHMtRiM2Ki1GSTYkUSMxOEYnRi9GTEZic0ZMLUYjNiZGaHJGZ3BGaXFGL0ZMLUZTNiVGWkZIRmNvRi9GZHMtRiM2KEZfcEZMRmJzRkxGWkYvRl1vLUYjNipGW3RGTEZfcEZMRmV0RkxGXXJGL0Zkcy1GIzYqRl9zRkxGX3BGTEZldEZMRlpGL0Zdby1GIzYqLUZJNiRRIzM2RidGL0ZMRmJzRkxGZXRGTEZaRi9GZHMtRiM2Ki1GSTYkUSI0RidGL0ZMLUZTNiVGX3BGSEZjb0ZMRltzRkxGZ3RGL0Zkcy1GIzYsRlxwRkxGX3BGTEZgckZMRltzRkxGZ3RGL0Zdby1GIzYqRmZ1RkxGaXVGTEZbc0ZMRlpGL0Zdby1GIzYsLUZJNiRRIzE2RidGL0ZMRl9wRkxGYHJGTEZbc0ZMRlpGL0Zdby1GIzYsRlt0RkxGYnNGTEZgckZMRl1yRkxGZ3RGL0Zdby1GIzYoRml1RkxGXXJGTEZaRi9GXW8tRiM2LEZIRkxGX3BGTEZgckZMRl1yRkxGWkYvRmRzLUYjNiwtRkk2JFEjMjRGJ0YvRkxGYnNGTEZgckZMRl1yRkxGWkYvRmRzLUYjNigtRkk2JFEiOUYnRi9GTC1GUzYlRmJzRkhGY29GTEZndEYvRl1vLUYjNihGYXdGTEZkd0ZMRlpGL0Zdby1GIzYsRlt0RkxGX3BGTEZic0ZMRl1yRkxGZ3RGL0Zdby1GIzYsRlt0RkxGX3BGTEZldEZMRl1yRkxGZ3RGL0Zkcy1GIzYsRlt0RkxGX3BGTEZic0ZMRl1yRkxGWkYvRmRzLUYjNixGXHdGTEZfcEZMRmV0RkxGXXJGTEZaRi9GZHMtRiM2KEZfc0ZMRml1RkxGZXRGL0Zdby1GIzYoRl9zRkxGX3BGTEZldEYvRmRzLUYjNihGYnRGTEZic0ZMRmV0Ri9GZHMtRiM2JkZic0ZMRmByRi9GL0YvRi9GLw==">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35847" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(e1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PChJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKA==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L35845" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">edRt</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35851" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e2:=numer(factor(subs(isolate(edRt,(D@@2)(R)(t)),factor(convert(diff(e1,t),D))))): nops(%); indets(e2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkMzI1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiREJA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35837" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">e3:=numer(factor(subs(isolate(edRt,(D@@2)(R)(t)),factor(convert(diff(e2,t),D))))): nops(%); indets(e3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFElMTk0N0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiVaPg==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCpJInRHNiJJInZHRiQtSSJMR0YkNiNGIy1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tLUY4NiRGLSIiJEYxRig=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L35839" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now we eliminate R and R' between these three equations to obtain a DE of third order for L</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35841" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(D(R)(t)=dR,R(t)=R,(D@@3)(L)(t)=L3, (D@@2)(L)(t)=L2,D(L)(t)=L1, L(t)=L,[e1,e2,e3]):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35830" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eqs)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCpJIkxHNiJJI0wxR0YkSSNMMkdGJEkjTDNHRiRJIlJHRiRJI2RSR0YkSSJ0R0YkSSJ2R0Yk</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35858" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(degree,eqs,R); map(degree,eqs,dR); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUiIiMiIiUiIig=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUiIiMiIiUiIic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35853" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res1:=factor(resultant(eqs[1],eqs[2],dR)): nops(res1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiN0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIo</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35856" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,res1),i=1..nops(res1))])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Nyk8IjwjSSJSRzYiPCNJInZHRiY8JUYlSSJ0R0YmRig8JUkiTEdGJkYqRig8JUYsRiVGKDwoRixJI0wxR0YmSSNMMkdGJkYlRipGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35860" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser:=proc(N) factor(series(t^2*(v+subs(omega=1,Qser(N))),t,N+1)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35884" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser(6)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiJJInZHRiQiIiMqJkYlIiIiLCZGJUYoIiIkRihGKEYqKihGJUYoLCZGJUYoIiInRihGKCwmKiZGJkYoRiVGKEYoRipGKEYoIiIlKihGJUYoLCZGJUYoRihGKEYoLCgqJiIiJkYoKUYlRiZGKEYoKiYiI2hGKEYlRihGKCIkTiJGKEYoRjUqJkYlRigsLComIiM5RigpRiVGMEYoRigqJiIkeiNGKClGJUYqRihGKComIiVfOUYoRjZGKEYoKiYiJWJDRihGJUYoRigiJU02RihGKEYtLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35867" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=3:factor(series(subs(R=R1ser, L=Lser(N),op(4,res1)),t,N+1));
factor(series(subs(R=R1ser, L=Lser(N),op(5,res1)),t,N+1));
factor(series(subs(R=R1ser, L=Lser(N),op(6,res1)),t,N+1));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInRHNiIqJClJInZHRiQiIiMiIiJGKCwkKigiIiVGKUYmRiksJiomRixGKUYnRilGKSIjNkYpRikhIiIiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKUYs</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiIsJEkidkdGJCEiIiIiIiomRiZGKCwmKiYiIiVGKEYmRihGKEYoRidGKCIiIywkKigiIiRGKEYmRigsJkYmRihGMEYoRihGKEYwLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGLA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInRHNiJJInZHRiQiIiIsJComIiIkRiZGJUYmISIiIiIjLCQqKCIiJUYmRiVGJiwmRiVGJkYrRiZGJkYqRiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJkYu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35893" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8:factor(series(subs(R=R1ser, L=Lser(N),L1=diff(Lser(N+1),t),L2=diff(Lser(N+2),t$2),L3=diff(Lser(N+3),t$3),op(7,res1)),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35869" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res2:=op(7,res1): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNjU2RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiRjJw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35877" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res3:=factor(resultant(eqs[1],eqs[3],dR)): nops(res3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiNkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35880" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(indets,[seq(op(i,res3),i=1..nops(res3))])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Nyg8IjwlSSJMRzYiSSJ0R0YmSSJ2R0YmPCNJIlJHRiY8I0YoPCVGKkYnRig8KUYlSSNMMUdGJkkjTDJHRiZJI0wzR0YmRipGJ0Yo</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35882" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res4:=op(6,res3): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEmMjY3NjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiZpbiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35901" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10:factor(series(subs(R=R1ser, L=Lser(N),L1=diff(Lser(N+1),t),L2=diff(Lser(N+2),t$2),L3=diff(Lser(N+3),t$3),res4),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L35888" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35895" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">It remains to eliminate R between res2 and res4 - but this is too big.</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35875" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res5:=factor(resultant(res2,res4,R)): nops(res5):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L35871" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Let us try with Gr\303\266bner bases ; or for specific values of v. But later!</Font></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36037" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L35914" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36075" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="presentation" inline-output="false" labelreference="L36072" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L36001" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35942" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L35936" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">v-Derivatives of Q1</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L35965" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We write (Q1+v)t^2=Lambda(R,t(v-1)). </Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L35905" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lhv_def:=Lh(v)=Lah(R(v),t*(v-1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShMaHZfZGVmR0YoLy1JI0xoR0YoNiNJInZHRigtSSRMYWhHRig2JC1JIlJHRihGMSomSSJ0R0YoIiIiLCZGMkY6RjohIiJGOjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36023" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">idv1_phi</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsKComLS0mSSJER0YlNiMiIiI2I0kjT21HRig2JC1JIlJHRig2I0kidkdGKComSSJ0R0YoRjMsJkY6RjNGMyEiIkYzRjMtSSVkaWZmR0YmNiRGN0Y6RjNGMyomRj1GPi1JJFBoaUdGKEY2RjNGPiomRjxGM0Y9Rj5GM0Yr</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35907" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lhv_phi:=convert(collect(subs(subs(r=R(v),u=t*(v-1),edLah_0),isolate(idv1_phi, D[1](Om)(R(v), t*(v - 1))),Lhv_def),Phi),D)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShMaHZfcGhpR0YoLy1JI0xoR0YoNiNJInZHRigsJiomLCYqLCMiIiIiIidGOC1JIlJHRihGMUY4LCYqKCIjN0Y4SSJ0R0YoRjgsJkYyRjhGOCEiIkY4RjhGOEY4RjhGQEZBLS1JIkRHRiU2I0Y7RjFGQUY4KipGN0Y4LCgqKCIiKUY4KUY/IiIjRjgpRkBGS0Y4RkEqJiIiJEY4RjpGOEY4KihGS0Y4Rj9GOEZARjhGOEY4Rj9GQUZARkFGOEY4LUkkUGhpR0YoNiRGOiomRj9GOEZARjhGOEY4Ki5GN0Y4RjpGOEY8RjhGP0Y4RkBGQUZCRkFGQTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36017" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36019" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lh1v_phi:=convert(map(Z-&gt;map(factor,Z),collect(subs(subs(u=t*(v-1),r=R(v),{ed1_Phi,ed2_Phi}),isolate(idv1_phi, D[1](Om)(R(v), t*(v - 1))), diff(Lhv_phi,v)),Phi)),D): indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYzLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JVEidkYnRjJGNUY4LUYsNiYtRi82JVEmJlBoaTtGJy9GM0ZARjwtRjk2LVEwJkFwcGx5RnVuY3Rpb247RidGPEY+L0ZCRkBGQ0ZFRkdGSUZLRk0vRlFGTy1GIzYkLUYsNiktRiw2Ji1GLzYlUSJSRidGMkY1RmZuLUYjNiQtRiw2J0ZTLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkBGPEY8RjxGOC1GLDYmRi4tRjk2LVExJkludmlzaWJsZVRpbWVzO0YnRjxGPkZpbkZDRkVGR0ZJRktGTUZqbi1GIzYkLUYsNiZGUy1GOTYtUSgmbWludXM7RidGPEY+RmluRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZdcS1JI21uR0YkNiRRIjFGJ0Y8RjxGPEY8RmhvRltwRl5wRjxGPEY8RjhGX29GOC1GLDYmLUYsNiYtRi82JVEiREYnRmVuRjxGZm4tRiM2JC1GLDYnLUYvNiVRI0xoRidGMkY1RmhvRltwRl5wRjxGPEY8RmZuRmRvRjxGOC1GLDYmLUYsNiZGZ3FGZm4tRiM2JC1GLDYnRmFvRmhvRltwRl5wRjxGPEY8RmZuRmRvRjxGOC1GLDYmLUYsNiYtSSVtc3VwR0YkNiZGZ3EtRiM2JC1GLDYnLUZgcTYkUSIyRidGPEZob0ZbcEZecEY8RjwvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnL0krbXNlbWFudGljc0dGJFEjQEBGJ0ZmbkZlckY8RmZuRmRvRjxGaG9GW3BGXnBGPEY8LyUlb3BlbkdRJyZsY3ViO0YnLyUmY2xvc2VHUScmcmN1YjtGJw==">PClJInRHNiJJInZHRiQtSSRQaGlHRiQ2JC1JIlJHRiQ2I0YlKiZGIyIiIiwmRiVGLUYtISIiRi1GKS0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJI0xoR0YkRistLUYyNiNGKkYrLS0tSSNAQEdGMzYkRjIiIiNGOkYr</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L36022" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">An equation without Phi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36029" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=numer(factor(subs(isolate(Lhv_phi,Phi(R(v), t*(v - 1))),op(2,Lh1v_phi)-D(Lh)(v)))): nops(%) ; indets(%%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkNDY2RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiRtJQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSNMaEdGJDYjRiUtSSJSR0YkRigtLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRidGKC0tRi02I0YqRigtLS1JI0BAR0YuNiRGLSIiI0Y0Rig=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36010" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36011" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev1:=factor(convert(numer(eval(subs(Lh(v)=L(v)+v*R(v)/2/(v-1),convert(res,diff)))),D)): nops(factor(ev1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36007" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(1,ev1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUklbXJvd0dGJDYmLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGUi1JI21uR0YkNiRRIjFGJ0Y/Rj9GPy1GVjYkUSI0RidGPy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=">KiQpLCZJInZHNiIiIiJGJyEiIiIiJUYn</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36008" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev1:=op(2,ev1): nops(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEkMzA5RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">IiQ0JA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36004" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(ev1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PClJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjRGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36044" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(edRv)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PChJInRHNiJJInZHRiQtSSJSR0YkNiNGJS0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS0tSSNAQEdGLDYkRisiIiNGL0YoLS0tRjM2JEYrIiIkRi9GKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36003" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev2:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev1,v),D))))): nops(%); indets(ev2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFElMjAwN0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiUyPw==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDY1LUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82JVEidkYnRjJGNUY4LUYsNiYtRi82JVEiTEYnRjJGNS1GOTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y8Rj4vRkJGQEZDRkVGR0ZJRktGTS9GUUZPLUYjNiQtRiw2J0ZTLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkBGPEY8RjxGOC1GLDYmLUYvNiVRIlJGJ0YyRjVGZW5Gam5GPEY4LUYsNiYtRiw2Ji1GLzYlUSJERicvRjNGQEY8RmVuLUYjNiQtRiw2J0ZYRl5vRmFvRmRvRjxGPEY8RmVuRmpuRjxGOC1GLDYmLUYsNiZGX3BGZW4tRiM2JC1GLDYnRmhvRl5vRmFvRmRvRjxGPEY8RmVuRmpuRjxGOC1GLDYmLUYsNiYtSSVtc3VwR0YkNiZGX3AtRiM2JC1GLDYnLUkjbW5HRiQ2JFEiMkYnRjxGXm9GYW9GZG9GPEY8LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRI0BARidGZW5GY3BGPEZlbkZqbkY8RjgtRiw2Ji1GLDYmRmNxRmVuRltxRjxGZW5Gam5GPEZeb0Zhb0Zkb0Y8RjwvJSVvcGVuR1EnJmxjdWI7RicvJSZjbG9zZUdRJyZyY3ViO0Yn">PCpJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYo</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35924" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev3:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev2,v),D))))): nops(%); indets(ev3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEmMTk0MDlGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiY0JT4=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCtJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYoLS0tRjg2JEYtIiIkRjFGKA==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L36006" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ev4:=numer(factor(subs(isolate(edRv,(D@@3)(R)(v)),factor(convert(diff(ev3,v),D))))): nops(%); indets(ev4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEmOTU2NjBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiZnYyo=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCxJInRHNiJJInZHRiQtSSJMR0YkNiNGJS1JIlJHRiRGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJ0YoLS1GLTYjRipGKC0tLUkjQEBHRi42JEYtIiIjRjFGKC0tRjdGNEYoLS0tRjg2JEYtIiIkRjFGKC0tLUY4NiRGLSIiJUYxRig=</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L36033" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now if we could eliminate R , R' and R'' between these four equations we would obtain a DE of fourth order for L</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36031" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqsv:=subs((D@@2)(R)(v)=d2R, D(R)(v)=dR,R(v)=R,(D@@4)(L)(v)=L4,(D@@3)(L)(v)=L3, (D@@2)(L)(v)=L2,D(L)(v)=L1, L(v)=L,[ev1,ev2,ev3,ev4]):</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36026" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">indets(eqsv)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCxJIkxHNiJJI0wxR0YkSSNMMkdGJEkjTDNHRiRJI0w0R0YkSSJSR0YkSSRkMlJHRiRJI2RSR0YkSSJ0R0YkSSJ2R0Yk</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L36000" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(degree,eqsv,R); map(degree,eqsv,dR);  map(degree,eqsv,d2R); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDYtLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYvNiRRIjZGJ0YyRjUtRi82JFEjMTBGJ0YyRjUtRi82JFEjMTVGJ0YyLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjtGMkYyLyUlb3BlbkdRJyZsc3FiO0YnLyUmY2xvc2VHUScmcnNxYjtGJw==">NyYiIiUiIiciIzUiIzo=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYiIiQiIiciIioiIzc=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYiIiIiIiMiIiQiIiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36038" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Lser(6)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiJJInZHRiQiIiMqJkYlIiIiLCZGJUYoIiIkRihGKEYqKihGJUYoLCZGJUYoIiInRihGKCwmKiZGJkYoRiVGKEYoRipGKEYoIiIlKihGJUYoLCZGJUYoRihGKEYoLCgqJiIiJkYoKUYlRiZGKEYoKiYiI2hGKEYlRihGKCIkTiJGKEYoRjUqJkYlRigsLComIiM5RigpRiVGMEYoRigqJiIkeiNGKClGJUYqRihGKComIiVfOUYoRjZGKEYoKiYiJWJDRihGJUYoRigiJU02RihGKEYtLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35999" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R1ser, dR=diff(R1ser,v), d2R=diff(R1ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[1]),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35922" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R1ser, dR=diff(R1ser,v), d2R=diff(R1ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[2]),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R1ser, dR=diff(R1ser,v), d2R=diff(R1ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[3]),t,N+1))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzs=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=12:factor(series(subs(R=R1ser, dR=diff(R1ser,v), d2R=diff(R1ser,v$2),L=Lser(N),L1=diff(Lser(N),v),L2=diff(Lser(N),v$2),L3=diff(Lser(N),v$3),L4=diff(Lser(N),v$4),eqsv[4]),t,N+1))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiI0A=</Equation></Text-field>
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<Group view="code" labelreference="L35918" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
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<Group view="code" labelreference="L35972" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L36067" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">Combinatorial interpretation in terms of trees</Text-field></Title><Presentation-Block>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqU:=-U+(x)*(t+U-U0)*(t*v+U-U0)+ (t+U-U0)/x</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcVVHRigsKEkiVUdGKCEiIiooSSJ4R0YoIiIiLChJInRHRihGM0YvRjNJI1UwR0YoRjBGMywoKiZGNUYzSSJ2R0YoRjNGM0YvRjNGNkYwRjNGMyomRjRGM0YyRjBGMzcjRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">res:=expand(subs(x=1/y,U=U0+y*M-t*v,eqU))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRyZXNHRigsNComKUkiTUdGKCIiIyIiIkkieUdGKEYzRjMqKEYxRjNJInRHRihGM0kidkdGKEYzISIiKiZGMUYzKUY0RjJGM0YzKihGNkYzRjdGM0Y0RjNGOComRjFGM0Y2RjNGMyomRjFGM0Y0RjNGOComRjZGM0Y3RjNGMyomRjZGM0Y0RjNGM0kjVTBHRihGODcjRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(%+U0-t)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKEkiTUc2IiIiIkkieUdGJUYmRiYhIiJGJiwoKiZGJEYmRidGJkYmKiZJInRHRiVGJkkidkdGJUYmRihGLEYmRiY=</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=5:factor(series(subs(M=subs(omega=1,x=y,Mser(N)),res),t,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIsJEkjVTBHRiQhIiIiIiEsJiomIiIjIiIiSSJ2R0YkRixGLEYsRixGKywoKiZGK0YsKUYtRitGLEYsKiYiIilGLEYtRixGLEYrRiwiIiQsKiomIiIlRiwpRi1GM0YsRiwqJiIjT0YsRjBGLEYsKiYiI2NGLEYtRixGLCIiKkYsRjYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGLCIiJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34361" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">U0ser:=series(%+U0,t,N+1)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZVMHNlckdGKCsrSSJ0R0YoLCYqJiIiIyIiIkkidkdGKEYzRjNGM0YzRjIsKComRjJGMylGNEYyRjNGMyomIiIpRjNGNEYzRjNGMkYzIiIkLCoqJiIiJUYzKUY0RjpGM0YzKiYiI09GM0Y3RjNGMyomIiNjRjNGNEYzRjMiIipGM0Y9LUkiT0dGJTYjRjMiIiY3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34364" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">User:=factor(series(subs(M=subs(omega=1,x=1/y,Mser(N)),1/y*M+U0ser-t*v),t,N+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVVc2VyR0YoKy1JInRHRigqJCwmIiIiISIiSSJ5R0YoRjJGM0YyKiYsNComSSJ2R0YoRjIpRjQiIiVGMkYyKiZGOEYyKUY0IiIkRjJGMyooIiIjRjJGOEYyKUY0Rj9GMkYzKiRGPEYyRjIqKEY6RjJGOEYyRjRGMkYyKiRGQEYyRjMqJkY/RjJGOEYyRjMqJkY/RjJGNEYyRjJGMkYzRjIpRjFGPUYzRj8qJixOKiYpRjhGP0YyKUY0IiIoRjJGMiooRjpGMkZKRjIpRjQiIidGMkYzKiZGOEYyRktGMkYyKihGTEYyRkpGMilGNCIiJkYyRjIqKEY/RjJGOEYyRk5GMkYzKigiIilGMkZKRjJGOUYyRjMqKEY9RjJGOEYyRlJGMkYyKigiIzVGMkZKRjJGPEYyRjIqKCIiKkYyRjhGMkY5RjJGMyomRj9GMkZSRjJGMiooIiM3RjJGSkYyRkBGMkYzKigiI0pGMkY4RjJGPEYyRjIqJEY5RjJGMyooRlZGMkZKRjJGNEYyRjIqKCIjW0YyRjhGMkZARjJGMyomRkxGMkY8RjJGMiomRj9GMkZKRjJGMyooIiNLRjJGOEYyRjRGMkYyKiZGaG5GMkZARjJGMyomRlZGMkY4RjJGMyomRlZGMkY0RjJGMkY/RjNGMilGMUZTRjNGPSomLF5wKiYpRjhGPUYyKUY0RllGMkYyKihGU0YyRmpvRjIpRjRGZW5GMkYzKihGPUYyRkpGMkZbcEYyRjIqKEZlbkYyRmpvRjIpRjRGVkYyRjIqKEZobkYyRkpGMkZdcEYyRjMqJkY4RjJGW3BGMkYyKihGPUYyRmpvRjJGS0YyRjMqKCIjOkYyRkpGMkZgcEYyRjIqJkY4RjJGXXBGMkYzKigiIztGMkZqb0YyRk5GMkYzKihGZXBGMkZKRjJGS0YyRjIqKEY9RjJGOEYyRmBwRjJGMyooIiNVRjJGam9GMkZSRjJGMiooIiMnKkYyRkpGMkZORjJGMyooIiNARjJGOEYyRktGMkYyKigiI3FGMkZqb0YyRjlGMkYzKigiJHojRjJGSkYyRlJGMkYyKigiI3VGMkY4RjJGTkYyRjMqJkZlbkYyRktGMkYyKigiIyMpRjJGam9GMkY8RjJGMiooIiRxJkYyRkpGMkY5RjJGMyooIiRDJEYyRjhGMkZSRjJGMiomRmVuRjJGTkYyRjMqKCIjZ0YyRmpvRjJGQEYyRjMqKCIkRShGMkZKRjJGPEYyRjIqKCIkQSlGMkY4RjJGOUYyRjMqJiIjWEYyRlJGMkYyKigiI0NGMkZqb0YyRjRGMkYyKigiJFMmRjJGSkYyRkBGMkYzKigiJTk2RjJGOEYyRjxGMkYyKiYiJEciRjJGOUYyRjMqJkY6RjJGam9GMkYzKigiJDsjRjJGSkYyRjRGMkYyKigiJFMpRjJGOEYyRkBGMkYzKiYiJHkiRjJGPEYyRjIqJiIjT0YyRkpGMkYzKigiJE8kRjJGOEYyRjRGMkYyKiYiJE4iRjJGQEYyRjMqJiIjY0YyRjhGMkYzKiYiI2FGMkY0RjJGMkZlbkYzRjIpRjFGTEYzRjotSSJPR0YlNiNGMkZTNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34363" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(coeff(User,t,1),y=infinity,3)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(coeff(User,t,2),y=infinity,5)</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(coeff(User,t,3),y=infinity,8)</Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">Predicted singular point (Prediction 5.4)</Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal">We want the discriminant to have a double root yc (we write u=t(v-1))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR1</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKCMiIiIiIiNGJSwmKiZJInlHNiJGJSwmRiVGJUYpISIiRiVGJSomSSJ0R0YqRiUsJkkidkdGKkYlRiVGLEYlRiVGJUYpRixGJSoqRiRGJSwmRihGJUYtRixGJUYpRiwpLCZGJUYlKioiIiVGJUYpRiVJIlJHRipGJSlGMkYmRixGLEYkRiVGLA==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">R1ser := t + (-2*v - 1)*t^2 + (-2*v^2 - 8*v - 2)*t^3 + (-4*v^3 - 36*v^2 - 56*v - 9)*t^4 + (-10*v^4 - 152*v^3 - 524*v^2 - 466*v - 54)*t^5 + (-28*v^5 - 628*v^4 - 3648*v^3 - 7088*v^2 - 4232*v - 378)*t^6 + (-84*v^6 - 2568*v^5 - 22020*v^4 - 71760*v^3 - 92532*v^2 - 40536*v - 2916)*t^7 + (-264*v^7 - 10440*v^6 - 122160*v^5 - 586560*v^4 - 1262856*v^3 - 1183536*v^2 - 402504*v - 24057)*t^8 + O(t^9)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36728" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">disc:=subs(t=u/(v-1),1 - 4*y*R/(y*(1 - y) - t*(v - 1))^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVkaXNjR0YoLCYiIiJGLyoqIiIlRi9JInlHRihGL0kiUkdGKEYvKSwmKiZGMkYvLCZGL0YvRjIhIiJGL0YvSSJ1R0YoRjgiIiNGOEY4NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L36722" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">ndisc:=collect((y*(1 - y) - u)^2-4*y*R,y,factor)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZuZGlzY0dGKCwsKiQpSSJ5R0YoIiIlIiIiRjMqJiIiI0YzKUYxIiIkRjMhIiIqJiwmKiZGNUYzSSJ1R0YoRjNGM0YzRjNGMylGMUY1RjNGMyomLCZGO0Y4KiZGMkYzSSJSR0YoRjNGOEYzRjFGM0YzKiQpRjxGNUYzRjM3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L40322" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The 4 roots</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L40321" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(allvalues,algeqtoseries(subs(u=t*(v-1),R=convert(R1ser,polynom), ndisc),t,y,2))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyYsKCIiIkYkKiYiIiNGJClJInRHNiIjRiRGJkYkRiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiNGKEYkLChGJEYkRiUhIiJGK0YkKylGKCwoSSJ2R0YpRiRGJEYkKiZGJkYkKUY1RipGJEYkRiQsLCooIyIiJEYmRiRGNEYkRjVGJEYkKiZGKkYkKUY1RiZGJEYyKiYjIiIqRiZGJEY1RiRGJEY7RiQqJiIiKEYkRjdGJEYkRiYtRiw2I0YkRjsrKUYoLChGNUYkRiRGJEY2RjJGJCwsKihGOkYkRkZGJEY1RiRGJEY8RjJGPkYkRjtGJEZBRjJGJkZDRjs=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L40320" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L36729" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">dndisc:=diff(ndisc,y)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdkbmRpc2NHRigsLComIiIlIiIiKUkieUdGKCIiJEYxRjEqJiIiJ0YxKUYzIiIjRjEhIiIqKEY4RjEsJiomRjhGMUkidUdGKEYxRjFGMUYxRjFGM0YxRjEqJkYwRjFJIlJHRihGMUY5RjxGOTcjRi4=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">By eliminating R or u we can express u and R in terms of yc</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(resultant(ndisc,dndisc,R))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCIiJSIiIiwoKiQpSSJ5RzYiIiIjRiVGJUkidUdGKkYlRikhIiJGJSwoKiYiIiRGJUYoRiVGLUYsRiVGKUYlRiVGJQ==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor({solve(%,u)})</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCQqJkkieUc2IiIiIiwmKiYiIiRGJkYkRiZGJkYmISIiRiYsJComRiRGJiwmRiZGKkYkRiZGJkYq</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">uc:=yc*(3*yc-1);</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1Y0dGKComSSN5Y0dGKCIiIiwmKiYiIiRGMEYvRjBGMEYwISIiRjA3I0Yu</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(resultant(ndisc,dndisc,u))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCIjOyIiIkkiUkc2IkYlLCoqJiIiJUYlKUkieUdGJyIiJEYlISIiKiZGKkYlKUYsIiIjRiVGJUYmRiVGLEYuRiVGJQ==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rc:=subs(y=yc,factor(solve(op(3,%),R)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNSY0dGKComSSN5Y0dGKCIiIiksJiomIiIjRjBGL0YwRjBGMCEiIkY0RjA3I0Yu</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39626" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L39628" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font size="14" bold="true">The characterization of yc given in the paper, and a numerical check</Font></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal">Numerics</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">fv:=Pi*v/(v-1)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNmdkdGKCooSSNQaUdGJiIiIkkidkdGKEYwLCZGMUYwRjAhIiJGMzcjRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(fv,v=0..20, y=-10..10)</Text-field>
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<Input><Text-field style="Text" layout="Normal">Two equivalent expressions</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">gy:=2*arctan(sqrt((6*y-1)/(1-2*y)))+sqrt((6*y-1)*(1-2*y))/4/y/(3*y-1);
hy:=arccos((1-4*y)/2/y)+sqrt((6*y-1)*(1-2*y))/4/y/(3*y-1);
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">vy:=isolate(fv-gy,v)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN2eUdGKC9JInZHRigqJiwoKigiI0MiIiItSSdhcmN0YW5HRiU2IyokKSwkKiYsJiomIiInRjRJInlHRihGNEY0RjQhIiJGNCwmKiYiIiNGNEY/RjRGNEY0RkBGQEZAI0Y0RkNGNEY0KUY/RkNGNEY0KigiIilGNEY1RjRGP0Y0RkAqJCksJComRjxGNEZBRjRGQEZERjRGNEY0LCxGMkY0KigiIzdGNEZFRjRJI1BpR0YmRjRGQEZGRkAqKCIiJUY0Rj9GNEZPRjRGNEZIRjRGQDcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39689" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc_val:=proc(u) if u=1 then 1/3 else fsolve(subs(v=u,fv)-gy,y=1/6..1/2)fi: end:
</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39687" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">yc_val(2);yc_val(4);yc_val(0)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC4zNjU0MDUyMzQ1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrWEIwYU8hIzU=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC4zOTYyMzIzMjkxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrIkhCQidSISM1</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMC4xNjY2NjY2NjY3RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JCIrbm1tbTshIzU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39685" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([seq([u,yc_val(u)],u=1..10)],style=point)</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [[[1, 1/3], [2, .3654052345], [3, .3837494594], [4, .3962323291], [5, .4054949095], [6, .4127430402], [7, .4186245457], [8, .4235254261], [9, .4276929665], [10, .4312943608]]], 3 = (style = point)]), &quot;originalview&quot; = [1. .. 10., .333333333333333315 .. .431294360799999998]])">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Ig==</Plot></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39679" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tc_val:=proc(u)
if u=1 then 1/4/Pi/sqrt(3) else yc_val(u)*(3*yc_val(u)-1)/(u-1):fi: end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39684" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">tc_val(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEuMC4wMzUxNTc3MjE4OEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JCIrKT1zZF4kISM2</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39670" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=plot([seq([i/10,tc_val(i/10)],i=0..100)],thickness=3,font=[helvetica,roman,16])</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [[[0, 0.8333333333e-1], [1/10, 0.7237660458e-1], [1/5, 0.6663629818e-1], [3/10, 0.6235354567e-1], [2/5, 0.5889648472e-1], [1/2, 0.5598958584e-1], [3/5, 0.5348133205e-1], [7/10, 0.5127749063e-1], [4/5, 0.4931470050e-1], [9/10, 0.4754797897e-1], [1, (1/12)*3^(1/2)/Pi], [11/10, 0.4447763274e-1], [6/5, 0.4312883553e-1], [13/10, 0.4188186563e-1], [7/5, 0.4072388735e-1], [3/2, 0.3964433422e-1], [8/5, 0.3863439712e-1], [17/10, 0.3768665166e-1], [9/5, 0.3679478098e-1], [19/10, 0.3595336571e-1], [2, 0.3515772188e-1], [21/10, 0.3440377078e-1], [11/5, 0.3368794304e-1], [23/10, 0.3300709422e-1], [12/5, 0.3235844161e-1], [5/2, 0.3173951093e-1], [13/5, 0.3114809199e-1], [27/10, 0.3058220421e-1], [14/5, 0.3004006464e-1], [29/10, 0.2952006312e-1], [3, 0.2902074164e-1], [31/10, 0.2854077497e-1], [16/5, 0.2807895610e-1], [33/10, 0.2763418200e-1], [17/5, 0.2720544273e-1], [7/2, 0.2679181118e-1], [18/5, 0.2639243447e-1], [37/10, 0.2600652619e-1], [19/5, 0.2563336031e-1], [39/10, 0.2527226452e-1], [4, 0.2492261555e-1], [41/10, 0.2458383494e-1], [21/5, 0.2425538432e-1], [43/10, 0.2393676202e-1], [22/5, 0.2362750021e-1], [9/2, 0.2332716163e-1], [23/5, 0.2303533741e-1], [47/10, 0.2275164409e-1], [24/5, 0.2247572241e-1], [49/10, 0.2220723483e-1], [5, 0.2194586380e-1], [51/10, 0.2169131078e-1], [26/5, 0.2144329425e-1], [53/10, 0.2120154864e-1], [27/5, 0.2096582338e-1], [11/2, 0.2073588156e-1], [28/5, 0.2051149909e-1], [57/10, 0.2029246375e-1], [29/5, 0.2007857470e-1], [59/10, 0.1986964125e-1], [6, 0.1966548233e-1], [61/10, 0.1946592609e-1], [31/5, 0.1927080927e-1], [63/10, 0.1907997624e-1], [32/5, 0.1889327917e-1], [13/2, 0.1871057709e-1], [33/5, 0.1853173564e-1], [67/10, 0.1835662658e-1], [34/5, 0.1818512753e-1], [69/10, 0.1801712175e-1], [7, 0.1785249750e-1], [71/10, 0.1769114803e-1], [36/5, 0.1753297118e-1], [73/10, 0.1737786914e-1], [37/5, 0.1722574816e-1], [15/2, 0.1707651862e-1], [38/5, 0.1693009432e-1], [77/10, 0.1678639275e-1], [39/5, 0.1664533472e-1], [79/10, 0.1650684403e-1], [8, 0.1637084763e-1], [81/10, 0.1623727535e-1], [41/5, 0.1610605950e-1], [83/10, 0.1597713529e-1], [42/5, 0.1585043997e-1], [17/2, 0.1572591359e-1], [43/5, 0.1560349801e-1], [87/10, 0.1548313742e-1], [44/5, 0.1536477795e-1], [89/10, 0.1524836778e-1], [9, 0.1513385681e-1], [91/10, 0.1502119660e-1], [46/5, 0.1491034067e-1], [93/10, 0.1480124388e-1], [47/5, 0.1469386273e-1], [19/2, 0.1458815525e-1], [48/5, 0.1448408076e-1], [97/10, 0.1438160002e-1], [49/5, 0.1428067502e-1], [99/10, 0.1418126895e-1], [10, 0.1408334622e-1]]], 3 = (thickness = 3), 4 = (font = [helvetica, roman, 16])]), &quot;originalview&quot; 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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">read(&quot;Q1.txt&quot;):</Text-field>
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<Group view="code" labelreference="L39671" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q1pol:=convert(Q_1,polynom):</Text-field>
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<Group view="code" hide-input="false" labelreference="L39681" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(Q_1,t)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInRHNiIsJiokKUkidkdGJCIiIyIiIkYqKiYiIiRGKkYoRipGKkYqLCgqJkYpRiopRihGLEYqRioqJiIjOkYqRidGKkYqKiYiIz1GKkYoRipGKkYpLCoqJiIiJkYqKUYoIiIlRipGKiomIiNtRipGL0YqRioqJiIkJz5GKkYnRipGKiomIiROIkYqRihGKkYqRiwsLComIiM5RiopRihGNkYqRioqJiIkeiNGKkY3RipGKiomIiVfOUYqRi9GKkYqKiYiJWJDRipGJ0YqRioqJiIlTTZGKkYoRipGKkY4LC4qJiIjVUYqKUYoIiInRipGKiomIiVlNkYqRkJGKkYqKiYiJSEzKkYqRjdGKkYqKiYiJitvI0YqRi9GKkYqKiYiJic9SUYqRidGKkYqKiYiJjEtIkYqRihGKkYqRjYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKkZP</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">nops(Q1pol); coeff(Q1pol,t,38)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEjMzhGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">IiNR</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" 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<Group view="code" hide-input="false" labelreference="L39683" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot([seq(coeff(Q1pol,t,(5*n+7))/coeff(Q1pol,t,5*n+8),n=0..6)],v=0..10,colour=blue)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">discc:=factor(subs(u=uc,R=Rc,disc))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">di:=op(1,numer(%)); collect(%,y,factor)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNkaUdGKCwuKiQpSSJ5R0YoIiIjIiIiRjMqKEYyRjNGMUYzSSN5Y0dGKEYzRjMqJiIiKkYzKUY1RjJGM0YzKiZGMkYzRjFGMyEiIiomIiInRjNGNUYzRjpGM0YzNyNGLg==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEnJnBsdXM7RidGPC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZWLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2Ji1GIzYmRjgtRkI2LVExJkludmlzaWJsZVRpbWVzO0YnRjxGRUZIRkpGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZgby1GLzYlUSN5Y0YnRjJGNUY8LUZCNi1RKCZtaW51cztGJ0Y8RkVGSEZKRkxGTkZQRlJGVEZXRjhGPEY8RlxvRi5GPEZBLUYsNiUtRmZuNiQtRiM2Ji1GIzYmLUY5NiRRIjNGJ0Y8RlxvRmJvRjxGZW8tRjk2JFEiMUYnRjxGPEY8RjhGPkY8">LCgqJClJInlHNiIiIiMiIiJGKComLCYqJkYnRihJI3ljR0YmRihGKEYnISIiRihGJUYoRigqJCksJiomIiIkRihGLEYoRihGKEYtRidGKEYo</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L39101" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">disol:=factor([solve(di,y)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZkaXNvbEdGKDckLChJI3ljR0YoISIiIiIiRjIqJiIiI0YyKSwkKiZGMEYyLCYqJkY0RjJGMEYyRjJGMkYxRjJGMSNGMkY0RjJGMiwoRjBGMUYyRjJGM0YxNyNGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39100" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L38876" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We need to explore the modulus of this, for values of yc between 1/6 and 1/2</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L36741" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">mo:=factor(subs(u=uc,R=Rc,1-disc))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNtb0dGKCwkKiwiIiUiIiJJInlHRihGMUkjeWNHRihGMSksJiomIiIjRjFGM0YxRjFGMSEiIkY3RjEpLCoqJClGMkY3RjFGMSomIiIkRjEpRjNGN0YxRjFGMkY4RjNGOEY3RjhGMTcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L39091" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(mo-1);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCwuKiQpSSJ5RzYiIiIjIiIiRioqKEYpRipGJ0YqSSN5Y0dGKEYqRioqJiIiKkYqKUYsRilGKkYqKiZGKUYqRidGKiEiIiomIiInRipGLEYqRjFGKkYqRiopLCZGJ0YqRixGMUYpRiopLCpGJUYqKiYiIiRGKkYvRipGKkYnRjFGLEYxRilGMUYx</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39530" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" layout="Heading 4"><Font size="14" bold="true">The region where the expression of M(y) holds analytically, for various values of yc</Font></Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L39539" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example: yc=1/6 (minimal value): three loops</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39541" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/6,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiJEciIiIkIiIiSSJ5RzYiRicpLCgqJiIjN0YnKUYoIiIjRidGJyomRi1GJ0YoRichIiJGJ0YxRi9GMUYn</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39543" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39545" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqLCMiJiVROyIiKiIiIiwmSSJ1R0YoRjMqJl4jRjNGM0kidkdGKEYzRjNGMyksKiomIiM3RjMpRjQiIiNGM0YzKiZGPEYzRjVGMyEiIiomLCQqJkY8RjNGN0YzRjNGM0Y4RjNGQEYzRkBGPkZALCZGNUYzKiYsJEY3RjNGM0Y4RjNGQEYzKSwqKiZGPEYzKUZERj5GM0YzRj9GQComRkNGM0Y4RjNGM0YzRkBGPkZARjM3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L39540" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCMiJiVROyIiKiIiIiwmKiQpSSJ1R0YoIiIjRjNGMyokKUkidkdGKEY4RjNGM0YzKSw0KiYiJFciRjMpRjciIiVGM0YzKigiJClHRjNGNkYzRjpGM0YzKiZGP0YzKUY7RkFGM0YzKiZGQ0YzKUY3IiIkRjMhIiIqKEZDRjNGN0YzRjpGM0ZJKiYiJD8iRjNGNkYzRjMqJiIkbyJGM0Y6RjNGMyomIiNDRjNGN0YzRjNGM0YzRjhGSUYzNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39544" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/6,disol[2])..subs(yc=1/6,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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<Group view="code" labelreference="L39596" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example:</Text-field>
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<Group view="code" hide-input="false" labelreference="L39602" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/6+1/10,mo));</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiJT9SIiIkIiIiSSJ5RzYiRicpLCgqJiIjdkYnKUYoIiIjRidGJyomRi1GJ0YoRichIiIiIiVGMUYvRjFGJw==</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqLCMiKStrTzoiIioiIiIsJkkidUdGKEYzKiZeI0YzRjNJInZHRihGM0YzRjMpLCoqJiIjdkYzKUY0IiIjRjNGMyomRjxGM0Y1RjMhIiIqJiwkKiZGPEYzRjdGM0YzRjNGOEYzRkAiIiVGQEY+RkAsJkY1RjMqJiwkRjdGM0YzRjhGM0ZARjMpLCoqJkY8RjMpRkVGPkYzRjNGP0ZAKiZGQ0YzRjhGM0YzRkRGQEY+RkBGMzcjRi4=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L39601" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCMiKStrTzoiIioiIiIsJiokKUkidUdGKCIiI0YzRjMqJClJInZHRihGOEYzRjNGMyksNComIiVEY0YzKUY3IiIlRjNGMyooIiZdNyJGM0Y2RjNGOkYzRjMqJkY/RjMpRjtGQUYzRjMqJkZDRjMpRjciIiRGMyEiIiooRkNGM0Y3RjNGOkYzRkkqJiIlRF1GM0Y2RjNGMyomIiVEaUYzRjpGM0YzKiYiJCsnRjNGN0YzRjMiIztGM0Y4RklGMzcjRi4=</Equation></Text-field>
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<Group view="code" labelreference="L39579" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/6+1/10,disol[2])..subs(yc=1/6+1/10,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39577" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39580" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/3,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiIiUiI0YiIiJJInlHNiIhIiIpLCZGJ0YqRihGJyIiI0YqRic=</Equation></Text-field>
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<Group view="code" labelreference="L39584" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L39585" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqLCMiIzsiJEgoIiIiLCZJInVHRihGMyomXiNGM0YzSSJ2R0YoRjNGMyEiIiksKEYzRjlGNUYzRjZGMyIiI0Y5LCZGNUYzKiYsJEY3RjNGM0Y4RjNGOUY5KSwoRjNGOUY1RjNGPkY5RjxGOUYzNyNGLg==</Equation></Text-field>
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<Group view="code" hide-input="false" labelreference="L39582" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCMiIzsiJEgoIiIiLCYqJClJInVHRigiIiNGM0YzKiQpSSJ2R0YoRjhGM0YzISIiKSwqRjVGM0Y5RjMqJkY4RjNGN0YzRjxGM0YzRjhGPEYzNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39586" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/3,disol[2])..subs(yc=1/3,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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<Input><Text-field style="Text" layout="Normal">Example:</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/3+1/10,mo));</Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
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<Group view="code" hide-input="false" labelreference="L39604" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqLCMiKStDQXAiJEgoIiIiLCZJInVHRihGMyomXiNGM0YzSSJ2R0YoRjNGM0YzKSwqKiYiJCsiRjMpRjQiIiNGM0YzKiZGPEYzRjVGMyEiIiomLCQqJkY8RjNGN0YzRjNGM0Y4RjNGQCIjOEYzRj5GQCwmRjVGMyomLCRGN0YzRjNGOEYzRkBGMyksKiomRjxGMylGRUY+RjNGM0Y/RkAqJkZDRjNGOEYzRjNGREYzRj5GQEYzNyNGLg==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L39606" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCMiKStDQXAiJEgoIiIiLCYqJClJInVHRigiIiNGM0YzKiQpSSJ2R0YoRjhGM0YzRjMpLDQqJiImKysiRjMpRjciIiVGM0YzKigiJisrI0YzRjZGM0Y6RjNGMyomRj9GMylGO0ZBRjNGMyomRkNGMylGNyIiJEYzISIiKihGQ0YzRjdGM0Y6RjNGSSomIiYrRSJGM0Y2RjNGMyomIiUrdUYzRjpGM0YzKiYiJStFRjNGN0YzRkkiJHAiRjNGOEZJRjM3I0Yu</Equation></Text-field>
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<Group view="code" labelreference="L39589" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/3+1/10,disol[2])..subs(yc=1/3+1/10,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39609" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39590" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L39594" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/3+1/8,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCMiJTM5IiNGIiIiSSJ5RzYiRicpLCgqJiIja0YnKUYoIiIjRidGJyomRi1GJ0YoRichIiIiIzZGJ0YvRjFGJw==</Equation></Text-field>
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<Group view="code" labelreference="L39599" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L39597" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqLCMiKGtDKT4iJEgoIiIiLCZJInVHRihGMyomXiNGM0YzSSJ2R0YoRjNGM0YzKSwqKiYiI2tGMylGNCIiI0YzRjMqJkY8RjNGNUYzISIiKiYsJComRjxGM0Y3RjNGM0YzRjhGM0ZAIiM2RjNGPkZALCZGNUYzKiYsJEY3RjNGM0Y4RjNGQEYzKSwqKiZGPEYzKUZFRj5GM0YzRj9GQComRkNGM0Y4RjNGM0ZERjNGPkZARjM3I0Yu</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCMiKGtDKT4iJEgoIiIiLCYqJClJInVHRigiIiNGM0YzKiQpSSJ2R0YoRjhGM0YzRjMpLDQqJiIlJzQlRjMpRjciIiVGM0YzKigiJSM+KUYzRjZGM0Y6RjNGMyomRj9GMylGO0ZBRjNGMyomRkNGMylGNyIiJEYzISIiKihGQ0YzRjdGM0Y6RjNGSSomIiUvYkYzRjZGM0YzKiYiJSlvI0YzRjpGM0YzKiYiJTM5RjNGN0YzRkkiJEAiRjNGOEZJRjM3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39603" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..2,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/3+1/8,disol[2])..subs(yc=1/3+1/8,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
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<Group view="code" labelreference="L39591" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Example:</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(subs(yc=1/2-1/200,mo));</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCInK29KIiIiSSJ5RzYiRiUpLCgqJiImKyslRiUpRiYiIiNGJUYlKiZGK0YlRiZGJSEiIiIlLicqRiVGLUYvRiU=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The modulus of this must be less than 1</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L39598" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=subs(y=u+I*v,%)*subs(y=u-I*v,%)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cond:=factor(expand(numer(cond))/expand(denom(cond)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVjb25kR0YoLCQqKCItKytDaS41IiIiLCYqJClJInVHRigiIiNGMUYxKiQpSSJ2R0YoRjZGMUYxRjEpLDQqJiIrKysrKztGMSlGNSIiJUYxRjEqKCIrKysrK0tGMUY0RjFGOEYxRjEqJkY9RjEpRjlGP0YxRjEqJkZBRjEpRjUiIiRGMSEiIiooRkFGMUY1RjFGOEYxRkcqJiIrKytDb0JGMUY0RjFGMSomIiorK3dKKUYxRjhGMUYxKiYiKisrQ28oRjFGNUYxRkciKTR3QCMqRjFGNkZHRjE3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39576" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=implicitplot(cond-1,u=-1..1,v=-1..1,scaling=constrained,numpoints=10000):
P2:=plot(0,u=subs(yc=1/2-1/200,disol[2])..subs(yc=1/2-1/200,disol[1]),thickness=6): display(P1,P2)</Text-field>
</Input>
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<Group view="code" labelreference="L39583" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39542" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39529" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L39528" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="code" labelreference="L39527" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L39526" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Group>
<Group view="code" labelreference="L39525" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group view="presentation" inline-output="false" labelreference="L39524" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv</Equation></Text-field>
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</Section><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L38938" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">MR1;discc</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKCMiIiIiIiNGJSwmKiZJInlHNiJGJSwmRiVGJUYpISIiRiVGJSomSSJ0R0YqRiUsJkkidkdGKkYlRiVGLEYlRiVGJUYpRixGJSoqRiRGJSwmRihGJUYtRixGJUYpRiwpLCZGJUYlKioiIiVGJUYpRiVJIlJHRipGJSlGMkYmRixGLEYkRiVGLA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsLiokKUkieUc2IiIiIyIiIkYpKihGKEYpRiZGKUkjeWNHRidGKUYpKiYiIipGKSlGK0YoRilGKSomRihGKUYmRikhIiIqJiIiJ0YpRitGKUYwRilGKUYpKSwmRiZGKUYrRjBGKEYpKSwqRiRGKSomIiIkRilGLkYpRilGJkYwRitGMEYoRjA=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L39041" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">When y is a large real</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L38915" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">M_alt:=map(factor,subs(t=u/(v-1),u=uc,(y*(1 - y) + t*(v - 1))/(2*y)+(y*(1 - y) -t*(v - 1))/2/y*  (y-yc)/(y^2 + 3*yc^2 - y - yc)*(1-y-yc)*sqrt((y^2 + 2*y*yc + 9*yc^2 - 2*y - 6*yc + 1)/(1-y-yc)^2)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZNX2FsdEdGKCwmKigjIiIiIiIjRjEsKiokKUkieUdGKEYyRjFGMSomIiIkRjEpSSN5Y0dGKEYyRjEhIiJGNkY7RjpGMUYxRjZGO0Y7KixGMEYxKSomLC5GNEYxKihGMkYxRjZGMUY6RjFGMSomIiIqRjFGOUYxRjEqJkYyRjFGNkYxRjsqJiIiJ0YxRjpGMUY7RjFGMUYxKSwoRjFGO0Y2RjFGOkYxRjJGO0YwRjFGR0YxLCZGNkYxRjpGO0YxRjZGO0YxNyNGLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L40153" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Check</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L40152" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,series(M_alt-subs(t=u/(v-1),u=uc,R=Rc,MR1),y=infinity,18))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiQpSSJ5R0YnIiM7ISIi</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L40272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Under the square root</Text-field>
</Input>
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<Group view="code" hide-input="false" labelreference="L40069" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr:=sqrt((y^2 + 2*y*yc + 9*yc^2 - 2*y - 6*yc + 1)/(-1 + y + yc)^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoKiQpKiYsLiokKUkieUdGKCIiIyIiIkY2KihGNUY2RjRGNkkjeWNHRihGNkY2KiYiIipGNilGOEY1RjZGNiomRjVGNkY0RjYhIiIqJiIiJ0Y2RjhGNkY9RjZGNkY2KSwoRjZGPUY0RjZGOEY2RjVGPSNGNkY1RjY3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L40071" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([1-yc,solve(y^2 + 2*y*yc + 9*yc^2 - 2*y - 6*yc + 1,y)],yc=1/6..1/2,z=0..1.5)</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Sy:=sqrt((y^2 + 2*y*yc + 9*yc^2 - 2*y - 6*yc + 1)/(-1 + y + yc)^2)*(-1 + y + yc)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNTeUdGKComKSomLC4qJClJInlHRigiIiMiIiJGNiooRjVGNkY0RjZJI3ljR0YoRjZGNiomIiIqRjYpRjhGNUY2RjYqJkY1RjZGNEY2ISIiKiYiIidGNkY4RjZGPUY2RjZGNiksKEY2Rj1GNEY2RjhGNkY1Rj0jRjZGNUY2RkFGNjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L40192" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Mhat:=yc*(3*yc-1)*log(1-y-3*yc-Sy)-1/4*(1+yc-y)*Sy+(2*y-y^2)/4</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVNaGF0R0YoLCoqKEkjeWNHRigiIiIsJiomIiIkRjFGMEYxRjFGMSEiIkYxLUkjbG5HRiU2IywqRjFGMUkieUdGKEY1RjNGNSomKSomLC4qJClGOiIiI0YxRjEqKEZBRjFGOkYxRjBGMUYxKiYiIipGMSlGMEZBRjFGMSomRkFGMUY6RjFGNSomIiInRjFGMEYxRjVGMUYxRjEpLChGMUY1RjpGMUYwRjFGQUY1I0YxRkFGMUZKRjFGNUYxRjEqKiNGMSIiJUYxLChGMUYxRjBGMUY6RjVGMUY8RjFGSkYxRjUqJkZNRjFGQEYxRjUqJkZLRjFGOkYxRjE3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L40196" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(diff(Mhat,y)-M_alt)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L40307" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The term inside the log: negative for y real positive</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L40195" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expr:=1 - y - 3*yc - sqrt((y^2 + 2*y*yc + 9*yc^2 - 2*y - 6*yc + 1)/(-1 + y + yc)^2)*(-1 + y + yc)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVleHByR0YoLCoiIiJGL0kieUdGKCEiIiomIiIkRi9JI3ljR0YoRi9GMSomKSomLC4qJClGMCIiI0YvRi8qKEY7Ri9GMEYvRjRGL0YvKiYiIipGLylGNEY7Ri9GLyomRjtGL0YwRi9GMSomIiInRi9GNEYvRjFGL0YvRi8pLChGL0YxRjBGL0Y0Ri9GO0YxI0YvRjtGL0ZERi9GMTcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L40200" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">complexplot3d(subs(yc=1/3,expr),y=-2-2*I..2+3*I,view=0..4)</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJKGVwc2lsb25HNiIqJiwmKiYiIiciIiJJI3ljR0YkRilGKUYpISIiRiksJiomIiIjRilGKkYpRilGKUYrRisiIiEsJCooLCQqJiIiKUYpXiNGKUYpRilGKUYqRikpRixGLkYrRitGKS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpRi4=</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">sq_plus:=-I*sqrt((6*yc-1)/(1-2*yc));
sq_minus:=I*sqrt((6*yc-1)/(1-2*yc))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShzcV9wbHVzR0YoLCQqJiwkXiMiIiJGMkYyKSomLCYqJiIiJ0YySSN5Y0dGKEYyRjJGMiEiIkYyLCZGMkYyKiYiIiNGMkY4RjJGOUY5I0YyRjxGMkY5NyNGLg==</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEpc3FfbWludXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEtJkltYWdpbmFyeUk7RidGOS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlctSSZtc3FydEdGJDYjLUkmbWZyYWNHRiQ2KC1GIzYmLUYjNiYtRlA2JFEiNkYnRjlGUy1GLDYlUSN5Y0YnRi9GMkY5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZ28tRlA2JFEiMUYnRjlGOS1GIzYmRmlvRmNvLUYjNiYtRlA2JFEiMkYnRjlGU0Zgb0Y5RjkvJS5saW5ldGhpY2tuZXNzR0ZbcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZncC8lKWJldmVsbGVkR0Y9Rjk=">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlzcV9taW51c0dGKComXiMiIiJGMCkqJiwmKiYiIidGMEkjeWNHRihGMEYwRjAhIiJGMCwmRjBGMComIiIjRjBGNkYwRjdGNyNGMEY6RjA3I0Yu</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">The polynomial part gives 0
The part with the square root gives a multiple of the above value</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Input><Text-field style="Text" layout="Normal">Part with logs</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">(subs(y=yc,1 - y - 3*yc - sq_plus*(-1 + y + yc)));
(subs(y=yc,1 - y - 3*yc - sq_minus*(-1 + y + yc)))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyomIiIlRiNJI3ljRzYiRiMhIiIqKF4jRiNGIykqJiwmKiYiIidGI0YmRiNGI0YjRihGIywmRiNGIyomIiIjRiNGJkYjRihGKCNGI0YyRiMsJkYxRiNGI0YoRiNGIw==</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyomIiIlRiNJI3ljRzYiRiMhIiIqKCwkXiNGI0YjRiMpKiYsJiomIiInRiNGJkYjRiNGI0YoRiMsJkYjRiMqJiIiI0YjRiZGI0YoRigjRiNGM0YjLCZGMkYjRiNGKEYjRig=</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal">squared modulus</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor((1-4*yc)^2+((6*yc - 1)*(-2*yc + 1)))</Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSN5Y0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYkUSIyRidGLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGLw==">LCQqJiIiJSIiIilJI3ljRzYiIiIjRiVGJQ==</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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</Group><Presentation-Block>
<Group view="code" labelreference="L30671" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Group labelreference="L33901" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">The case v=1 (Section 6)</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L36801" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L36802" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L33909" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">thetaser:=proc(N) local n: add((-1)^n*q^(n*(n+1)/2)*sin(z*(2*n+1)),n=0..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33839" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">thetaser(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCotSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiekdGKCIiIiomSSJxR0YoRistRiQ2IywkKiYiIiRGK0YqRitGK0YrISIiKiYpRi1GMkYrLUYkNiMsJComIiImRitGKkYrRitGK0YrKiYpRi0iIidGKy1GJDYjLCQqJiIiKEYrRipGK0YrRitGMw==</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L34113" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The product expression of theta</Text-field>
</Input>
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<Group view="code" labelreference="L33950" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">prod:=proc(N) local n: product((1-q^n)*(1-q^n*exp(2*I*z))*(1-q^n/exp(2*I*z)),n=1..N): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33850" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">prod(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KjQsJiIiIkYkSSJxRzYiISIiRiQsJkYkRiQqJkYlRiQtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IyomKiYiIiNGJF4jRiRGJEYkSSJ6R0YmRiRGJEYnRiQsJkYkRiQqJkYlRiRGKkYnRidGJCwmKiQpRiVGMkYkRidGJEYkRiQsJkYkRiQqJkY5RiRGKkYkRidGJCwmRiRGJComRjlGJEYqRidGJ0YkLCYqJClGJSIiJEYkRidGJEYkRiQsJkYkRiQqJkZARiRGKkYkRidGJCwmRiRGJComRkBGJEYqRidGJ0Yk</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33840" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=7: simplify(convert(map(expand,simplify(series(thetaser(n)/prod(n),q,n+1))),trig),trig)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInFHNiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kiekdGJCIiIS1JIk9HRic2IyIiIiIiKQ==</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L34114" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Some ingredients of the Ansatz construction of Section 6.1</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34097" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">psi:=theta(z+a)/theta(z)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRwc2lHRigqJi1JJnRoZXRhR0YoNiMsJkkiekdGKCIiIkkiYUdGKEY0RjQtRjA2I0YzISIiNyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33904" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">psiser:=proc(N) 
simplify(factor(convert(series(subs(z=z+a,thetaser(N))/thetaser(N),q,N+1),exp))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33944" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">psiser(2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCZJInpHRiQiIiJJImFHRiRGLkYuLUYnNiNGLSEiIiIiISwkKigjRi4iIiNGLiwqLUkkY29zR0YoNiMsJiomRjdGLkYtRi5GMkYvRi5GLi1GOjYjLCZGPUYuKiYiIiRGLkYvRi5GLkYyLUY6NiMsJiomIiIlRi5GLUYuRi5GL0YuRjItRjo2IywmRkZGLkZBRi5GLkYuKUYwRjdGMkYuRi4sJCoqRjZGLkY4Ri4tRic2IywkKiZGQkYuRi1GLkYuRi4pRjBGQkYyRi5GNy1JIk9HRig2I0YuRkI=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33903" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(series,%,z,3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIrKUkiekdGJC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJhR0YkISIiLUkkY29zR0YpRiwiIiEtSSJPR0YpNiMiIiJGNUYxKylGJiwmKiYiIiRGNUYnRjVGNS1GKDYjLCQqJkY5RjVGLUY1RjVGLkYuLCYqJkY5RjVGL0Y1RjUqJkY5RjUtRjBGO0Y1Ri5GMUYyRjVGNSsnRiYsJiomIiIqRjVGJ0Y1RjUqJkY5RjVGOkY1Ri5GLkYyRjEiIiMrJUYmRjJGMUY5</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34093" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">We want the following expression to be zero at z=0. Let us write theta(z)=z Gamma(z), with Gamma even</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34092" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">c*theta(z+a)/theta(z)+c*theta(a-z)/theta(-z)+1/4/s^2;
subs(theta(z)=z *Gamma(z),theta(-z)=-z *Gamma(z),%)
</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqKEkiY0c2IiIiIi1JJnRoZXRhR0YlNiMsJkkiekdGJUYmSSJhR0YlRiZGJi1GKDYjRishIiJGJiooRiRGJi1GKDYjLCZGLEYmRitGL0YmLUYoNiMsJEYrRi9GL0YmKiYjRiYiIiVGJilJInNHRiUiIiNGL0Ym</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1GIzYmLUYxNiVRKCZ0aGV0YTtGJy9GNUZCRj4tRjs2LVEwJkFwcGx5RnVuY3Rpb247RidGPkZARkNGRUZHRklGS0ZNRk9GUi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYxNiVRInpGJ0Y0RjctRjs2LVEnJnBsdXM7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmNvLUYxNiVRImFGJ0Y0RjdGPkY+Rj5GPi1GIzYmRlxvRjotRiM2Ji1GMTYlUSZHYW1tYUYnRllGPkZaLUZobjYkLUYjNidGXG8vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGQkY+Rj5GPkY+LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgcS8lKWJldmVsbGVkR0ZCLUY7Ni1RKCZtaW51cztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GYm9GZG8tRiw2KC1GIzYmRjBGOi1GIzYmRlZGWi1GaG42JC1GIzYmRmVvRmVxRlxvRj5GPkY+Rj5GaG9GW3FGXnFGYXFGY3FGX28tRiw2KC1JI21uR0YkNiRGXXFGPi1GIzYmLUZlcjYkUSI0RidGPkY6LUklbXN1cEdGJDYlLUYxNiVRInNGJ0Y0RjctRmVyNiRRIjJGJ0Y+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y+RltxRl5xRmFxRmNxRj4=">LCgqKkkiY0c2IiIiIi1JJnRoZXRhR0YlNiMsJkkiekdGJUYmSSJhR0YlRiZGJkYrISIiLUkmR2FtbWFHRiU2I0YrRi1GJioqRiRGJi1GKDYjLCZGLEYmRitGLUYmRitGLUYuRi1GLSomI0YmIiIlRiYpSSJzR0YlIiIjRi1GJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34094" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%,z,2));
cconst:=solve(convert(%,polynom),c)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbWZyYWNHRiQ2KC1GIzYmLUYjNiotSSNtbkdGJDYkUSI4RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GIzYmLUYjNiYtSSNtaUdGJDYlUSJERicvJSdpdGFsaWNHRj9GNi1GOjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y2Rj1GQEZCRkRGRkZIRkpGTEZPLUkobWZlbmNlZEdGJDYkLUYjNictRlY2JVEoJnRoZXRhO0YnRllGNi8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y/RjZGNkY2RmVuLUZpbjYkLUYjNictRlY2JVEiYUYnL0ZaUSV0cnVlRicvRjdRJ2l0YWxpY0YnRmBvRmNvRmZvRjZGNkY2RjktRlY2JVEiY0YnRl9wRmFwRjktSSVtc3VwR0YkNiUtRlY2JVEic0YnRl9wRmFwLUYzNiRRIjJGJ0Y2LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y2LUY6Ni1RJyZwbHVzO0YnRjZGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZmcS1GIzYmLUZWNiVRJkdhbW1hRidGWUY2RmVuLUZpbjYkLUYjNictRjM2JEZhcUY2RmBvRmNvRmZvRjZGNkY2RjYtRiM2KC1GMzYkUSI0RidGNkY5RmhxRjlGZnBGNi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXXMvJSliZXZlbGxlZEdGP0ZicS1GIzYmLUY6Ni1RIk9GJ0Y2Rj1GQEZCRkRGRkZIRkpGTEZPRmVuLUZpbjYkLUYjNictRlY2JVEiekYnRl9wRmFwRmBvRmNvRmZvRjZGNkY2RjY=">KydJInpHNiIsJCoqIyIiIiIiJUYoLUkmR2FtbWFHRiQ2IyIiISEiIiwmKioiIilGKC0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJnRoZXRhR0YkNiNJImFHRiRGKEkiY0dGJEYoKUkic0dGJCIiI0YoRihGKkYoRihGPUYuRihGLS1JIk9HRjU2I0YoRig=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdjY29uc3RHRigsJCoqIyIiIiIiKUYxLUkmR2FtbWFHRig2IyIiIUYxLS1JIkRHRiU2I0kmdGhldGFHRig2I0kiYUdGKCEiIilJInNHRigiIiNGPkY+NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34095" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cconst:=subs(Gamma(0)=D(theta)(0),s=sin(a),cconst)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdjY29uc3RHRigsJCoqIyIiIiIiKUYxLS1JIkRHRiU2I0kmdGhldGFHRig2IyIiIUYxLUY0NiNJImFHRighIiIpLUkkc2luR0YlRjsiIiNGPUY9NyNGLg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33945" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cconstser:=proc(n) 
simplify(series(-1/8/sin(a)^2*eval(subs(z=0,diff(thetaser(n),z)))/subs(z=a,diff(thetaser(n),z)),q,n)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33894" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cconstser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIsJCooIyIiIiIiKUYoKS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJhR0YkIiIjISIiLUkkY29zR0YtRjBGM0YzIiIhLCQqJiMiIiRGMkYoRjRGM0YoRigsJCooIyIiKkYyRigsJiomIiIlRigpRjRGMkYoRihGOkYzRihGNEYzRihGMiomLCgqJiIkOyNGKClGNEZBRihGKComIiRNJEYoRkJGKEYzIiRDIkYoRihGNEYzRjotSSJPR0YtNiNGKEZB</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35451" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for N from 1 to 5 do subs(cos(a)=sqrt((2-omega)/4), expand(cos((2*N+1)*a)/cos(a))) od;</Text-field>
</Input>
<Input><Text-field prompt="&gt; " style="Maple Input" spaceabove="0" linebreak="space" rightmargin="0" linespacing="0.0" initial="0" firstindent="0" leftmargin="0" bulletsuffix="" alignment="left" bullet="none" spacebelow="0" pagebreak-before="false"></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1JI21pR0YkNiVRKCZvbWVnYTtGJy8lJ2l0YWxpY0dGNEYvRi8=">LCYiIiIhIiJJJm9tZWdhRzYiRiQ=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJCksJiIiIyIiIkkmb21lZ2FHNiIhIiJGJkYnRiciIiZGKiomRitGJ0YoRidGJw==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCoqJCksJiIiIyIiIkkmb21lZ2FHNiIhIiIiIiRGJ0YnKiYiIihGJylGJUYmRidGKiIjQEYnKiYiIzlGJ0YoRidGKg==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJCksJiIiIyIiIkkmb21lZ2FHNiIhIiIiIiVGJ0YnKiYiIipGJylGJSIiJEYnRioqJiIjRkYnKUYlRiZGJ0YnIiNeRioqJiIjSUYnRihGJ0Yn</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJCksJiIiIyIiIkkmb21lZ2FHNiIhIiIiIiZGJ0YnKiYiIzZGJylGJSIiJUYnRioqJiIjV0YnKUYlIiIkRidGJyomIiN4RicpRiVGJkYnRioiIyoqRicqJiIjYkYnRihGJ0Yq</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35450" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">for N from 1 to 5 do expand(subs(cos(z)=sqrt(1-sin(z)^2), sin(z)=sqrt(v)/2, expand(sin((2*N+1)*z)/sin(z)))) od;</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKCZtaW51cztGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJ2RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8=">LCYiIiQiIiJJInZHNiIhIiI=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJClJInZHNiIiIiMiIiJGKComIiImRihGJUYoISIiRipGKA==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCoqJClJInZHNiIiIiQiIiIhIiIqJiIiKEYoKUYlIiIjRihGKComIiM5RihGJUYoRilGK0Yo</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJClJInZHNiIiIiUiIiJGKComIiIqRigpRiUiIiRGKCEiIiomIiNGRigpRiUiIiNGKEYoKiYiI0lGKEYlRihGLUYqRig=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJClJInZHNiIiIiYiIiIhIiIqJiIjNkYoKUYlIiIlRihGKComIiNXRigpRiUiIiRGKEYpKiYiI3hGKClGJSIiI0YoRigqJiIjYkYoRiVGKEYpRitGKA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L33884" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series chi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L33864" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">chi:= (1- D(theta)(0)/D(theta)(a)/2*(psi+subs(z=-z,psi)))/4/sin(a)^2;</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRjaGlHRigsJCooIyIiIiIiJUYxLCZGMUYxKiojRjEiIiNGMS0tSSJER0YlNiNJJnRoZXRhR0YoNiMiIiFGMS1GODYjSSJhR0YoISIiLCYqJi1GOzYjLCZJInpHRihGMUZARjFGMS1GOzYjRkdGQUYxKiYtRjs2IywmRkBGMUZHRkFGMS1GOzYjLCRGR0ZBRkFGMUYxRkFGMSktSSRzaW5HRiVGP0Y2RkFGMTcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34105" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Expansion of chi in q</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34104" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">chiser:=proc(n)
factor(subs(sin(a)=sqrt(1-cos(a)^2),cos(z)=sqrt(1-sin(z)^2),expand(eval(series(subs(theta(z)=thetaser(n),theta(-z)=subs(z=-z,thetaser(n)), 
theta(z+a)=subs(z=z+a,thetaser(n)),theta(a-z)=subs(z=a-z,thetaser(n)), 
D(theta)(0)=subs(z=0,diff(thetaser(n),z)),D(theta)(a)=subs(z=a,diff(thetaser(n),z)),chi),q,n+1))))):
end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34103" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">chiser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34115" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%/4/q/sin(z)^2,q,5))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIiIiIiIiEsKComIiM3RiUpLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJImFHRiQiIiNGJUYlKiYiIiVGJSktSSRzaW5HRi02I0kiekdGJEYyRiUhIiIiIidGOkYlLC4qJiIkVyJGJSlGK0Y0RiVGJSooIiNLRiVGKkYlRjVGJUY6KiYiIztGJSlGNkY0RiVGJSomIiQrI0YlRipGJUY6KiYiIilGJUY1RiVGJSIjb0YlRjIsNComIiVHPEYlKUYrRjtGJUYlKigiJCVRRiVGP0YlRjVGJUY6KigiJEciRiVGKkYlRkRGJUYlKiYiI2tGJSlGNkY7RiVGOiomIiV3UEYlRj9GJUY6KigiJGslRiVGKkYlRjVGJUYlKiYiJSdwI0YlRipGJUYlKiYiJG8iRiVGNUYlRjoiJD8nRjoiIiQtSSJPR0YtNiNGJUY0</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34102" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us expand chi one step further near z=0. We introduce again the even function theta(z)/z, denoted Gamma(z^2)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34099" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqtg:=theta(z)-z*Gamma(z^2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcXRnR0YoLCYtSSZ0aGV0YUdGKDYjSSJ6R0YoIiIiKiZGMkYzLUkmR2FtbWFHRig2IyokKUYyIiIjRjNGMyEiIjcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34098" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(eqtg,z,4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUYjNiYtSSNtaUdGJDYlUSgmdGhldGE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjQvJSZmZW5jZUdGMy8lKnNlcGFyYXRvckdGMy8lKXN0cmV0Y2h5R0YzLyUqc3ltbWV0cmljR0YzLyUobGFyZ2VvcEdGMy8lLm1vdmFibGVsaW1pdHNHRjMvJSdhY2NlbnRHRjMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZLLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIwRidGNC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0YzRjRGNEY0LUY4Ni1RJyZwbHVzO0YnRjRGO0Y9Rj9GQUZDRkVGRy9GSlEsMC4yMjIyMjIyZW1GJy9GTUZdby1GIzYmLUZPNiQtRiM2Ji1GIzYmLUYjNiYtRi42JVEiREYnRjFGNEY3LUZPNiQtRiM2J0YtRldGWkZnbkY0RjRGNEY3Rk5GNC1GODYtUSgmbWludXM7RidGNEY7Rj1GP0ZBRkNGRUZHRlxvRl5vLUYjNiYtRi42JVEmR2FtbWFGJ0YxRjRGN0ZORjRGNEY0LUY4Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y0RjtGPUY/RkFGQ0ZFRkdGSUZMLUYuNiVRInpGJy9GMlEldHJ1ZUYnL0Y1USdpdGFsaWNGJ0Y0RmluLUYjNigtSSZtZnJhY0dGJDYoLUZUNiRRIjFGJ0Y0LUZUNiRRIjJGJ0Y0LyUubGluZXRoaWNrbmVzc0dGaXEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYXIvJSliZXZlbGxlZEdGM0ZocC1GIzYmLUYjNiYtSSVtc3VwR0YkNiZGaW8tRk82JC1GIzYnRmpxRldGWkZnbkY0RjQvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZWL0krbXNlbWFudGljc0dGJFEjQEBGJ0Y3RlxwRjRGN0ZORjRGaHAtRltzNiVGW3FGanFGYXNGNEZpbi1GIzYmLUZPNiQtRiM2Ji1GZXE2KC1GIzYmLUYjNiYtRltzNiZGaW8tRk82JC1GIzYnLUZUNiRRIjNGJ0Y0RldGWkZnbkY0RjRGYXNGY3NGN0ZccEY0RjdGTkY0LUZUNiRRIjZGJ0Y0Rl1yRl9yRmJyRmRyRmBwLUYjNiYtRiM2JkZpb0Y3LUZPNiQtRiM2J0ZlcEZXRlpGZ25GNEY0RjRGN0ZORjRGNEY0RmhwLUZbczYlRltxRmp0RmFzRjRGaW4tRiM2Ji1GODYtUSJPRidGNEY7Rj1GP0ZBRkNGRUZHRklGTEY3LUZPNiQtRiM2Jy1GW3M2JUZbcS1GVDYkUSI0RidGNEZhc0ZXRlpGZ25GNEY0RjRGNA==">Ky1JInpHNiItSSZ0aGV0YUdGJDYjIiIhRigsJi0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJkYnIiIiLUkmR2FtbWFHRiRGJyEiIkYxLCQqJiNGMSIiI0YxLS0tSSNAQEdGLTYkRixGOEYwRidGMUYxRjgsJiomI0YxIiInRjEtLS1GPDYkRiwiIiRGMEYnRjFGMS0tRiw2I0YzRidGNEZGLUkiT0dGLTYjRjEiIiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33906" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(theta(z)=z*Gamma(z^2),theta(-z)=-z*Gamma(z^2),chi):
series(%,z,4);
factor(subs(Gamma(0)=D(theta)(0),D(Gamma)(0)=(D@@3)(theta)(0)/6 ,%))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInpHNiIsJCooIyIiIiIiJUYoLCZGKEYoKiYtLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSZ0aGV0YUdGJDYjIiIhRigtSSZHYW1tYUdGJEY0ISIiRjhGKCktSSRzaW5HRi82I0kiYUdGJCIiI0Y4RihGNSwkKiwjRigiIilGKEYsRigtRi1GPEY4LCYqJiwmKiYjRigiIidGKC0tLUkjQEBHRi82JEYuIiIkRjJGPEYoRigqKEY2RjhGQ0YoLS1GLjYjRjdGNEYoRjhGKEY2RjhGKComLCZGR0Y4RlBGKEYoRjZGOEY4RihGOUY4RjhGPi1JIk9HRi82I0YoRk8=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInpHNiIsJCosIyIiIiIjQ0YoLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kmdGhldGFHRiQ2IyIiISEiIiwmKiYtRis2I0kiYUdGJEYoLS0tSSNAQEdGLTYkRiwiIiRGMEYyRihGKComLUY7RjhGKEYqRihGNEYoRjdGNCktSSRzaW5HRi1GOCIiI0Y0RihGRS1JIk9HRi02I0YoRj8=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L33844" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">c2:=coeff(%,z,2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjMkdGKCwkKiwjIiIiIiNDRjEtLUkiREdGJTYjSSZ0aGV0YUdGKDYjIiIhISIiLCYqJi1GNDYjSSJhR0YoRjEtLS1JI0BAR0YlNiRGNSIiJEY2RjhGMUYxKiYtRkFGPkYxRjNGMUY6RjFGPUY6KS1JJHNpbkdGJUY+IiIjRjpGMTcjRi4=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34100" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand(c2)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKiMiIiIiI0NGJS0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJnRoZXRhR0YtNiMiIiEhIiIpLUkkc2luR0YqNiNJImFHRi0iIiNGMi0tLUkjQEBHRio2JEYpIiIkRi5GMEYlRiUqKkYkRiUtRihGNkYyRjNGMi1GOkY2RiVGMg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34116" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,map(expand,series((subs(z=z+a,thetaser(n))+ subs(z=z-a,thetaser(n)))/2/sin(z)/cos(a),q,n+1)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIiIiIiIiEsJCooLCYqJiIiI0YlLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJInpHRiRGJUYlRiUhIiJGJSwmRipGJUYlRiVGJSwmKiYiIiVGJSktRi02I0kiYUdGJEYrRiVGJSIiJEYzRiVGM0YlKigsKComRjdGJSlGLEYrRiVGJUYqRjNGJUYzRiUsKEY/RiVGKkYlRiVGM0YlLCgqJiIjO0YlKUY5RjdGJUYlKiYiIz9GJUY4RiVGMyIiJkYlRiVGPC1JIk9HRi42I0YlIiIn</Equation></Text-field>
</Output>
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<Group view="code" labelreference="L34198" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L34199" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L36810" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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<Group view="code" labelreference="L34204" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" layout="Heading 3">The solution from scratch (Section 6.2)</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34232" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eexpr:=1-u/2/q*(1-sqrt(1-4*q/u));
series(Eexpr,q)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZFZXhwckdGKCwmIiIiRi8qKiNGLyIiI0YvSSJ1R0YoRi9JInFHRighIiIsJkYvRi8qJCksJkYvRi8qKCIiJUYvRjRGL0YzRjVGNUYxRi9GNUYvRjU3I0Yu</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIsJCokSSJ1R0YkISIiRigiIiIsJComIiIjRikpRidGLEYoRihGLCwkKiYiIiZGKSlGJyIiJEYoRihGMiwkKiYiIzlGKSlGJyIiJUYoRihGNy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpRjA=</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34294" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">rationalize(q*(2-Eexpr-1/Eexpr))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">SSJ1RzYi</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34293" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">uE:=q*(2-E-1/E); factor(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1RUdGKComSSJxR0YoIiIiLCgiIiNGMEkiRUdGKCEiIiokRjNGNEY0RjA3I0Yu</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkicUc2IiIiIiksJkkiRUdGJUYmRiYhIiIiIiNGJkYpRipGKg==</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34305" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">algE:=numer(u-uE)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdFR0YoLCoqJilJIkVHRigiIiMiIiJJInFHRihGM0YzKihGMkYzRjFGM0Y0RjMhIiIqJkYxRjNJInVHRihGM0YzRjRGMzcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34302" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">qE:=factor(solve(%,q))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjcUVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZTLUkmbWZyYWNHRiQ2KC1GIzYmLUYsNiVRInVGJ0YvRjItRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZbby1GLDYlUSJFRidGL0YyRjktSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtRiM2JkZdby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRlJGVC1JI21uR0YkNiRRIjFGJ0Y5RjlGOS1GXHA2JFEiMkYnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUubGluZXRoaWNrbmVzc0dGXnAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXAvJSliZXZlbGxlZEdGPUY5">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNxRUdGKCwkKihJInVHRigiIiJJIkVHRihGMSksJkYyRjFGMSEiIiIiI0Y1RjU3I0Yu</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34285" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(rationalize((Eexpr+1)/(Eexpr-1))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJCksJComLCZJInVHNiIhIiIqJiIiJSIiIkkicUdGKUYtRi1GLUYoRipGKiNGLSIiI0YtRio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34239" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eser:=proc(n) factor(series(Eexpr,q,n+1)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34231" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eser(10)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzdJInFHNiIsJCokSSJ1R0YkISIiRigiIiIsJComIiIjRikpRidGLEYoRihGLCwkKiYiIiZGKSlGJyIiJEYoRihGMiwkKiYiIzlGKSlGJyIiJUYoRihGNywkKiYiI1VGKSlGJ0YwRihGKEYwLCQqJiIkSyJGKSlGJyIiJ0YoRihGQCwkKiYiJEglRikpRiciIihGKEYoRkUsJComIiVJOUYpKUYnIiIpRihGKEZKLCQqJiIlaVtGKSlGJyIiKkYoRihGTy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpIiM1</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34214" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The shift</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34234" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Sser:=proc(n) factor(series(2*q-Eser(n)-q^2/Eser(n),q,n)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34263" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(expand,Sser(10))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzVJInFHNiIsKCIiIyIiIiokSSJ1R0YkISIiRidGKUYnRicsJiomRiZGJylGKUYmRipGJ0YmRipGJiwmKiYiIiZGJylGKSIiJEYqRidGKEYqRjIsJiomIiM5RicpRikiIiVGKkYnRixGKkY3LCYqJiIjVUYnKUYpRjBGKkYnRi9GKkYwLCYqJiIkSyJGJylGKSIiJ0YqRidGNEYqRkAsJiomIiRIJUYnKUYpIiIoRipGJ0Y5RipGRSwmKiYiJUk5RicpRikiIilGKkYnRj1GKkZKLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiciIio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34210" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Recall the definition of theta and cconst</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L35452" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(thetaser)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kiTkc2IjYjSSJuR0YlRiVGJS1JJGFkZEclKnByb3RlY3RlZEc2JCooKSEiIkYnIiIiKUkicUdGJSwkKigjRi8iIiNGL0YnRi8sJkYnRi9GL0YvRi9GL0YvLUkkc2luRzYkRipJKF9zeXNsaWJHRiU2IyomSSJ6R0YlRi8sJiomRjVGL0YnRi9GL0YvRi9GL0YvL0YnOyIiIUYkRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L35453" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">op(cconstser)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kibkc2IkYlRiVGJS1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMtSSdzZXJpZXNHRik2JSwkKiojIiIiIiIpRjIpLUkkc2luR0YoNiNJImFHRiUiIiMhIiItSSVldmFsR0YpNiMtSSVzdWJzR0YpNiQvSSJ6R0YlIiIhLUklZGlmZkdGKTYkLUkpdGhldGFzZXJHRiVGI0ZCRjItRj82JC9GQkY4RkRGOkY6SSJxR0YlRiRGJUYlRiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34212" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">thetaser:=proc(N)
    local n;
    add((-1)^n*q^(1/2*n*(n + 1))*sin(z*(2*n + 1)), n = 0 .. N);
end proc:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34209" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cconstser:=proc(n)
    simplify(series(-1/8*eval(subs(z = 0, diff(thetaser(n), z)))/(sin(a)^2*subs(z = a, diff(thetaser(n), z))), q, n));
end proc:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34277" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">cconstser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIsJCooIyIiIiIiKUYoKS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJhR0YkIiIjISIiLUkkY29zR0YtRjBGM0YzIiIhLCQqJiMiIiRGMkYoRjRGM0YoRigsJCooIyIiKkYyRigsJiomIiIlRigpRjRGMkYoRihGOkYzRihGNEYzRihGMiomLCgqJiIkOyNGKClGNEZBRihGKComIiRNJEYoRkJGKEYzIiRDIkYoRihGNEYzRjotSSJPR0YtNiNGKEZB</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34296" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10: for n from 0 to 4 do series((Eser(N)^(n+1)-Eser(2*N)^(-n))/(Eser(N*2)-1),q,N+2) od</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInFHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNQ==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInFHNiIsJEkidUdGJCEiIkYnIiIkIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiM1</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUYjNiYtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiMkYnL0Y4USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYLUYuNiUtRjE2JVEicUYnRjRGNy1GOzYkUSsmdW1pbnVzMDsyRidGPkZARj4tRkQ2LVEoJm1pbnVzO0YnRj5GR0ZKRkxGTkZQRlJGVC9GV1EsMC4yMjIyMjIyZW1GJy9GWkZhby1GIzYoLUY7NiRRIjVGJ0Y+RkNGMEZDLUYuNiVGZ24tRjs2JFErJnVtaW51czA7MUYnRj5GQEY+LUZENi1RJyZwbHVzO0YnRj5GR0ZKRkxGTkZQRlJGVEZgb0Zib0Zlb0ZdcC1GIzYmLUZENi1RIk9GJ0Y+RkdGSkZMRk5GUEZSRlRGVkZZLUZENi1RMCZBcHBseUZ1bmN0aW9uO0YnRj5GR0ZKRkxGTkZQRlJGVEZWRlktSShtZmVuY2VkR0YkNiQtRiM2Jy1GLjYlRmduLUY7NiRRIzEwRidGPkZALyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRklGPkY+Rj5GPg==">KytJInFHNiIqJClJInVHRiQiIiMiIiIhIiMsJComIiImRilGJ0YpISIiRi5GLSIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpIiM1</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIsJCokKUkidUdGJCIiJCIiIiEiIiEiJCwkKiYiIihGKilGKCIiI0YqRiohIiMsJComIiM5RipGKEYqRitGK0YvIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIio=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIqJClJInVHRiQiIiUiIiIhIiUsJComIiIqRikpRiciIiRGKSEiIiEiJCwkKiYiI0ZGKSlGJyIiI0YpRikhIiMsJComIiNJRilGJ0YpRjBGMEYtIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIik=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34284" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10: for n from 0 to 4 do series((Eser(N)^(n+1)+Eser(2*N)^(-n))/(Eser(N*2)+1),q,N+2) od</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInFHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNg==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInFHNiIsJEkidUdGJCEiIkYnIiIiIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIzY=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIqJClJInVHRiQiIiMiIiIhIiMsJComIiIkRilGJ0YpISIiRi5GKSIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpIiM1</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInFHNiIsJCokKUkidUdGJCIiJCIiIiEiIiEiJCwkKiYiIiZGKilGKCIiI0YqRiohIiMsJComIiInRipGKEYqRitGK0YqIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRioiIio=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIqJClJInVHRiQiIiUiIiIhIiUsJComIiIoRikpRiciIiRGKSEiIiEiJCwkKiYiIzpGKSlGJyIiI0YpRikhIiMsJComIiM1RilGJ0YpRjBGMEYpIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIik=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34260" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tser:=proc(N) local n: factor(series(add ((-1)^n*q^(n*(n+1)/2)* (Eser(N)^(n+1)-Eser(2*N)^(-n))/(Eser(N)-1),n=0..N),q,N+1)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34262" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tser(70)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">K2NzSSJxRzYiLCZJInVHRiQiIiJGJ0YnIiIhLCYqJClGJiIiI0YnRiciIiQhIiJGJywkKiYiIiZGJ0YmRidGLkYsLCYqJClGJkYtRidGJ0YxRidGLSwkKiYiIihGJ0YrRidGLiIiJSwkKiYiIzlGJ0YmRidGJ0YxLCYqJClGJkY4RidGJ0Y3Ri4iIicsJComIiIqRidGNEYnRi5GNywkKiYiI0ZGJ0YrRidGJyIiKSwkKiYiI0lGJ0YmRidGLkZCLCYqJClGJkYxRidGJ0ZCRiciIzUsJComIiM2RidGPkYnRi5GUCwkKiYiI1dGJ0Y0RidGJyIjNywkKiYiI3hGJ0YrRidGLiIjOCwkKiYiI2JGJ0YmRidGJ0Y7LCYqJClGJkY/RidGJ0ZQRi4iIzosJComRlhGJ0ZMRidGLiIjOywkKiYiI2xGJ0Y+RidGJyIjPCwkKiYiJGMiRidGNEYnRi4iIz0sJComIiQjPUYnRitGJ0YnIiM+LCQqJiIjIipGJ0YmRidGLiIjPywmKiQpRiZGN0YnRidGWEYnIiNALCQqJkZpbkYnRmhuRidGLiIjQSwkKiYiIyEqRidGTEYnRiciI0IsJComIiR2I0YnRj5GJ0YuIiNDLCQqJiIkXSVGJ0Y0RidGJyIjRCwkKiYiJHkkRidGK0YnRi4iI0UsJComIiRTIkYnRiZGJ0YnRkUsJiokKUYmRkZGJ0YnRmluRi4iI0csJComRmBvRidGX3BGJ0YuIiNILCQqJiIkPiJGJ0ZobkYnRidGSSwkKiYiJFUlRidGTEYnRi4iI0osJComIiROKkYnRj5GJ0YnIiNLLCQqJiIlQTZGJ0Y0RidGLiIjTCwkKiYiJDkoRidGK0YnRiciI00sJComIiQvI0YnRiZGJ0YuIiNOLCYqJClGJkZCRidGJ0Zgb0YnIiNPLCQqJkZob0YnRmlxRidGLiIjUCwkKiYiJF8iRidGX3BGJ0YnIiNRLCQqJiIkbCdGJ0ZobkYnRi4iI1IsJComIiVIPEYnRkxGJ0YnIiNTLCQqJiIlPEZGJ0Y+RidGLiIjVCwkKiYiJTNERidGNEYnRiciI1UsJComIiVhN0YnRitGJ0YuIiNWLCQqJiIkJkdGJ0YmRidGJ0ZTLCYqJClGJkZNRidGJ0Zob0YuIiNYLCQqJkZgcEYnRmdzRidGLiIjWSwkKiYiJCo9RidGaXFGJ0YnIiNaLCQqJiIkXypGJ0ZfcEYnRi4iI1ssJComIiVTSEYnRmhuRidGJyIjXCwkKiYiJUxkRidGTEYnRi4iI10sJComIiUycUYnRj5GJ0YnIiNeLCQqJiIlW15GJ0Y0RidGLiIjXywkKiYiJXo/RidGK0YnRiciI2AsJComIiQmUUYnRiZGJ0YuIiNhLCYqJClGJkZQRidGJ0ZgcEYnRmVuLCQqJkZncEYnRml1RidGLiIjYywkKiYiJEkjRidGZ3NGJ0YnIiNkLCQqJiIlNjhGJ0ZpcUYnRi4iI2UsJComIiUjcCVGJ0ZfcEYnRiciI2YsJComIiZbNCJGJ0ZobkYnRi4iI2csJComIiZXbiJGJ0ZMRidGJyIjaCwkKiYiJlhrIkYnRj5GJ0YuIiNpLCQqJiIlbikqRidGNEYnRiciI2osJComIiUqRyRGJ0YrRidGLiIjaywkKiYiJDEmRidGJkYnRidGX28tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIjbQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34283" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(u=0,Tser(40))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzVJInFHNiIiIiIiIiEhIiRGJSIiJiIiJCEiKCIiJyIiKiIjNSEjNiIjOiIjOCIjQCEjOiIjRy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiNP</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34230" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=20: Tser(n)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZCLUYjNiYtSSNtaUdGJDYlUSJ1RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEnJnBsdXM7RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4tSSNtbkdGJDYkUSIxRidGO0Y7RjctRiM2Ji1JKG1mZW5jZWRHRiQ2JC1GIzYmLUklbXN1cEdGJDYlRi0tRlI2JFEiMkYnRjsvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY4Ni1RKCZtaW51cztGJ0Y7Rj1GQEZCRkRGRkZIRkpGTEZPLUZSNiRRIjNGJ0Y7RjtGOy1GODYtUTEmSW52aXNpYmxlVGltZXM7RidGO0Y9RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRmlvLUYuNiVRInFGJ0YxRjRGO0Zfby1GIzYoLUZSNiRRIjVGJ0Y7RmVvRi1GZW8tRmduNiVGW3BGaW5GXG9GO0Y3LUYjNiYtRlg2JC1GIzYmLUZnbjYlRi1GYm9GXG9GN0ZgcEY7RjtGZW8tRmduNiVGW3BGYm9GXG9GO0Zfby1GIzYoLUZSNiRRIjdGJ0Y7RmVvRmZuRmVvLUZnbjYlRltwLUZSNiRRIjRGJ0Y7RlxvRjtGNy1GIzYoLUZSNiRRIzE0RidGO0Zlb0YtRmVvLUZnbjYlRltwRmBwRlxvRjtGNy1GIzYmLUZYNiQtRiM2Ji1GZ242JUYtRmZxRlxvRl9vRmFxRjtGO0Zlby1GZ242JUZbcC1GUjYkUSI2RidGO0Zcb0Y7Rl9vLUYjNigtRlI2JFEiOUYnRjtGZW9GW3FGZW8tRmduNiVGW3BGYXFGXG9GO0Y3LUYjNigtRlI2JFEjMjdGJ0Y7RmVvRmZuRmVvLUZnbjYlRltwLUZSNiRRIjhGJ0Y7RlxvRjtGX28tRiM2KC1GUjYkUSMzMEYnRjtGZW9GLUZlby1GZ242JUZbcEZfc0Zcb0Y7RjctRiM2Ji1GWDYkLUYjNiYtRmduNiVGLUZgcEZcb0Y3Rl9zRjtGO0Zlby1GZ242JUZbcC1GUjYkUSMxMEYnRjtGXG9GO0Zfby1GIzYoLUZSNiRRIzExRidGO0Zlb0ZmckZlby1GZ242JUZbcEZkdUZcb0Y7RjctRiM2KC1GUjYkUSM0NEYnRjtGZW9GW3FGZW8tRmduNiVGW3AtRlI2JFEjMTJGJ0Y7RlxvRjtGX28tRiM2KC1GUjYkUSM3N0YnRjtGZW9GZm5GZW8tRmduNiVGW3AtRlI2JFEjMTNGJ0Y7RlxvRjtGNy1GIzYoLUZSNiRRIzU1RidGO0Zlb0YtRmVvLUZnbjYlRltwRltyRlxvRjtGNy1GIzYmLUY4Ni1RIk9GJ0Y7Rj1GQEZCRkRGRkZIRkpGaG9Gam8tRjg2LVEwJkFwcGx5RnVuY3Rpb247RidGO0Y9RkBGQkZERkZGSEZKRmhvRmpvLUZYNiQtRiM2Jy1GZ242JUZbcC1GUjYkUSMxNUYnRjtGXG8vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGP0Y7RjtGO0Y7">K0NJInFHNiIsJkkidUdGJCIiIkYnRiciIiEsJiokKUYmIiIjRidGJyIiJCEiIkYnLCQqJiIiJkYnRiZGJ0YuRiwsJiokKUYmRi1GJ0YnRjFGJ0YtLCQqJiIiKEYnRitGJ0YuIiIlLCQqJiIjOUYnRiZGJ0YnRjEsJiokKUYmRjhGJ0YnRjdGLiIiJywkKiYiIipGJ0Y0RidGLkY3LCQqJiIjRkYnRitGJ0YnIiIpLCQqJiIjSUYnRiZGJ0YuRkIsJiokKUYmRjFGJ0YnRkJGJyIjNSwkKiYiIzZGJ0Y+RidGLkZQLCQqJiIjV0YnRjRGJ0YnIiM3LCQqJiIjeEYnRitGJ0YuIiM4LCQqJiIjYkYnRiZGJ0YnRjstSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIjOg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34250" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(subs(u=4*q*sin(z)^2,convert(Tser(n),polynom)),q,15)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIiIiIiIiEsJiomIiIlRiUpLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJInpHRiQiIiNGJUYlIiIkISIiRiUsKComIiM7RiUpRitGKUYlRiUqJiIjP0YlRipGJUY0IiImRiVGMywqKiYiI2tGJSlGKyIiJ0YlRiUqJiIkNyJGJUY4RiVGNComIiNjRiVGKkYlRiUiIihGNEZALCwqJiIkYyNGJSlGKyIiKUYlRiUqJiIkdyZGJUY/RiVGNComIiRLJUYlRjhGJUYlKiYiJD8iRiVGKkYlRjQiIipGJSIjNS1JIk9HRi02I0YlIiM6</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34228" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(series(sin(z)*%-thetaser(15),q,15))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34229" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34286" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tpser:=proc(N) local n: factor(series(2*add ((-1)^n*q^(n*(n+1)/2)* cos((2*n+1)*a)*(Eser(N)^(n+1)-Eser(2*N)^(-n))/(Eser(N)-1),n=0..N),q,N)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34287" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tpser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIsJiomIiIjIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJImFHRiRGKEYoKihGJ0YoLUYqNiMsJComIiIkRihGL0YoRihGKEkidUdGJEYoRigiIiEsJiomIiInRihGMUYoISIiKihGJ0YoLUYqNiMsJComIiImRihGL0YoRihGKClGNkYnRihGKEYoLCQqKCIjNUYoRj1GKEY2RihGO0YnLUkiT0dGKzYjRihGNQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34207" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,map(expand,%)):
map(factor,subs(cos(a)=sqrt((2-omega)/4),series(%/cos(a),q)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIsKCooIiIjIiIiSSZvbWVnYUdGJEYoSSJ1R0YkRighIiIqJkYnRihGKkYoRitGJ0YoIiIhLCwqKEYnRigpRilGJ0YoKUYqRidGKEYoKihGJ0YoRilGKEYxRihGKComRidGKEYxRihGKyomIiInRihGKUYoRihGNUYoRigsJCooIiM1RihGKkYoLCgqJEYwRihGKEYpRihGKEYrRihGK0YnLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiQ=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34227" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=20: Tpser(n)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34217" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(subs(u=4*q*sin(z)^2,convert(Tpser(n),polynom)),q,15);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34218" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(expand(series(subs(z=z+a,thetaser(n))+subs(z=z-a,thetaser(n))-%*sin(z),q,15)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34219" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34243" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tmser:=proc(N) local n: factor(series(-2*add ((-1)^n*q^(n*(n+1)/2)* sin((2*n+1)*a)*(Eser(N)^(n+1)+Eser(2*N)^(-n))/(Eser(N)+1),n=0..N),q,N)): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34275" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tmser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIsJiomIiIjIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJImFHRiRGKCEiIiooRidGKC1GKjYjLCQqJiIiJEYoRi9GKEYoRihJInVHRiRGKEYwIiIhLCYqJkYnRihGMkYoRigqKEYnRigtRio2IywkKiYiIiZGKEYvRihGKEYoKUY3RidGKEYwRigsJCooIiInRihGPEYoRjdGKEYoRictSSJPR0YrNiNGKEY2</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34206" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">map(factor,map(expand,%)):
map(factor,map(expand,subs(cos(a)=sqrt((2-omega)/4),series(%/sin(a),q))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KytJInFHNiIsKCooIiIjIiIiSSZvbWVnYUdGJEYoSSJ1R0YkRihGKComRidGKEYqRighIiJGJ0YsIiIhLCwqKEYnRigpRilGJ0YoKUYqRidGKEYsKihGJ0YoRilGKEYxRihGKComRidGKEYxRihGKComRidGKEYpRihGLEYnRihGKCwkKigiIidGKEYqRigsKCokRjBGKEYoRilGLEYoRixGKEYoRictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJA==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34225" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=20: Tmser(n)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34223" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(subs(u=4*q*sin(z)^2,convert(Tmser(n),polynom)),q,15);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
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<Group view="code" hide-input="false" labelreference="L34222" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(expand(series(subs(z=z+a,thetaser(n))-subs(z=z-a,thetaser(n))+%*cos(z),q,15)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34235" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34226" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34289" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Behaviour of the  series T under the shift</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34290" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Sser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInFHNiIqJiksJkkidUdGJCIiIkYpRikiIiNGKUYoISIiRiksJCoqRipGKSwmRihGKUYpRitGKUYnRikpRihGKkYrRitGKi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpIiIk</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34246" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us work with the expressions in terms of E</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34238" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tserform:=proc(N)
    local n;
    add((-1)^n*q^(1/2*n*(n + 1))*(E^(n + 1) - E^(-n))/(E - 1), n = 0 .. N):
end proc:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34300" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tserform(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwiIiJGIyooSSJxRzYiRiMsJiokKUkiRUdGJiIiI0YjRiMqJEYqISIiRi1GIywmRipGI0YjRi1GLUYtKigpRiUiIiRGIywmKiQpRipGMUYjRiMqJEYpRi1GLUYjRi5GLUYjKigpRiUiIidGIywmKiQpRioiIiVGI0YjKiRGNEYtRi1GI0YuRi1GLSooKUYlIiM1RiMsJiokKUYqIiImRiNGIyokRjtGLUYtRiNGLkYtRiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34297" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tpserform:=proc(N)
    local n;
    2*add((-1)^n*q^(1/2*n*(n + 1))*cos((2*n + 1)*a)*(E^(n + 1) - E^(-n))/(E - 1), n = 0 .. N);
end proc:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34303" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tpserform(3)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCoqJiIiIyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJhR0YrRiVGJSosRiRGJUkicUdGK0YlLUYnNiMsJComIiIkRiVGLUYlRiVGJSwmKiQpSSJFR0YrRiRGJUYlKiRGOCEiIkY6RiUsJkY4RiVGJUY6RjpGOiosRiRGJSlGL0Y0RiUtRic2IywkKiYiIiZGJUYtRiVGJUYlLCYqJClGOEY0RiVGJSokRjdGOkY6RiVGO0Y6RiUqLEYkRiUpRi8iIidGJS1GJzYjLCQqJiIiKEYlRi1GJUYlRiUsJiokKUY4IiIlRiVGJSokRkVGOkY6RiVGO0Y6Rjo=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34211" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Tmserform:=proc(N)
    local n;
    -2*add((-1)^n*q^(1/2*n*(n + 1))*sin((2*n + 1)*a)*(E^(n + 1) + E^(-n))/(E + 1), n = 0 .. N);
end proc:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34306" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Checking the three identities</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34298" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20:factor(series( subs(E=E/q,Tserform(N))/Tserform(N),q,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">K0NJInFHNiIsJiIiIkYmSSJFR0YkISIiIiIhLCQqJiwmRidGJkYmRihGJkYnRihGKEYmLCQqJkYsRiYpRiciIiNGKEYoRjAsJComRixGJilGJyIiJEYoRihGNCwkKiZGLEYmKUYnIiIlRihGKEY4LCQqJkYsRiYpRiciIiZGKEYoRjwsJComRixGJilGJyIiJ0YoRihGQCwkKiZGLEYmKUYnIiIoRihGKEZELCQqJkYsRiYpRiciIilGKEYoRkgsJComRixGJilGJyIiKkYoRihGTCwkKiZGLEYmKUYnIiM1RihGKEZQLCQqJkYsRiYpRiciIzZGKEYoRlQsJComRixGJilGJyIjN0YoRihGWCwkKiZGLEYmKUYnIiM4RihGKEZmbiwkKiZGLEYmKUYnIiM5RihGKEZqbi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YmIiM6</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34304" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(convert(%,ratpoly))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiRUc2IiIiIiwmRiRGJkYmISIiRiYsJkYkRiZJInFHRiVGKEYoRig=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34247" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: simplify(normal(expand(series((q-E)*subs(E=E/q,Tpserform(N)) -cos(2*a)*E*(E-1)*Tpserform(N)-sin(2*a)*E*(1+E)*Tmserform(N) ,q,N))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34295" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20: simplify(normal(expand(series((q+E)*subs(E=E/q,Tmserform(N)) -sin(2*a)*E*(E-1)*Tpserform(N)+cos(2*a)*E*(1+E)*Tmserform(N) ,q,N))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34244" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The resulting expressions of shifted T-series</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34245" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">TS:=E*(E-1)*T/(q-E);
TpS:=(cos(2*a)*E*(E-1)*Tp+sin(2*a)*E*(E+1)*Tm)/(q-E);
TmS:=(sin(2*a)*E*(E-1)*Tp-cos(2*a)*E*(E+1)*Tm)/(q+E)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNUU0dGKCoqSSJFR0YoIiIiLCZGL0YwRjAhIiJGMEkiVEdGKEYwLCZJInFHRihGMEYvRjJGMjcjRi4=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEkVHBTRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2Ji1GIzYqLUYjNiYtRiw2JVEkY29zRicvRjBGPUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZqbi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEiMkYnRjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZpbkZbby1GLDYlUSJhRidGL0YyRjlGOUY5RmVvLUYsNiVRIkVGJ0YvRjJGZW8tRl1vNiQtRiM2JkZbcC1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmZwLUZibzYkUSIxRidGOUY5RjlGZW8tRiw2JVEjVHBGJ0YvRjJGOS1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkhGZXBGZ3AtRiM2Ki1GIzYmLUYsNiVRJHNpbkYnRmVuRjlGZm5GXG9GOUZlb0ZbcEZlby1GXW82JC1GIzYmRltwRl5xRmhwRjlGOUZlby1GLDYlUSNUbUYnRi9GMkY5RjktRiM2Ji1GLDYlUSJxRidGL0YyRmJwRltwRjkvJS5saW5ldGhpY2tuZXNzR0ZqcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zoci8lKWJldmVsbGVkR0Y9Rjk=">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRUcFNHRigqJiwmKiotSSRjb3NHRiU2IywkKiYiIiMiIiJJImFHRihGN0Y3RjdJIkVHRihGNywmRjlGN0Y3ISIiRjdJI1RwR0YoRjdGNyoqLUkkc2luR0YlRjNGN0Y5RjcsJkY5RjdGN0Y3RjdJI1RtR0YoRjdGN0Y3LCZJInFHRihGN0Y5RjtGOzcjRi4=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRUbVNHRigqJiwmKiotSSRzaW5HRiU2IywkKiYiIiMiIiJJImFHRihGN0Y3RjdJIkVHRihGNywmRjlGN0Y3ISIiRjdJI1RwR0YoRjdGNyoqLUkkY29zR0YlRjNGN0Y5RjcsJkY5RjdGN0Y3RjdJI1RtR0YoRjdGO0Y3LCZJInFHRihGN0Y5RjdGOzcjRi4=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34291" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The series X</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34288" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xser:=proc(N)factor( simplify(factor(series(cconstser(N+3)*Tpser(N+3)/Tser(N+3)+1/4/sin(a)^2,q,N+1)))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34274" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xser(2);Xser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34261" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(u=0,Xser(4))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34251" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=20:map(factor,series(subs(q=q*(1+u),(1+u)*Xser(n)),q,n)):
map(degree,%,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">K0tJInFHNiIiIiIiIiEiIiRGJSIiJiIiIyIiKEYnIiIqIiIlIiM2RigiIzgiIiciIzpGKiIjPCIiKSIjPkYrIiNAIiM1IiNCRi0iI0QiIzciI0ZGLiIjSCIjOSIjSkYwIiNMIiM7IiNORjEiI1AiIz0iI1JGMw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34278" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Connection with chi</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34241" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=5: normal(series(subs(u=4*q*sin(z)^2, convert(Xser(n),polynom)),q,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34221" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">normal(series(%-chiser(n),q,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34255" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xpser:=proc(N) factor( simplify(factor(series(
cconstser(N)*cos(2*a)*Tpser(N+3)/Tser(N+3)
+cconstser(N+3)*sin(2*a)*sqrt(1-4*q/u)*Tmser(N+3)/Tser(N+3)
+1/4/sin(a)^2,q,N)))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34248" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xpser(4)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkmbWZyYWNHRiQ2KC1GIzYoLUYjNigtSSNtbkdGJDYkUSI0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1JJW1zdXBHRiQ2JS1GIzYmLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHRj9GNi1GOjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y2Rj1GQEZCRkRGRkZIRkpGTEZPLUkobWZlbmNlZEdGJDYkLUYjNictRlc2JVEiYUYnL0ZlblEldHJ1ZUYnL0Y3USdpdGFsaWNGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y/RjZGNkY2LUYzNiRRIjJGJ0Y2LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5LUZXNiVRInVGJ0Zhb0Zjb0Y2LUY6Ni1RKCZtaW51cztGJ0Y2Rj1GQEZCRkRGRkZIRkovRk1RLDAuMjIyMjIyMmVtRicvRlBGanBGY3AtRjo2LVEnJnBsdXM7RidGNkY9RkBGQkZERkZGSEZKRmlwRltxLUYzNiRRIjFGJ0Y2RjYtRiM2JkZjcEZccUZfcUY2LyUubGluZXRoaWNrbmVzc0dGYXEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaHEvJSliZXZlbGxlZEdGP0ZccS1GIzYmLUYsNigtRiM2OC1GIzYoLUYzNiRRIzE2RidGNkY5LUZSNiVGVEYyRmBwRjktRlI2JUZjcEYyRmBwRjZGXHEtRiM2KC1GMzYkUSM2NEYnRjZGOUZockY5LUZSNiVGY3AtRjM2JFEiM0YnRjZGYHBGNkZccS1GIzYoLUYzNiRRIzQ4RidGNkY5RmhyRjktRlI2JUZjcEZdcEZgcEY2RmZwLUYjNihGZXJGOUZRRjlGanJGNkZmcC1GIzYoLUYzNiRRIzcyRidGNkY5RlFGOUZhc0Y2RmZwLUYjNihGaHNGOUZRRjlGW3RGNkZccS1GIzYmRmNzRjlGanJGNkZccS1GIzYmRmVyRjlGYXNGNkZccS1GIzYmLUYzNiRRIjZGJ0Y2RjlGW3RGNkZmcC1GIzYmRjJGOUZjcEY2RmZwRl9xRjYtRiM2JkZjcEY5LUZSNiUtRmpuNiRGYnFGNkZdcEZgcEY2RmRxRmZxRmlxRltyRjktRlc2JVEicUYnRmFvRmNvRjZGXHEtRiM2Ji1GLDYoLUYjNlItRiM2KC1GMzYkUSQxOTJGJ0Y2RjktRlI2JUZURlx1RmBwRjktRlI2JUZjcEZcdUZgcEY2RlxxLUYjNigtRjM2JFEkOTYwRidGNkY5RmV2RjktRlI2JUZjcC1GMzYkUSI1RidGNkZgcEY2RmZwLUYjNihGZXJGOUZockY5LUZSNiVGY3AtRjM2JFEiN0YnRjZGYHBGNkZccS1GIzYoLUYzNiRRJTEzNDRGJ0Y2RjlGZXZGOUZqckY2RmZwLUYjNigtRjM2JFEkNDAwRidGNkY5RmhyRjlGZ3ZGNkZccS1GIzYoLUYzNiRRJDU3NkYnRjZGOUZldkY5RmFzRjZGZnAtRiM2KC1GMzYkUSUxOTA0RidGNkY5RmhyRjlGXndGNkZccS1GIzYoRmVyRjlGUUY5RmV3RjZGZnAtRiM2KC1GMzYkUSUyNjA4RidGNkY5RmhyRjlGanJGNkZccS1GIzYoLUYzNiRRJDI0MEYnRjZGOUZRRjlGZ3ZGNkZmcC1GIzYoLUYzNiRRJTEwODhGJ0Y2RjlGaHJGOUZhc0Y2RlxxLUYjNigtRjM2JFElMTEzNkYnRjZGOUZRRjlGXndGNkZmcC1GIzYmRmNzRjlGZXdGNkZccS1GIzYoLUYzNiRRJTE0OTZGJ0Y2RjlGUUY5RmpyRjZGZnAtRiM2Ji1GMzYkUSMzN0YnRjZGOUZndkY2RlxxLUYjNigtRjM2JFEkNTUyRidGNkY5RlFGOUZhc0Y2RmZwLUYjNiYtRjM2JFEkMTg5RidGNkY5Rl53RjZGZnAtRiM2KC1GMzYkUSM2MEYnRjZGOUZRRjlGW3RGNkZmcC1GIzYmLUYzNiRRJDIyM0YnRjZGOUZqckY2RmZwLUYjNigtRjM2JFEjMTJGJ0Y2RjlGUUY5RmNwRjZGZnAtRiM2JkZdW2xGOUZhc0Y2RlxxLUYjNiYtRjM2JFEjNDdGJ0Y2RjlGW3RGNkZccS1GIzYmRmd3RjlGY3BGNkZmcEZfcUY2LUYjNiZGW3RGOS1GUjYlRmV1RmNzRmBwRjZGZHFGZnFGaXFGW3JGOS1GUjYlRmd1Rl1wRmBwRjZGXHEtRiM2Ji1GLDYoLUYjNl9wLUY6Ni1RKiZ1bWludXMwO0YnRjZGPUZARkJGREZGRkhGSkZpcEZbcUZdcEZccS1GIzYoLUYzNiRRJjIzMDQwRidGNkY5LUZSNiVGVC1GMzYkUSI4RidGNkZgcEY5Rl53RjZGXHEtRiM2KC1GMzYkUSU2OTEyRidGNkY5RmZebEY5RmpyRjZGZnAtRiM2KC1GMzYkUSY3NTc3NkYnRjZGOUZldkY5Rmd2RjZGZnAtRiM2Ji1GMzYkUSQ0ODRGJ0Y2RjlGYXNGNkZmcC1GIzYmLUYzNiRRJDEwMUYnRjZGOUZqckY2RlxxLUYjNigtRjM2JFElMTMwNEYnRjZGOUZRRjlGYXNGNkZccS1GIzYoLUYzNiRRJDE2OEYnRjZGOUZRRjlGW3RGNkZmcC1GIzYoLUYzNiRRJjIyMzM2RidGNkY5RlFGOUZed0Y2RmZwLUYjNigtRjM2JFElNDQyNEYnRjZGOUZRRjlGanJGNkZmcC1GIzYoRmVyRjlGUUY5RmNwRjZGXHEtRiM2KC1GMzYkUSY3NDA0OEYnRjZGOUZockY5Rmd2RjZGXHEtRiM2KC1GMzYkUSY1OTUyMEYnRjZGOUZockY5Rl53RjZGZnAtRiM2KC1GMzYkUSYxNTU2OEYnRjZGOUZRRjlGZXdGNkZccS1GIzYoLUYzNiRRJjE2MTc2RidGNkY5RmhyRjlGanJGNkZmcC1GIzYoLUYzNiRRJjI5NjcyRidGNkY5RlFGOUZndkY2RmZwLUYjNigtRjM2JFEkODY0RidGNkY5RmhyRjlGYXNGNkZccS1GIzYoLUYzNiRRJTIzMDRGJ0Y2RjlGZl5sRjktRlI2JUZjcEZoXmxGYHBGNkZccS1GIzYoLUYzNiRRJjEzODI0RidGNkY5RmZebEY5RmV3RjZGZnAtRiM2KC1GMzYkUSQxMjhGJ0Y2RjlGZXZGOS1GUjYlRmNwLUYzNiRRIjlGJ0Y2RmBwRjZGXHEtRiM2KC1GMzYkUSYyNzY0OEYnRjZGOUZmXmxGOUZndkY2RmZwLUYjNigtRjM2JFElNjUyOEYnRjZGOUZldkY5RmhjbEY2RlxxLUYjNihGZXJGOUZockY5LUZSNiVGY3AtRjM2JFEjMTBGJ0Y2RmBwRjZGZnAtRiM2KC1GMzYkUSYzODE0NEYnRjZGOUZldkY5RmV3RjZGXHEtRiM2KC1GMzYkUSQzMjBGJ0Y2RjlGaHJGOUZkZGxGNkZmcC1GIzYoRmVyRjlGUUY5RmVlbEY2RlxxLUYjNigtRjM2JFElNjczNkYnRjZGOUZockY5RmhjbEY2RlxxLUYjNigtRjM2JFEmMzc4NTZGJ0Y2RjlGaHJGOUZld0Y2RmZwLUYjNigtRjM2JFEkMjE2RidGNkY5RlFGOUZkZGxGNkZmcC1GIzYoLUYzNiRRJTI4NTZGJ0Y2RjlGUUY5RmhjbEY2RmZwLUYjNigtRjM2JFEkMTQ0RidGNkY5RmhyRjlGW3RGNkZccS1GIzYmLUYzNiRRIzM2RidGNkY5RmRkbEY2RlxxLUYjNiYtRjM2JFEkMzc5RidGNkY5RmhjbEY2RlxxLUYjNiYtRjM2JFElMjExMkYnRjZGOUZld0Y2RlxxLUYjNiYtRjM2JFElMzg1NUYnRjZGOUZndkY2RmZwLUYjNigtRjM2JFEmNjI1OTJGJ0Y2RjlGZXZGOUZed0Y2RmZwLUYjNigtRjM2JFEmMTg1NjBGJ0Y2RjlGZXZGOUZqckY2RlxxLUYjNiYtRjM2JFElMjQyOEYnRjZGOUZed0Y2RmZwLUYjNiYtRjM2JFEjNTRGJ0Y2RjlGW3RGNkZccS1GIzYmRmNzRjlGZWVsRjZGXHFGX3VGNi1GIzYmRmFzRjktRlI2JUZldUYyRmBwRjZGZHFGZnFGaXFGW3JGOS1GUjYlRmd1RmNzRmBwRjZGXHEtRiM2Ji1GOjYtUSJPRidGNkY9RkBGQkZERkZGSEZKRkxGT0Zmbi1Gam42JC1GIzYnLUZSNiVGZ3VGMkZgcEZlb0Zob0ZbcEY2RjZGNkY2">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34267" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xmser:=proc(N) factor( simplify(factor(series(cconstser(N)*cos(2*a)*Tpser(N)/Tser(N)-cconstser(N)*sin(2*a)*sqrt(1-4*q/u)*Tmser(N)/Tser(N)+1/4/sin(a)^2,q,N)))): end:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34273" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xmser(8);</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIqJiksJkkidUdGJCIiIkYpRikiIiNGKUYoISIiRikqKClGKEYqRitGJ0YpLC4qKCIjN0YpKS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJhR0YkRipGKUYtRilGKSooRjBGKUYxRilGKEYpRikqJClGKCIiJEYpRisqJiIiKkYpRi1GKUYrKiYiIzZGKUYoRilGK0YpRilGKUYqKiZGO0YrLEAqKCIkVyJGKSlGMiIiJUYpKUYoRkZGKUYpKigiJClHRilGRUYpRjtGKUYpKigiIilGKUYxRikpRigiIiZGKUYrKihGREYpRkVGKUYtRilGKSooIiRLI0YpRjFGKUZHRilGKyokKUYoIiInRilGKSooIiRzJUYpRjFGKUY7RilGKyomRktGKUZMRilGKSooRlBGKUYxRilGLUYpRisqJiIjJipGKUZHRilGKSooIiM7RilGMUYpRihGKUYpKiYiJCk9RilGO0YpRikqJiIjISpGKUYtRilGKSomRjBGKUYoRilGK0YqRilGKUY8KiZGR0YrLFIqKCIlRzxGKSlGMkZTRilGTEYpRikqKCIlY01GKUZfb0YpRkdGKUYpKigiIycqRilGRUYpRlJGKUYrKihGXm9GKUZfb0YpRjtGKUYpKigiJWdURilGRUYpRkxGKUYrKihGS0YpRjFGKSlGKCIiKEYpRikqKCIlOyUpRilGRUYpRkdGKUYrKigiJGsiRilGMUYpRlJGKUYpKiQpRihGS0YpRisqKEZmb0YpRkVGKUY7RilGKyooIiU3TEYpRjFGKUZMRilGKSomRktGKUZob0YpRisqKCIkIz5GKUZFRilGLUYpRikqKCIlN25GKUYxRilGR0YpRikqJiIjd0YpRlJGKUYrKigiJW9LRilGMUYpRjtGKUYpKiYiJHcpRilGTEYpRisqKCIkKyRGKUYxRilGLUYpRisqJiIlWTxGKUZHRilGKyooIiNPRilGMUYpRihGKUYpKiYiJE0pRilGO0YpRisqJiIkNSJGKUYtRilGKSomIiNFRilGKEYpRitGTUYpRilGRiomRkxGKyxibyIjOUYpKigiJnM5JUYpKUYyRktGKUZMRilGKSooIiZPMiNGKUZfckYpRkdGKUYpKigiJktrJ0YpRl9vRilGUkYpRisqJiIlNzVGKUY7RilGKyomIiVheEYpRkdGKUYpKigiJT9URilGMUYpRjtGKUYpKigiJHMnRilGMUYpRi1GKUYrKigiJl9SKUYpRjFGKUZMRilGKyooIiY3MiVGKUYxRilGR0YpRisqKEZjb0YpRjFGKUYoRilGKSooIiYlPXpGKUZFRilGUkYpRikqKCInKUdnIkYpRkVGKUZMRilGKSooIiVrQ0YpRjFGKUZob0YpRisqKCImYyd5RilGRUYpRkdGKUYpKigiJis7JUYpRjFGKUZSRilGKyooIiUzYUYpRkVGKUY7RilGKyooRmFyRilGX3JGKUZSRilGKSooIiVfNkYpRl9vRilGaG9GKUYrKihGY29GKUZFRilGX3BGKUYpKigiJTdIRilGRUYpRmhvRilGKSooRktGKUYxRikpRihGPkYpRisqKCIkbyJGKUYxRilGX3BGKUYrKigiJEslRilGRUYpRi1GKUYpKiZGS0YpRmR0RilGKSomIiMhKUYpRl9wRilGKSomIiQvKEYpRmhvRilGKSomIiVNIilGKUZSRilGKSooIic7UzhGKUZfb0YpRkxGKUYrKihGY3JGKUZfb0YpRkdGKUYrKigiJS9CRilGX29GKUY7RilGKSomIiY3aSJGKUZMRilGKSomIiRVI0YpRi1GKUYpKiQpRigiIzVGKUYpKiYiI29GKUYoRilGK0YpRk0tSSJPR0Y0NiNGKUZT</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34213" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=15: map(degree, Xmser(n),u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KzVJInFHNiIiIiJGJSIiI0YmIiIkRiciIiVGKCIiJkYpIiInRioiIihGKyIiKUYsIiIqRi0=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34269" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=10: simplify(factor(series(Xpser(N)+Xmser(N)-2*cos(2*a)*Xser(N),q,N)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInFHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" hide-input="false" labelreference="L34249" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(expand(rationalize((Eexpr+1)/(Eexpr-1))))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJCksJComLCZJInVHNiIhIiIqJiIiJSIiIkkicUdGKUYtRi1GLUYoRipGKiNGLSIiI0YtRio=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34271" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The shift identities</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=5: factor(series(subs(u=convert(Sser(N+2),polynom),convert( Xser(N+2),polynom)),q,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34270" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%-Xmser(8),q))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KyVJInFHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34237" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Now a proof</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34292" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">XT:=c*Tp/T+1/4/sin(a)^2;
XpT:=c*(cos(2*a)*Tp/T+sin(2*a)*sqrt(1-4*q/u)*Tm/T)+ 1/4/sin(a)^2;
XmT:=c*(cos(2*a)*Tp/T-sin(2*a)*sqrt(1-4*q/u)*Tm/T)+ 1/4/sin(a)^2;</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNYVEdGKCwmKihJImNHRigiIiJJI1RwR0YoRjFJIlRHRighIiJGMSomI0YxIiIlRjEpLUkkc2luR0YlNiNJImFHRigiIiNGNEYxNyNGLg==</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRYcFRHRigsJiomSSJjR0YoIiIiLCYqKC1JJGNvc0dGJTYjLCQqJiIiI0YxSSJhR0YoRjFGMUYxSSNUcEdGKEYxSSJUR0YoISIiRjEqKi1JJHNpbkdGJUY2RjEpLCZGMUYxKigiIiVGMUkicUdGKEYxSSJ1R0YoRj1GPSNGMUY5RjFJI1RtR0YoRjFGPEY9RjFGMUYxKiYjRjFGREYxKS1GQDYjRjpGOUY9RjE3I0Yu</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRYbVRHRigsJiomSSJjR0YoIiIiLCYqKC1JJGNvc0dGJTYjLCQqJiIiI0YxSSJhR0YoRjFGMUYxSSNUcEdGKEYxSSJUR0YoISIiRjEqKi1JJHNpbkdGJUY2RjEpLCZGMUYxKigiIiVGMUkicUdGKEYxSSJ1R0YoRj1GPSNGMUY5RjFJI1RtR0YoRjFGPEY9Rj1GMUYxKiYjRjFGREYxKS1GQDYjRjpGOUY9RjE3I0Yu</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34264" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The shift identities</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34236" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">TS;TpS;TmS</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2KC1JI21pR0YkNiVRIkVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk8tSShtZmVuY2VkR0YkNiQtRiw2JkYuLUY5Ni1RKCZtaW51cztGJ0Y8Rj5GQUZDRkVGR0ZJRksvRk5RLDAuMjIyMjIyMmVtRicvRlFGZW4tSSNtbkdGJDYkUSIxRidGPEY8RjxGOC1GLzYlUSJURidGMkY1RjwtRiw2Ji1GLzYlUSJxRidGMkY1RldGLkY8LyUubGluZXRoaWNrbmVzc0dGam4vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ28vJSliZXZlbGxlZEdGQA==">KipJIkVHNiIiIiIsJkYjRiVGJSEiIkYlSSJUR0YkRiUsJkkicUdGJEYlRiNGJ0Yn</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsJioqLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComIiIjIiIiSSJhR0YqRi9GL0YvSSJFR0YqRi8sJkYxRi9GLyEiIkYvSSNUcEdGKkYvRi8qKi1JJHNpbkdGJ0YrRi9GMUYvLCZGMUYvRi9GL0YvSSNUbUdGKkYvRi9GLywmSSJxR0YqRi9GMUYzRjM=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsJioqLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComIiIjIiIiSSJhR0YqRi9GL0YvSSJFR0YqRi8sJkYxRi9GLyEiIkYvSSNUcEdGKkYvRi8qKi1JJGNvc0dGJ0YrRi9GMUYvLCZGMUYvRi9GL0YvSSNUbUdGKkYvRjNGLywmRjFGL0kicUdGKkYvRjM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34281" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(subs(sqrt(1 - 4*q/u)=(1+E)/(1-E),subs(T=TS,Tp=TpS,XT)-XmT))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34216" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand( XpT*XmT);indets(%)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDIqLCIiJSIiIilJImNHNiIiIiNGJSlJI1RwR0YoRilGJSlJIlRHRihGKSEiIiktSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2I0kiYUdGKEYkRiVGJSosRiRGJUYmRiVGKkYlRixGLilGMEYpRiVGLiosRidGJUYrRiVGLUYuRjhGJSktSSRzaW5HRjJGNUYpRi5GJSooRiZGJUYqRiVGLEYuRiUqLCNGJUYpRiVGJ0YlRitGJUYtRi5GOkYuRi4qLkYkRiVGJkYlKUkjVG1HRihGKUYlRixGLkY6RiVGOEYlRi4qMiIjO0YlRiZGJUZBRiVGLEYuRjpGJUY4RiVJInFHRihGJUkidUdGKEYuRiUqJiNGJUZERiUpRjtGJEYuRiU=</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCtJIlRHNiJJI1RtR0YkSSNUcEdGJEkiYUdGJEkiY0dGJEkicUdGJEkidUdGJC1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRictSSRzaW5HRi1GMA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34299" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">numer(factor(simplify(subs(sqrt(1 - 4*q/u)=(1+E)/(1-E),
subs({Tp=TpS, Tm=TmS,T=TS,u=2*q-E-q^2/E}, expand( XpT*XmT))
-XT*(1-XT+2*cos(2*a)*XmT))))); </Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34258" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Let us check for the product</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34252" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=8: ser:=factor(series(u*Xpser(N)*Xmser(N),q,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEkc2VyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEpJkFzc2lnbjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYmLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJ1RidGL0YyLUY2Ni1RJyZwbHVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZpbi1JI21uR0YkNiRRIjFGJ0Y5RjlGOS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmNvLUZUNiQtRiM2KC1GIzYoLUZcbzYkUSI0RidGOUZfby1JJW1zdXBHRiQ2JS1GIzYmLUYsNiVRJGNvc0YnL0YwRj1GOS1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGYm9GZG8tRlQ2JC1GIzYnLUYsNiVRImFGJ0YvRjIvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RjlGOS1GXG82JFEiMkYnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRl9vRlhGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmhuRmpuRlhGZW5GW29GOUY5RjlGX28tRiw2JVEicUYnRi9GMkY5RmVuLUYjNiYtRlQ2JC1GIzY4LUYjNigtRlxvNiRRIzE2RidGOUZfby1GX3A2JUZhcEZbcEZcckZfby1GX3A2JUZYLUZcbzYkUSIzRidGOUZcckY5RmVuLUYjNigtRlxvNiRRJDExMkYnRjlGX29GYHNGX28tRl9wNiVGWEZpcUZcckY5RmVuLUYjNigtRlxvNiRRIzk2RidGOUZfb0ZYRl9vRmBzRjlGX3ItRiM2KC1GXG82JFEjMjBGJ0Y5Rl9vRl5wRl9vRmJzRjlGX3ItRiM2KC1GXG82JFEkMTIwRidGOUZfb0ZecEZfb0ZcdEY5Rl9yLUYjNigtRlxvNiRRIzkyRidGOUZfb0ZecEZfb0ZYRjlGZW4tRiM2JkZbcEZfb0Zic0Y5RmVuLUYjNiZGXXNGX29GXnBGOUZlbi1GIzYmLUZcbzYkUSMyNEYnRjlGX29GXHRGOUZlbi1GIzYmLUZcbzYkUSI4RidGOUZfb0ZYRjlGX3JGXXNGOUY5Rl9vLUZfcDYlRmJyRmlxRlxyRjlGZW4tRiM2Ji1GVDYkLUYjNkYtRiM2KC1GXG82JFEkMzg0RidGOUZfby1GX3A2JUZhcC1GXG82JFEiNkYnRjlGXHJGX29GYnNGOUZlbi1GIzYoLUZcbzYkUSUyMTEyRidGOUZfb0Zdd0Zfb0ZcdEY5Rl9yLUYjNigtRlxvNiRRIzMyRidGOUZfb0Zgc0Zfby1GX3A2JUZYRltwRlxyRjlGZW4tRiM2KC1GXG82JFElMTcyOEYnRjlGX29GWEZfb0Zdd0Y5Rl9yLUYjNigtRlxvNiRRJDgwMEYnRjlGX29GYHNGX29GYnNGOUZfci1GIzYoLUZcbzYkUSU0MDMyRidGOUZfb0Zgc0Zfb0ZcdEY5RmVuLUYjNigtRlxvNiRRIzM2RidGOUZfb0ZecEZfb0ZceEY5Rl9yLUYjNigtRlxvNiRRJTMxNjhGJ0Y5Rl9vRlhGX29GYHNGOUZlbi1GIzYoLUZcbzYkUSQ0OTZGJ0Y5Rl9vRl5wRl9vRmJzRjlGZW4tRiM2Ji1GXG82JFEkMjU2RidGOUZfb0Zgc0Y5RmVuLUYjNigtRlxvNiRRJTIzNDRGJ0Y5Rl9vRl5wRl9vRlx0RjlGX3ItRiM2Ji1GXG82JFEiN0YnRjlGX29GXHhGOUZlbi1GIzYoLUZcbzYkUSUxNjE2RidGOUZfb0ZecEZfb0ZYRjlGX3ItRiM2Ji1GXG82JFEjODBGJ0Y5Rl9vRmJzRjlGX3ItRiM2Ji1GXG82JFEkNDY0RidGOUZfb0ZecEY5Rl9yLUYjNiYtRlxvNiRRJDM3OUYnRjlGX29GXHRGOUZfci1GIzYmLUZcbzYkUSQxNjBGJ0Y5Rl9vRlhGOUZlbi1GXG82JFEkMjA4RidGOUY5RjlGX28tRl9wNiVGYnJGZHNGXHJGOUZlbi1GIzYmLUZUNiQtRiM2Vy1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGaG5Gam4tRlxvNiRRJTI0OTZGJ0Y5RmVuLUYjNigtRlxvNiRRJTY5MTJGJ0Y5Rl9vLUZfcDYlRmFwRl12RlxyRl9vRmJzRjlGZW4tRiM2KC1GXG82JFEmMzQ1NjBGJ0Y5Rl9vRmpdbEZfb0ZcdEY5RmVuLUYjNigtRlxvNiRRJjI3NjQ4RidGOUZfb0ZYRl9vRmpdbEY5RmVuLUYjNiYtRlxvNiRRJTM4NDBGJ0Y5Rl9vRl13RjlGX3ItRiM2Ji1GXG82JFEmMTAxMTJGJ0Y5Rl9vRmBzRjlGZW4tRiM2Ji1GXG82JFElMTE2MkYnRjlGX29GYnNGOUZlbi1GIzYmLUZcbzYkUSQxMjhGJ0Y5Rl9vRlx4RjlGX3ItRiM2KC1GXG82JFElODYyNEYnRjlGX29GXnBGX29GYnNGOUZfci1GIzYoLUZcbzYkUSYzNzA5NkYnRjlGX29GXnBGX29GXHRGOUZlbi1GIzYoLUZcbzYkUSY2ODA2NEYnRjlGX29GWEZfb0Zgc0Y5Rl9yLUYjNigtRlxvNiRRIzUyRidGOUZfb0ZecEZfby1GX3A2JUZYLUZcbzYkUSI1RidGOUZcckY5Rl9yLUYjNihGZXhGX29GXnBGX29GXHhGOUZfci1GIzYoLUZcbzYkUSYyNDI1MkYnRjlGX29GXnBGX29GWEY5RmVuLUYjNigtRlxvNiRRIzQ4RidGOUZfb0Zgc0Zfb0ZeYWxGOUZlbi1GIzYoLUZcbzYkUSUxMzEyRidGOUZfb0Zgc0Zfb0ZceEY5RmVuLUYjNigtRlxvNiRRJjIwNDAwRidGOUZfb0Zgc0Zfb0Zic0Y5RmVuLUYjNigtRlxvNiRRJjkxNzI4RidGOUZfb0Zgc0Zfb0ZcdEY5RmVuLUYjNiYtRlxvNiRRJTg3NjhGJ0Y5Rl9vRl5wRjlGX3ItRiM2KC1GXG82JFEkNjQwRidGOUZfb0Zdd0Zfb0ZceEY5Rl9yLUYjNigtRlxvNiRRJjE5ODQwRidGOUZfb0Zdd0Zfb0Zic0Y5Rl9yLUYjNigtRlxvNiRRJjk0MDgwRidGOUZfb0Zdd0Zfb0ZcdEY5Rl9yLUYjNigtRlxvNiRRJjczNzI4RidGOUZfb0ZYRl9vRl13RjlGZW4tRiM2Ji1GXG82JFEjMTBGJ0Y5Rl9vRl5hbEY5RmVuLUYjNiYtRlxvNiRRJTQ5ODRGJ0Y5Rl9vRlx0RjlGZW4tRiM2Ji1GXG82JFElMjI5NkYnRjlGX29GWEY5RjlGOUZfby1GX3A2JUZickZbcEZcckY5RmVuLUYjNiYtRlQ2JC1GIzZiby1GXG82JFEmMjg0MzJGJ0Y5Rl9yLUYjNigtRlxvNiRRJjEwNzUyRidGOUZfb0ZqXWxGX29GXHhGOUZfci1GIzYoLUZcbzYkUSc0MDQ5OTJGJ0Y5Rl9vRmpdbEZfb0Zic0Y5Rl9yLUYjNigtRlxvNiRRKDE4NTM0NDBGJ0Y5Rl9vRmpdbEZfb0ZcdEY5Rl9yLUYjNigtRlxvNiRRKDE0NDUzNzZGJ0Y5Rl9vRlhGX29Gal1sRjlGX3ItRiM2Ji1GXG82JFEnMTkwNDY0RidGOUZfb0Zdd0Y5RmVuLUYjNiYtRlxvNiRRJzI0MzU4NEYnRjlGX29GYHNGOUZlbi1GIzYmLUZcbzYkUSY1NTI5NkYnRjlGX29Gal1sRjlGX3ItRiM2Ji1GXG82JFEmMTQ2NTZGJ0Y5Rl9vRmJzRjlGX3ItRiM2Ji1GXG82JFElMTgwOEYnRjlGX29GXHhGOUZlbi1GIzYoLUZcbzYkUScxMjc0MjRGJ0Y5Rl9vRl5wRl9vRmJzRjlGZW4tRiM2KC1GXG82JFEnNTIyNzg0RidGOUZfb0ZecEZfb0ZcdEY5Rl9yLUYjNigtRlxvNiRRKDExOTM5NTJGJ0Y5Rl9vRlhGX29GYHNGOUZlbi1GIzYoLUZcbzYkUSUxMTA0RidGOUZfb0ZecEZfb0ZeYWxGOUZlbi1GIzYoLUZcbzYkUSYxMzM3NkYnRjlGX29GXnBGX29GXHhGOUZlbi1GIzYoLUZcbzYkUSczMzA5NjhGJ0Y5Rl9vRl5wRl9vRlhGOUZfci1GIzYoLUZcbzYkUSM2NEYnRjlGX29GYHNGX28tRl9wNiVGWEZfd0ZcckY5Rl9yLUYjNigtRlxvNiRRJTE4MjRGJ0Y5Rl9vRmBzRl9vRl5hbEY5Rl9yLUYjNigtRlxvNiRRJjMxNTg0RidGOUZfb0Zgc0Zfb0ZceEY5RmVuLUYjNigtRlxvNiRRIzY4RidGOUZfb0ZecEZfb0ZhW21GOUZfci1GIzYoLUZcbzYkUSczOTU1MjBGJ0Y5Rl9vRmBzRl9vRmJzRjlGZW4tRiM2KC1GXG82JFEnMTEwNTkyRidGOUZfby1GX3A2JUZ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</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34280" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=6: factor(series(subs(u=convert(Sser(N+2),polynom),convert(ser,polynom)),q,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZwbHVzO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZMLUYjNigtSSNtbkdGJDYkUSI0RidGOS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlktSSZtZnJhY0dGJDYoLUYjNiotRiM2Ji1JJW1zdXBHRiQ2JS1GIzYmLUYsNiVRJGNvc0YnL0YwRj1GOS1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGWEZaLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEiYUYnRi9GMi8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjlGOUY5LUZSNiRRIjJGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZVLUZdbzYlLUYsNiVRInVGJ0YvRjJGaHBGW3FGOUY1LUYjNigtRlI2JFEiNkYnRjlGVUZcb0ZVRmBxRjlGNUZcby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GIzYmRlFGVUZgcUY5RjlGYHEvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmJyLyUpYmV2ZWxsZWRHRj1GVS1GXW82JUYrRmhwRltxRjlGNS1GIzYmLUZmbjYoLUYjNjwtRiM2KC1GUjYkUSM5NkYnRjlGVS1GXW82JUZfb0ZRRltxRlUtRl1vNiVGYHEtRlI2JFEiM0YnRjlGW3FGOUY1LUYjNigtRlI2JFEkNDQ4RidGOUZVRmRzRlVGXnFGOUY1LUYjNihGUUZVRlxvRlUtRl1vNiVGYHFGUUZbcUY5RjUtRiM2KEZhc0ZVRmBxRlVGZHNGOUZocS1GIzYoLUZSNiRRIzc2RidGOUZVRlxvRlVGZnNGOUZocS1GIzYoLUZSNiRRJDYzMkYnRjlGVUZcb0ZVRl5xRjlGaHFGYnRGaHEtRiM2KEZodEZVRlxvRlVGYHFGOUY1LUYjNiZGUUZVRmZzRjlGNS1GIzYmLUZSNiRRIzEyRidGOUZVRlxvRjlGNS1GIzYmLUZSNiRRJDIxOEYnRjlGVUZecUY5RjVGW3JGaHEtRlI2JEZfckY5RjlGXnFGXXJGYHJGY3JGZXJGVS1GXW82JUYrRmhzRltxRjlGNS1GIzYoRlFGVS1GZm42KC1GIzZKLUYjNigtRlI2JFEkNDMyRidGOUZVLUZdbzYlRl9vRmVxRltxRlVGYnRGOUY1LUYjNigtRlI2JFElMTgyNEYnRjlGVUZdd0ZVRmZzRjlGNS1GIzYoLUZSNiRRIzI4RidGOUZVRmRzRlUtRl1vNiVGYHEtRlI2JFEiNUYnRjlGW3FGOUY1LUYjNihGanZGVUZdd0ZVRl5xRjlGaHEtRiM2KC1GUjYkUSQ2ODBGJ0Y5RlVGZHNGVUZidEY5RmhxLUYjNigtRlI2JFElMzk5MkYnRjlGVUZkc0ZVRmZzRjlGaHEtRiM2KC1GUjYkUSMzMEYnRjlGVUZcb0ZVRml3RjlGaHEtRiM2KEZieEZVRmRzRlVGXnFGOUY1LUYjNigtRlI2JFEkMjgwRidGOUZVRlxvRlVGYnRGOUY1LUYjNihGaHRGVUZgcUZVRmRzRjlGNS1GIzYoLUZSNiRRJTI4NThGJ0Y5RlVGXG9GVUZmc0Y5RjUtRiM2JkZlcUZVRml3RjlGNS1GIzYoLUZSNiRRJDI4M0YnRjlGVUZcb0ZVRl5xRjlGaHEtRiM2Ji1GUjYkUSMxNUYnRjlGVUZidEY5RmhxLUYjNigtRlI2JFEjNjhGJ0Y5RlVGXG9GVUZgcUY5RmhxLUYjNiYtRlI2JFEkNjcwRidGOUZVRmZzRjlGNS1GIzYmLUZSNiRRIjlGJ0Y5RlVGXG9GOUZocS1GIzYmLUZSNiRRIzE2RidGOUZVRl5xRjlGNS1GIzYmLUZSNiRRIjhGJ0Y5RlVGYHFGOUZocUZedkY5RmZzRl1yRmByRmNyRmVyRlUtRl1vNiVGK0ZRRltxRjlGNS1GIzYmLUZmbjYoLUYjNltvLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRlI2JFEjMTRGJ0Y5RjUtRiM2KC1GUjYkUSYyNzY0OEYnRjlGVS1GXW82JUZfb0ZfXGxGW3FGVUZpd0Y5RjUtRiM2KC1GUjYkUScxMTA1OTJGJ0Y5RlVGZV1sRlVGYnRGOUY1LUYjNigtRlI2JFElMjExMkYnRjlGVUZdd0ZVLUZdbzYlRmBxRmVxRltxRjlGNS1GIzYoRmJdbEZVRmVdbEZVRmZzRjlGNS1GIzYmLUZSNiRRJDgzNkYnRjlGVUZmc0Y5RjUtRiM2Ji1GUjYkUSYzMDk1NkYnRjlGVUZidEY5RmhxLUYjNigtRlI2JFEmMTUxMDBGJ0Y5RlVGXG9GVUZmc0Y5RjUtRiM2KC1GUjYkUSU0NDg4RidGOUZVRlxvRlVGXnFGOUY1LUYjNigtRlI2JFEkOTQ0RidGOUZVRmBxRlVGZHNGOUZocS1GIzYoLUZSNiRRJjE0Njk2RidGOUZVRlxvRlVGaXdGOUZocS1GIzYoLUZSNiRRJzE3Mzk1MkYnRjlGVUZcb0ZVRmJ0RjlGaHEtRiM2KC1GUjYkUSQ4ODBGJ0Y5RlVGXG9GVUZgcUY5RmhxLUYjNigtRlI2JFElMzkzNkYnRjlGVUZkc0ZVRmFebEY5RjUtRiM2KC1GUjYkUSY1MTcyOEYnRjlGVUZkc0ZVRml3RjlGaHEtRiM2KC1GUjYkUSMyMEYnRjlGVUZcb0ZVLUZdbzYlRmBxLUZSNiRRIjdGJ0Y5RltxRjlGNS1GIzYoLUZSNiRRJzM2MTI4MEYnRjlGVUZkc0ZVRmJ0RjlGNS1GIzYoLUZSNiRRJTIyMjRGJ0Y5RlVGXG9GVUZhXmxGOUY1LUYjNigtRlI2JFEmNTIwODBGJ0Y5RlVGZHNGVUZmc0Y5RjUtRiM2KEZqW2xGVUZkc0ZVRlxibEY5RmhxLUYjNigtRlI2JFElOTM3NkYnRjlGVUZkc0ZVRl5xRjlGNS1GIzYmRlFGVUZcYmxGOUZocS1GIzYmLUZSNiRRJDM1NUYnRjlGVUZhXmxGOUY1LUYjNiYtRlI2JFEkMTEyRidGOUZVRlxvRjlGaHEtRiM2KC1GUjYkUSY2NTI4MEYnRjlGVUZdd0ZVRml3RjlGaHEtRiM2KC1GUjYkUSczMjg3MDRGJ0Y5RlVGXXdGVUZidEY5RmhxLUYjNihGZWRsRlVGXXdGVUZmc0Y5RjUtRiM2KC1GUjYkUSU1NTY4RidGOUZVRl13RlVGXnFGOUY1LUYjNiYtRlI2JFEkNzQ0RidGOUZVRml3RjlGaHEtRiM2Ji1GUjYkUSQ0ODNGJ0Y5RlVGXnFGOUY1LUYjNiYtRlI2JFEkMTIwRidGOUZVRmBxRjlGOUZidEZdckZgckZjckZlckZVLUZdbzYlRitGW3hGW3FGOUY1LUYjNiYtRjY2LVEiT0YnRjlGO0Y+RkBGQkZERkZGSEZYRlpGZW8tRmlvNiQtRiM2Jy1GXW82JUYrRmVxRltxRmBwRmNwRmZwRjlGOUY5Rjk=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34279" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(simplify(series(Sser(N+2)*Xser(N+2)*(1-Xser(N+2)+2*cos(2*a)*Xmser(N+2)),q,N)))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky9JInFHNiIiIiJGJSwkKigiIiVGJSwqKiYpLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJImFHRiQiIiNGJSlJInVHRiRGM0YlRiUqKCIiJ0YlRitGJUY1RiVGJSokRitGJUYlKiZGKEYlRjVGJSEiIkYlRjVGOkYlRjMqJiw8KigiIycqRiUpRixGKEYlKUY1IiIkRiVGJSooIiRbJUYlRj9GJUY0RiVGJSooRihGJUYrRiUpRjVGKEYlRiUqKEY+RiVGNUYlRj9GJUYlKigiI3dGJUYrRiVGQEYlRjoqKCIkSydGJUYrRiVGNEYlRjoqJEZFRiVGOiooRkhGJUYrRiVGNUYlRjoqJkYoRiVGQEYlRiUqJiIjN0YlRitGJUYlKiYiJD0jRiVGNEYlRiVGOUYlRiVGOkYlRjRGOkZBLCQqKEYoRiUsSiooIiRLJUYlKUYsRjdGJUZFRiVGJSooIiVDPUYlRldGJUZARiVGJSooIiNHRiVGP0YlKUY1IiImRiVGJSooRlZGJUZXRiVGNEYlRiUqKCIkIW9GJUY/RiVGRUYlRjoqKCIlIypSRiVGP0YlRkBGJUY6KigiI0lGJUYrRiVGZm5GJUY6KihGam5GJUY/RiVGNEYlRjoqKCIkIUdGJUYrRiVGRUYlRiUqKEZIRiVGNUYlRj9GJUYlKigiJWVHRiVGK0YlRkBGJUYlKiZGN0YlRmZuRiVGJSooIiQkR0YlRitGJUY0RiVGJSomIiM6RiVGRUYlRjoqKCIjb0YlRitGJUY1RiVGOiomIiRxJ0YlRkBGJUY6KiYiIipGJUYrRiVGJSomIiM7RiVGNEYlRjoqJiIiKUYlRjVGJUYlRiVGOkYlRkBGOkYlRigqJixqbiIjOUY6KigiJlt3I0YlKUYsRmNwRiVGZm5GJUYlKigiJyNmNSJGJUZpcEYlRkVGJUYlKigiJTdARiVGV0YlKUY1RjdGJUYlKihGaHBGJUZpcEYlRkBGJUYlKiYiJE8pRiVGQEYlRiUqJiImYzQkRiVGRUYlRiUqKCImK14iRiVGK0YlRkBGJUY6KigiJSlbJUYlRitGJUY0RiVGJSooIiRXKkYlRjVGJUY/RiVGJSooIiYncDlGJUYrRiVGZm5GJUY6KigiJ19SPEYlRitGJUZFRiVGOiooIiQhKSlGJUYrRiVGNUYlRjoqKCIlT1JGJUY/RiVGXnFGJUY6KigiJkc8JkYlRj9GJUZmbkYlRiUqKCIjP0YlRitGJSlGNSIiKEYlRjoqKCInIUdoJEYlRj9GJUZFRiVGJSooIiVDQUYlRitGJUZecUYlRiUqKCImITNfRiVGP0YlRkBGJUYlKihGYXBGJUY/RiVGZnJGJUYlKigiJXckKkYlRj9GJUY0RiVGOiomRihGJUZmckYlRiUqJiIkYiRGJUZecUYlRjoqJiIkNyJGJUYrRiVGJSooIiYhR2xGJUZXRiVGZm5GJUY6KigiJy8oRyRGJUZXRiVGRUYlRjoqKEZnc0YlRldGJUZARiVGOiooIiVvYkYlRldGJUY0RiVGJSomIiRXKEYlRmZuRiVGJSomIiQkW0YlRjRGJUY6KiYiJD8iRiVGNUYlRiVGJUZFRjpGZ24tSSJPR0YuNiNGJUY3</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34215" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(series(%%-%,q))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34253" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=6: factor(series(Xser(N)*Xpser(N)*Xmser(N),q,N))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KylJInFHNiIsKCooIiIlIiIiKS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJhR0YkIiIjRihJInVHRiRGKEYoRjIhIiJGKEYoRigsMiooIiNLRigpRipGJ0YoKUYyRjFGKEYoKigiJFciRihGMkYoRjdGKEYoKihGNkYoRilGKEY4RihGMyooIiRTIkYoRilGKEYyRihGMyomIiNHRihGKUYoRigqJiIiJ0YoRjhGKEYoKiYiI0VGKEYyRihGKCIjQUYzRjEtSSJPR0YsNiNGKCIiJA==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34259" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=16: ser:=factor(series(Xser(N)*Xpser(N)*Xmser(N),q,N)):
map(degree,%,u);
map(ldegree,%%,u)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Kz9JInFHNiIiIiJGJSIiI0YmIiIkRiciIiVGKCIiJkYpIiInRioiIihGKyIiKUYsIiIqRi0iIzVGLiIjNkYvIiM3RjAiIzhGMSIjOUYy</Equation></Text-field>
</Output>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L34268" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">The compositional inverse of X(u)</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34265" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=5:pol:= mtaylor(series(convert(Xser(N),polynom),u,N),[u,q],N)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L34242" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">unassign('coU'):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34220" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">User:=proc(n) local i: add(coU[i]*x^i,i=1..n): end:</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L34233" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=0:</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L34240" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=n+1: factor(series(subs(u=User(n+2),add(X[i]*u^i,i=1..n)-x),x,n+1))</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KydJInhHNiIqJiwuKiYpJkkiWEdGJDYjIiIiIiIqRiwmSSRjb1VHRiQ2IyIiJkYsRiwqJilGKSIiJEYsJkYqRjBGLEYsKioiIidGLClGKSIiI0YsJkYqNiNGOUYsJkYqNiMiIiVGLCEiIiooRjRGLEY4RiwpJkYqNiNGNEY5RixGPyoqIiNARixGKUYsKUY6RjlGLEZCRixGLComIiM5RiwpRjpGPkYsRj9GLClGKSIiKUY/RjEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkRitGNw==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34208" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">coU[n]:=solve(coeff(%,x,n),coU[n])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkkY29VR0YoNiMiIiYsJComLCwqJikmSSJYR0YoNiMiIiIiIiRGOSZGN0YvRjlGOSoqIiInRjkpRjYiIiNGOSZGNzYjRj9GOSZGNzYjIiIlRjkhIiIqKEY6RjlGPkY5KSZGNzYjRjpGP0Y5RkUqKiIjQEY5RjZGOSlGQEY/RjlGSEY5RjkqJiIjOUY5KUZARkRGOUZFRjkpRjYiIipGRUZFNyNGMQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34224" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">User(n)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJiZJIlhHNiI2IyIiIiEiIkkieEdGJkYoRigqKCZGJTYjIiIjRigpRiQiIiRGKSlGKkYuRihGKSooLCYqJkYkRigmRiU2I0YwRihGKComRi5GKClGLEYuRihGKUYoKUYkIiImRikpRipGMEYoRikqKCwoKiYpRiRGLkYoJkYlNiMiIiVGKEYoKipGOkYoRiRGKEYsRihGNUYoRikqJkY6RigpRixGMEYoRihGKClGJCIiKEYpKUYqRkJGKEYpKigsLComRi9GKCZGJTYjRjpGKEYoKioiIidGKEY/RihGLEYoRkBGKEYpKihGMEYoRj9GKClGNUYuRihGKSoqIiNARihGJEYoRjhGKEY1RihGKComIiM5RigpRixGQkYoRilGKClGJCIiKkYpKUYqRjpGKEYp</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L34266" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">Xser(3)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">n:=4: normal(series(u/Xser(n),q,n))</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">series(Qw,t,5)</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ky1JInRHNiIsJiomIiIjIiIiSSJ3R0YkRihGKEYnRihGKCwoKiYiIipGKClGKUYnRihGKComIiM7RihGKUYoRigiIzVGKEYnLCoqJiIjYUYoKUYpIiIkRihGKComIiRLIkYoRi1GKEYoKiYiJF0iRihGKUYoRigiI21GKEY1LCwqJiIkeSRGKClGKSIiJUYoRigqJiIlXzZGKEY0RihGKComIiU3PUYoRi1GKEYoKiYiJSlbIkYoRilGKEYoIiQvJkYoRj8tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L44355" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">ratio test</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L36823" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=plot(subs(w=omega,[seq(coeff(Qw,t,n)/coeff(Qw,t,n+1),n=1..39)]),omega=0..8)</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [(2*omega+2)/(9*omega^2+16*omega+10), (9*omega^2+16*omega+10)/(54*omega^3+132*omega^2+150*omega+66), (54*omega^3+132*omega^2+150*omega+66)/(378*omega^4+1152*omega^3+1812*omega^2+1488*omega+504), (378*omega^4+1152*omega^3+1812*omega^2+1488*omega+504)/(2916*omega^5+10530*omega^4+20620*omega^3+23870*omega^2+15320*omega+4216), (2916*omega^5+10530*omega^4+20620*omega^3+23870*omega^2+15320*omega+4216)/(24057*omega^6+99792*omega^5+230244*omega^4+336024*omega^3+307746*omega^2+162048*omega+37548), (24057*omega^6+99792*omega^5+230244*omega^4+336024*omega^3+307746*omega^2+162048*omega+37548)/(208494*omega^7+972972*omega^6+2558808*omega^5+4437328*omega^4+5173630*omega^3+3919944*omega^2+1749734*omega+350090), (208494*omega^7+972972*omega^6+2558808*omega^5+4437328*omega^4+5173630*omega^3+3919944*omega^2+1749734*omega+350090)/(1876446*omega^8+9704448*omega^7+28462320*omega^6+56565952*omega^5+78974348*omega^4+76719808*omega^3+49571576*omega^2+19202144*omega+3380520), (1876446*omega^8+9704448*omega^7+28462320*omega^6+56565952*omega^5+78974348*omega^4+76719808*omega^3+49571576*omega^2+19202144*omega+3380520)/(17399772*omega^9+98598708*omega^8+317591280*omega^7+706164882*omega^6+1136757564*omega^5+1330352928*omega^4+1107967884*omega^3+624063654*omega^2+213514056*omega+33558024), (17399772*omega^9+98598708*omega^8+317591280*omega^7+706164882*omega^6+1136757564*omega^5+1330352928*omega^4+1107967884*omega^3+624063654*omega^2+213514056*omega+33558024)/(165297834*omega^10+1017217440*omega^9+3557906370*omega^8+8701801560*omega^7+15745437660*omega^6+21354931776*omega^5+21526014130*omega^4+15691507240*omega^3+7833643260*omega^2+2399966480*omega+340670720), (165297834*omega^10+1017217440*omega^9+3557906370*omega^8+8701801560*omega^7+15745437660*omega^6+21354931776*omega^5+21526014130*omega^4+15691507240*omega^3+7833643260*omega^2+2399966480*omega+340670720)/(1602117468*omega^11+10629922248*omega^10+40024929978*omega^9+106336841094*omega^8+212394834564*omega^7+325183750936*omega^6+381436608278*omega^5+337771022248*omega^4+218933920480*omega^3+98144935922*omega^2+27222536616*omega+3522993656), (1602117468*omega^11+10629922248*omega^10+40024929978*omega^9+106336841094*omega^8+212394834564*omega^7+325183750936*omega^6+381436608278*omega^5+337771022248*omega^4+218933920480*omega^3+98144935922*omega^2+27222536616*omega+3522993656)/(15792300756*omega^12+112300805376*omega^11+452097138636*omega^10+1292334156432*omega^9+2811284356608*omega^8+4768157993376*omega^7+6336491821212*omega^6+6551108351904*omega^5+5173476225240*omega^4+3018933437712*omega^3+1228055134560*omega^2+311177489088*omega+37003723200), (15792300756*omega^12+112300805376*omega^11+452097138636*omega^10+1292334156432*omega^9+2811284356608*omega^8+4768157993376*omega^7+6336491821212*omega^6+6551108351904*omega^5+5173476225240*omega^4+3018933437712*omega^3+1228055134560*omega^2+311177489088*omega+37003723200)/(157923007560*omega^13+1197582807330*omega^12+5126220180900*omega^11+15648677931510*omega^10+36693983787552*omega^9+67980624428496*omega^8+100394141617380*omega^7+117943279986714*omega^6+109038353496696*omega^5+77709076547310*omega^4+41236232417016*omega^3+15353130527280*omega^2+3580778908512*omega+393856445664), (157923007560*omega^13+1197582807330*omega^12+5126220180900*omega^11+15648677931510*omega^10+36693983787552*omega^9+67980624428496*omega^8+100394141617380*omega^7+117943279986714*omega^6+109038353496696*omega^5+77709076547310*omega^4+41236232417016*omega^3+15353130527280*omega^2+3580778908512*omega+393856445664)/(1598970451545*omega^14+12875369910480*omega^13+58331799112860*omega^12+189022835940120*omega^11+473906141934624*omega^10+948654102502400*omega^9+1534473790626952*omega^8+2008681734429704*omega^7+2115390731222538*omega^6+1768850818607880*omega^5+1148650086470264*omega^4+558888138864048*omega^3+191835719883668*omega^2+41443913852096*omega+4240313009272), (1598970451545*omega^14+12875369910480*omega^13+58331799112860*omega^12+189022835940120*omega^11+473906141934624*omega^10+948654102502400*omega^9+1534473790626952*omega^8+2008681734429704*omega^7+2115390731222538*omega^6+1768850818607880*omega^5+1148650086470264*omega^4+558888138864048*omega^3+191835719883668*omega^2+41443913852096*omega+4240313009272)/(16365932856990*omega^15+139413502115100*omega^14+665933128164000*omega^13+2279473916522400*omega^12+6070725652317120*omega^11+13018150595118720*omega^10+22805918728085160*omega^9+32776853830357440*omega^8+38549303026053390*omega^7+36795140671320480*omega^6+28087191021174900*omega^5+16752002684480760*omega^4+7525754108832750*omega^3+2396081084594040*omega^2+482115062989110*omega+46109094112170), (16365932856990*omega^15+139413502115100*omega^14+665933128164000*omega^13+2279473916522400*omega^12+6070725652317120*omega^11+13018150595118720*omega^10+22805918728085160*omega^9+32776853830357440*omega^8+38549303026053390*omega^7+36795140671320480*omega^6+28087191021174900*omega^5+16752002684480760*omega^4+7525754108832750*omega^3+2396081084594040*omega^2+482115062989110*omega+46109094112170)/(169114639522230*omega^16+1519064832199680*omega^15+7625213168113440*omega^14+27458516973293568*omega^13+77267110421725776*omega^12+176272718873605632*omega^11+331475556543446656*omega^10+517064614744024192*omega^9+669051522064560732*omega^8+714558313287046144*omega^7+623721292406194336*omega^6+437986602298337664*omega^5+241540878942787576*omega^4+100783163160574720*omega^3+29920821325058736*omega^2+5633690360640960*omega+505802627913960), (169114639522230*omega^16+1519064832199680*omega^15+7625213168113440*omega^14+27458516973293568*omega^13+77267110421725776*omega^12+176272718873605632*omega^11+331475556543446656*omega^10+517064614744024192*omega^9+669051522064560732*omega^8+714558313287046144*omega^7+623721292406194336*omega^6+437986602298337664*omega^5+241540878942787576*omega^4+100783163160574720*omega^3+29920821325058736*omega^2+5633690360640960*omega+505802627913960)/(1762352559231660*omega^17+16644440837187900*omega^16+87550099928146080*omega^15+330526235122652808*omega^14+978390788602279824*omega^13+2361096722647705248*omega^12+4731569401362440752*omega^11+7937606931921573428*omega^10+11168512543330860436*omega^9+13146541320859260138*omega^8+12861208668461144304*omega^7+10342811706580380576*omega^6+6724706970023388708*omega^5+3448714824715500672*omega^4+1343326251293908348*omega^3+373584179090043958*omega^2+66095921908463400*omega+5591751626721960), (1762352559231660*omega^17+16644440837187900*omega^16+87550099928146080*omega^15+330526235122652808*omega^14+978390788602279824*omega^13+2361096722647705248*omega^12+4731569401362440752*omega^11+7937606931921573428*omega^10+11168512543330860436*omega^9+13146541320859260138*omega^8+12861208668461144304*omega^7+10342811706580380576*omega^6+6724706970023388708*omega^5+3448714824715500672*omega^4+1343326251293908348*omega^3+373584179090043958*omega^2+66095921908463400*omega+5591751626721960)/(18504701871932430*omega^18+183284666160092640*omega^17+1007723306707899300*omega^16+3976815075136623072*omega^15+12337105017367787184*omega^14+31345088874069495744*omega^13+66542174311185566250*omega^12+119160838124739542448*omega^11+180622891067465148768*omega^10+231576341482186746552*omega^9+250074707363318865096*omega^8+225714051293453511264*omega^7+168283950828512099076*omega^6+101869960608704129328*omega^5+48823393584176587350*omega^4+17832236441622654216*omega^3+4664200939827096564*omega^2+778243979668035888*omega+62247732179078880), (18504701871932430*omega^18+183284666160092640*omega^17+1007723306707899300*omega^16+3976815075136623072*omega^15+12337105017367787184*omega^14+31345088874069495744*omega^13+66542174311185566250*omega^12+119160838124739542448*omega^11+180622891067465148768*omega^10+231576341482186746552*omega^9+250074707363318865096*omega^8+225714051293453511264*omega^7+168283950828512099076*omega^6+101869960608704129328*omega^5+48823393584176587350*omega^4+17832236441622654216*omega^3+4664200939827096564*omega^2+778243979668035888*omega+62247732179078880)/(195621134074714260*omega^19+2027346298592493240*omega^18+11625519722218714188*omega^17+47834934282430929540*omega^16+155030805667598006736*omega^15+413044437046704809544*omega^14+924268648165847097282*omega^13+1755940829453517199404*omega^12+2845598162808214541964*omega^11+3936293778568828535370*omega^10+4636517509527112018728*omega^9+4625573417107446407970*omega^8+3875392594934035975556*omega^7+2693140620256770033356*omega^6+1525144083509020403118*omega^5+686057788684715477786*omega^4+235876712336630840264*omega^3+58232051063170488402*omega^2+9193116417077633192*omega+697269028520326328), (195621134074714260*omega^19+2027346298592493240*omega^18+11625519722218714188*omega^17+47834934282430929540*omega^16+155030805667598006736*omega^15+413044437046704809544*omega^14+924268648165847097282*omega^13+1755940829453517199404*omega^12+2845598162808214541964*omega^11+3936293778568828535370*omega^10+4636517509527112018728*omega^9+4625573417107446407970*omega^8+3875392594934035975556*omega^7+2693140620256770033356*omega^6+1525144083509020403118*omega^5+686057788684715477786*omega^4+235876712336630840264*omega^3+58232051063170488402*omega^2+9193116417077633192*omega+697269028520326328)/(2080697516976506220*omega^20+22515760570180550400*omega^19+134395756963216053480*omega^18+575295535346660186400*omega^17+1942562429918378206560*omega^16+5408801463268486006560*omega^15+12704262822547535708460*omega^14+25473769784509313402880*omega^13+43856972779529665753920*omega^12+64950705299770887348240*omega^11+82653806782637225027760*omega^10+90055753211462691651600*omega^9+83493581863306186782720*omega^8+65272481160988497909440*omega^7+42476910416840655129300*omega^6+22598016635816265912080*omega^5+9577098694514730487880*omega^4+3110312721289143176880*omega^3+727041267932879288800*omega^2+108913982863211731520*omega+7854446696230804800), 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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P2:=plot(subs(w=omega,1/4/arccos(w/2)*sqrt(2-w)/(2+w)^(3/2)),omega=0..8,thickness=4,color=red)</Text-field>
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</Output>
</Group>
<Group view="code" labelreference="L44402" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Inclusing some negative values of omega</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L43444" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P1:=plot(subs(w=omega,[seq(coeff(Qw,t,n)/coeff(Qw,t,n+1),n=2..39)]),omega=-1/2..6):
P2:=plot(subs(w=omega,1/4/arccos(w/2)*sqrt(2-w)/(2+w)^(3/2)),omega=-1/2..6,thickness=4,color=red):</Text-field>
</Input>
</Group>
<Group view="code" labelreference="L43463" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">display(P1,P2)</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-3, t=-t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXJvd0dGJDZfcC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y7LyUqc3ltbWV0cmljR0Y7LyUobGFyZ2VvcEdGOy8lLm1vdmFibGVsaW1pdHNHRjsvJSdhY2NlbnRHRjsvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0YuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri5GNUYuRjVGLkY1Ri4vJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGO0YyRjIvJSVvcGVuR1EnJmxzcWI7RicvJSZjbG9zZUdRJyZyc3FiO0Yn">N0oiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L43478" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-2, t=-t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0oiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L43477" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-1, t=-t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0kiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L43488" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Mind the last coeff!</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L43486" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-9/10, t=-t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0oiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjISIi</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L43489" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">not clear</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L43485" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-8/10, t=-t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0oiIiJGIyEiIkYjRiRGI0YkRiNGI0YjRiNGJEYjRiRGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0Yk</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L43487" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Positive signs</Text-field>
</Input>
</Group>
<Group view="code" hide-input="false" labelreference="L43476" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-1/2, t=t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0oiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" hide-input="false" labelreference="L43484" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(w=-1/4, t=t,Qw): map(sign,[coeffs(%)])</Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">N0oiIiJGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiNGI0YjRiM=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L43483" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal">P3:=plot(subs(w=omega,[seq(coeff(Qw,t,n)/coeff(Qw,t,n+1),n=2..39)]),omega=-4..-3/2)</Text-field>
</Input>
<Output><Text-field style="Maple Plot" layout="Maple Plot"><Plot height="500.0" originalheight="500.0" type="two-dimensional" width="500.0" originalwidth="500.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false" input="_ATTRIBUTE(&quot;input&quot; = [TABLE([1 = plot, 2 = [(9*omega^2+16*omega+10)/(54*omega^3+132*omega^2+150*omega+66), (54*omega^3+132*omega^2+150*omega+66)/(378*omega^4+1152*omega^3+1812*omega^2+1488*omega+504), (378*omega^4+1152*omega^3+1812*omega^2+1488*omega+504)/(2916*omega^5+10530*omega^4+20620*omega^3+23870*omega^2+15320*omega+4216), (2916*omega^5+10530*omega^4+20620*omega^3+23870*omega^2+15320*omega+4216)/(24057*omega^6+99792*omega^5+230244*omega^4+336024*omega^3+307746*omega^2+162048*omega+37548), (24057*omega^6+99792*omega^5+230244*omega^4+336024*omega^3+307746*omega^2+162048*omega+37548)/(208494*omega^7+972972*omega^6+2558808*omega^5+4437328*omega^4+5173630*omega^3+3919944*omega^2+1749734*omega+350090), (208494*omega^7+972972*omega^6+2558808*omega^5+4437328*omega^4+5173630*omega^3+3919944*omega^2+1749734*omega+350090)/(1876446*omega^8+9704448*omega^7+28462320*omega^6+56565952*omega^5+78974348*omega^4+76719808*omega^3+49571576*omega^2+19202144*omega+3380520), (1876446*omega^8+9704448*omega^7+28462320*omega^6+56565952*omega^5+78974348*omega^4+76719808*omega^3+49571576*omega^2+19202144*omega+3380520)/(17399772*omega^9+98598708*omega^8+317591280*omega^7+706164882*omega^6+1136757564*omega^5+1330352928*omega^4+1107967884*omega^3+624063654*omega^2+213514056*omega+33558024), (17399772*omega^9+98598708*omega^8+317591280*omega^7+706164882*omega^6+1136757564*omega^5+1330352928*omega^4+1107967884*omega^3+624063654*omega^2+213514056*omega+33558024)/(165297834*omega^10+1017217440*omega^9+3557906370*omega^8+8701801560*omega^7+15745437660*omega^6+21354931776*omega^5+21526014130*omega^4+15691507240*omega^3+7833643260*omega^2+2399966480*omega+340670720), (165297834*omega^10+1017217440*omega^9+3557906370*omega^8+8701801560*omega^7+15745437660*omega^6+21354931776*omega^5+21526014130*omega^4+15691507240*omega^3+7833643260*omega^2+2399966480*omega+340670720)/(1602117468*omega^11+10629922248*omega^10+40024929978*omega^9+106336841094*omega^8+212394834564*omega^7+325183750936*omega^6+381436608278*omega^5+337771022248*omega^4+218933920480*omega^3+98144935922*omega^2+27222536616*omega+3522993656), (1602117468*omega^11+10629922248*omega^10+40024929978*omega^9+106336841094*omega^8+212394834564*omega^7+325183750936*omega^6+381436608278*omega^5+337771022248*omega^4+218933920480*omega^3+98144935922*omega^2+27222536616*omega+3522993656)/(15792300756*omega^12+112300805376*omega^11+452097138636*omega^10+1292334156432*omega^9+2811284356608*omega^8+4768157993376*omega^7+6336491821212*omega^6+6551108351904*omega^5+5173476225240*omega^4+3018933437712*omega^3+1228055134560*omega^2+311177489088*omega+37003723200), 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