This is Part 2 of the Maple files that accompany the paper "Walks avoiding a quadrant and the reflection principle" by Mireille Bousquet-M\303\251lou and Michael Wallner. #############################################################Abstract:We continue the enumeration of plane lattice walks with small steps avoiding the negative quadrant, initiated by the first author in 2016. We solve in detail a new case, namely the king model where all 8 nearest neighbour steps are allowed. The associated generating function is proved to be the sum of a simple, explicit D-finite series (related to the number of walks confined to the first quadrant), and an algebraic one. This was already the case for the two models solved by the first author in 2016. The principle of the approach is also the same, but challenging theoretical and computational difficulties arise as we now handle algebraic series of larger degree. We expect a similar algebraicity phenomenon to hold for the 7 Weyl step sets, which are those for which walks confined to the first quadrant can be counted using the reflection principle. With this paper, this is now proved for 3 of them. For the remaining 4, we predict the D-finite part of the solution, and in 3 of the 4 cases, give evidence for the algebraicity of the remaining part.#############################################################

For this section to work, we need to have at hand a number of equations and series expansions from Part 1. So we execute the session until the first section. The series C and Q K:=1-t*(x+1/x+y+1/y+(x+1/x)*(y+1/y)): eqC:=-K*C(x,y)+1-t/y*(x+1/x+1)*Cm(1/x)-t/x*(y+1/y+1)*Cm(1/y)-t/x/y*C00;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcUNHRigsLComLCYiIiJGMSomSSJ0R0YoRjEsLEkieEdGKEYxKiRGNSEiIkYxSSJ5R0YoRjEqJEY4RjdGMSomLCZGNUYxRjZGMUYxLCZGOEYxRjlGMUYxRjFGMUY3RjEtSSJDR0YoNiRGNUY4RjFGN0YxRjEqKkYzRjFGOEY3LChGNUYxRjZGMUYxRjFGMS1JI0NtR0YoNiNGNkYxRjcqKkYzRjFGNUY3LChGOEYxRjlGMUYxRjFGMS1GQzYjRjlGMUY3KipGM0YxRjVGN0Y4RjdJJEMwMEdGKEYxRjc3I0Yu

Cmex:=proc(n) local res,i: res:=coeff(convert(Cex(n),polynom),y,0): add(coeff(res,x,-i)/x^i,i=1..n): end: C00ex:=proc(n) local res: res:=coeff(convert(Cex(n),polynom),y,0): coeff(coeff(res,x,0),y,0): end: Cex:=proc(n) option remember: if n=0 then 1 else normal(series(subs(C00=C00ex(n-1),C(x,y)=Cex(n-1),Cm(1/x)=Cmex(n-1),Cm(1/y)=subs(x=y,Cmex(n-1)),eqC+C(x,y)),t,n+1)): fi: end: map(expand,Cex(2));

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

eqQ:=-K*Q(x,y)+1-t/y*(x+1/x+1)*Qp(x)-t/x*(y+1/y+1)*Qp(y)+t/x/y*Q00;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcVFHRigsLComLCYiIiJGMSomSSJ0R0YoRjEsLEkieEdGKEYxKiRGNSEiIkYxSSJ5R0YoRjEqJEY4RjdGMSomLCZGNUYxRjZGMUYxLCZGOEYxRjlGMUYxRjFGMUY3RjEtSSJRR0YoNiRGNUY4RjFGN0YxRjEqKkYzRjFGOEY3LChGNUYxRjZGMUYxRjFGMS1JI1FwR0YoNiNGNUYxRjcqKkYzRjFGNUY3LChGOEYxRjlGMUYxRjFGMS1GQzYjRjhGMUY3KipGM0YxRjVGN0Y4RjdJJFEwMEdGKEYxRjE3I0Yu

Qpex:=proc(n) subs(y=0,Qex(n)): end: Q00ex:=proc(n) subs(x=0,y=0,Qex(n)): end: Qex:=proc(n) option remember: if n=0 then 1 else normal(series(subs(Q00=Q00ex(n-1),Q(x,y)=Qex(n-1),Qp(x)=Qpex(n-1),Qp(y)=subs(x=y,Qpex(n-1)),eqQ+Q(x,y)),t,n+1)): fi: end: Qex(4);

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

The series A, P, M Aex:=proc(n) expand(series(Cex(n)-1/3*(Qex(n)-1/x^2*subs(x=1/x,Qex(n))-1/y^2*subs(y=1/y,Qex(n))),t,n+1)): end: Mex:=proc(n) local i: collect(add(1/x*coeff(convert(Aex(n),polynom),x,-i)*x^i,i=1..n+2),t,normal): end: Mex(2);

LCgqJiw6KiYiIiMiIiIpSSJ5RzYiRiZGJ0YnKiZGJkYnRilGJ0YnRiZGJyooIyIiKSIiJEYnSSJ4R0YqRidGKUYnRicqJkYvRidGMEYnRicqKCMiIiZGL0YnRjBGJ0YoRidGJyomI0YmRi9GJylGMEYmRidGJyooRjZGJ0Y3RidGKUYnRicqKEY2RidGN0YnRihGJ0YnKiZGNkYnKUYwRi9GJ0YnKigjRidGL0YnRjtGJ0YoRidGJyooRjZGJ0Y7RidGKUYnRidGJylJInRHRipGJkYnRicqJiwsRilGJ0YnRicqKEY9RidGMEYnRilGJ0YnKihGPUYnRjdGJ0YpRidGJyomRj1GJ0Y3RidGJ0YnRkBGJ0YnKiZGPUYnRjBGJ0Yn

Pex:=proc(n) local res,i,j: res:=convert(Aex(n),polynom): collect(add(add(coeff(coeff(res,x,i),y,j)*x^i*y^j,i=0..n),j=0..n),t): end: Pex(3);

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

The discriminant Delta:=(1-t*(x+1/x))^2-4*t^2*(1+x+1/x)^2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZEZWx0YUdGKCwmKiQpLCYiIiJGMiomSSJ0R0YoRjIsJkkieEdGKEYyKiRGNiEiIkYyRjJGOCIiI0YyRjIqKCIiJUYyKUY0RjlGMiksKEY2RjJGN0YyRjJGMkY5RjJGODcjRi4=

The series R(x) and S(x) Rex:=proc(n) t^2*subs(y=0,Mex(n)): end: series(Rex(5),t,5);

KytJInRHNiIsJComIyIiIiIiJEYoSSJ4R0YkRihGKCIiIywmRihGKComRidGKClGKkYrRihGKEYpLCpGK0YoKiZGKUYoRipGKEYoKiYjRitGKUYoRi5GKEYoKiZGMkYoKUYqRilGKEYoIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiY=

Sex:=proc(n) t*x*subs(x=0,y=x,Mex(n)): end: series(Sex(5),t,5);

KytJInRHNiIqJkkieEdGJCIiIiwmRiZGJ0YnRidGJyIiIyomRiZGJywoKiZGKUYnKUYmRilGJ0YnKiZGKUYnRiZGJ0YnRilGJ0YnIiIkKiZGJkYnLCoqJiIiJ0YnKUYmRi9GJ0YnKiYiIzdGJ0YtRidGJyomIiNCRidGJkYnRiciIzxGJ0YnIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiciIiY=

The equation in one catalytic variable satisfied by S(x) eqScat:=S(x)^3*(-(t*x^2+2*t*x+t+x)*(3*t*x^2+2*t*x+3*t-x)/x^2) +S(x)^2*(t*x^2+2*t*x+t+x)*(3*t*x^2+2*t*x+3*t-x)*(-2*t*x^2+3*R0*x-t)/(x^2*t*(x^2+x+1)) +S(x)*(-B1+(2*R0+t)*B2/t-9*R1^2-(3*(2*R0*t*x^4+t^2*x^4+2*R0*t*x^3-t^2*x^3+6*R0*t*x^2+t^2*x^2-t*x^3+2*R0*t*x+2*R0*x^2-t^2*x+2*R0*t+t^2-t*x))*R1/(t*x*(x^2+x+1)) -(R0^2*t^2*x^8+R0*t^3*x^8+4*t^4*x^8+4*R0^2*t^2*x^7-10*R0*t^3*x^7+10*t^4*x^7+13*R0^2*t^2*x^6-32*R0*t^3*x^6-R0*t^2*x^7+17*t^4*x^6+2*t^3*x^7+28*R0^2*t^2*x^5-52*R0*t^3*x^5-10*R0*t^2*x^6+20*t^4*x^5+32*R0^2*t^2*x^4+6*R0^2*t*x^5-56*R0*t^3*x^4-7*R0*t^2*x^5+18*t^4*x^4+4*t^3*x^5-t^2*x^6+28*R0^2*t^2*x^3+2*R0^2*t*x^4-38*R0*t^3*x^3-17*R0*t^2*x^4+3*R0*t*x^5+12*t^4*x^3+13*R0^2*t^2*x^2+6*R0^2*t*x^3-2*R0^2*x^4-16*R0*t^3*x^2-7*R0*t^2*x^3+7*t^4*x^2+2*t^3*x^3-t^2*x^4+4*R0^2*t^2*x-4*R0*t^3*x-6*R0*t^2*x^2+R0*t*x^3+2*t^4*x+R0^2*t^2+R0*t^3-R0*t^2*x+t^4)/(t^2*x^2*(x^2+x+1)^2)) +(2*R0^2*x^2+2*R0*t*x^2-t^2*x^2+3*R0*t*x-2*R0^2-2*R0*t-2*t^2)*B1/(3*t^2*(x^2+x+1)) -(2*R0+t)*x*(-t*x+R0)*B2/(t^2*(x^2+x+1)) +(9*(-t*x+ R0)*x*R1^2)/(t*(x^2+x+1)) +(3*(2*R0*t*x^4+t^2*x^4+2*R0*t*x^3-t^2*x^3+6*R0*t*x^2+t^2*x^2-t*x^3+2*R0*t*x+2*R0*x^2-t^2*x+2*R0*t+t^2-t*x))*(-t*x+R0)*R1/(t^2*(x^2+x+1)^2)+(-t*x+R0)*(R0^2*t*x^6+R0*t^2*x^6+t^3*x^6+3*R0^2*t*x^5-2*R0*t^2*x^5+t^3*x^5+3*R0^2*t*x^4-7*R0*t^2*x^4-R0*t*x^5+2*t^3*x^4+6*R0^2*t*x^3-10*R0*t^2*x^3-3*R0*t*x^4+t^3*x^3+3*R0^2*t*x^2+2*R0^2*x^3-7*R0*t^2*x^2-3*R0*t*x^3+2*t^3*x^2+3*R0^2*t*x-2*R0*t^2*x-3*R0*t*x^2+t^3*x+R0^2*t+R0*t^2-R0*t*x+t^3)/(x*t^2*(x^2+x+1)^2): In compact form: equation for S-tilde eqStcatz:=27*t^2*(2*t + z + 1)*(10*t - 3*z + 1)*St^3 + ((216*t^2 - 27*z^2 + 54*t)*R0^2 + 27*t*(6*R1*t - 6*R1*z + 6*t^2 + 2*t*z - z^2 + 2*B2 + t + z)*R0 - 9*t^2*(27*R1^2 - 27*R1*t + 9*R1*z + 5*t^2 - 2*t*z + 3*B1 - 3*B2 - 9*R1 + 6*t - 2*z + 1))*St + (72*t^2 - 9*z^2 + 18*B1 + 18*t)*R0^2 + 9*t*(6*R1*t - 6*R1*z + 6*t^2 + 2*t*z - z^2 + 2*B1 + 2*B2 + t + z)*R0 + t^2*(-81*R1^2 + 81*R1*t - 27*R1*z + 5*t^2 + 10*t*z - 3*z^2 + 9*B1 + 9*B2 + 27*R1 - 6*t + 4*z - 2)

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

zx:=t*(x+1+1/x)+(t+1)/(x+1+1/x); StS:=1/(x-1/x)*((x+1/x+1)*S(x)-R0/t+2*x/3+1/x/3)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN6eEdGKCwmKiZJInRHRigiIiIsKEkieEdGKEYxKiRGMyEiIkYxRjFGMUYxRjEqJiwmRjBGMUYxRjFGMUYyRjVGMTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRTdFNHRigqJiwmSSJ4R0YoIiIiKiRGMCEiIkYzRjMsKiomLChGMEYxRjJGMUYxRjFGMS1JIlNHRig2I0YwRjFGMSomSSNSMEdGKEYxSSJ0R0YoRjNGMyomIyIiIyIiJEYxRjBGMUYxKiYjRjFGQEYxRjBGM0YxRjE3I0Yu

The four univariate series involved in the equation for S(x) jj:=exp(2*I*Pi/3);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNqakdGKCwmIyIiIiIiIyEiIiomKiZGL0YwXiNGMEYwRjApIiIkRi9GMEYwNyNGLg==

B1ex:=proc(n) map(expand,map(rationalize,1/2*convert(normal(series((1+t)^2*jj*subs(x=jj,diff(Sex(n),x))+(1+t)^2/jj*subs(x=1/jj,diff(Sex(n),x)),t,n+1)),polynom))): end: B1ex(4);

LCYqJiMiIiQiIiMiIiIpSSJ0RzYiRiZGJyEiIiomRiVGJylGKSIiJUYnRis=

B2ex:=proc(n) collect(1/2/I/sqrt(3)*map(expand,map(rationalize,convert(normal(series((1+t)^2*jj*subs(x=jj,diff(Sex(n),x))-(1+t)^2/jj*subs(x=1/jj,diff(Sex(n),x)),t,n+1)),polynom))),t): end: B2ex(4);

LCgqJiIiJiIiIilJInRHNiIiIiVGJSEiIiomIiIjRiUpRiciIiRGJUYqKiYjRiVGLEYlKUYnRixGJUYq

R0ex:=proc(n) coeff(Rex(n),x,0): end: R1ex:=proc(n) coeff(Rex(n),x,1): end: Let us check n:=22: normal(series(subs(S(x)=Sex(n), R0=R0ex(n),R1=R1ex(n),B1=B1ex(n),B2=B2ex(n),eqScat),t,n+1));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiI0A=

Now we can start! LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Now we can start!

The coefficients of eqStcat are linearly related collect(eqStcatz,[St,z],distributed,factor)

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factor(isolate(coeff(coeff(eqStcatz,St,1),z,0)-c10,B2))

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eqStcatza:=collect(numer(factor(subs(%,eqStcatz))),[St,z],factor);

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map(factor,subs(c10=3*c10,%/3))

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eqStcatzb:=collect(%,[St,z],distributed,factor)

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factor(isolate(coeff(coeff(eqStcatzb,St,0),z,0)-c00,B1))

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numer(factor(subs(%,eqStcatzb)));

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eqStcatzc:=collect(%,[St,z],factor)

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factor(isolate(coeff(coeff(eqStcatzc,St,0),z,1)-c11,R1))

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numer(factor(subs(%,eqStcatzc)));

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factor(%)

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eqStcatzd:=collect(%,[St,z],factor)

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coeff(coeff(eqStcatzd,St,0),z,2)

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eqStcatze:=collect((eqStcatzd+ 3*(3*R0^2+3*R0*t+t^2 -c02)*(z^2+ z^2*3*St)),[St,z],factor)

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eqStcatzsmall:=collect(subs(c00=3*A0*t^2,c11=3*t^2*A1,c02=-t^2*A2,c10=A3*t^2,eqStcatze/t^2/3),[St,z],factor)

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factor(coeff(%,St,3))

LCQqKCIiKiIiIiwoKiYiIiNGJUkidEc2IkYlRiVJInpHRipGJUYlRiVGJSwoKiYiIzVGJUYpRiVGJSomIiIkRiVGK0YlISIiRiVGJUYlRiU=

collect(eqStcatz-3*t^2*eqStcatzsmall,[St,z],distributed,factor)

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

rel:={coeffs(%,[St,z])}

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

Aisolens:=op(solve(rel,[A0, A1,A2,A3]))

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

n:=10:subs(R0=R0ex(n),R1=R1ex(n),B1=B1ex(n),B2=B2ex(n), Aisolens): Aiserens:=map(Z->series(op(2,Z),t,n),%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlBaXNlcmVuc0dGKDcmKzVJInRHRigjISIjIiIkIiIhRjIiIiIjISIlRjMiIiMiIidGMyIjNyIiJSIkMyIiIiYiJClcRjkiJVdNIiIoLUkiT0dGJTYjRjUiIikrNUYwI0Y7RjNGNCMiIzVGM0Y1RjpGMyIjSUY7IiRlI0Y9IiUnSCJGOSIlTSopRkAiJllhJkZERkEiIiorM0YwISIiRjQhIiRGOCEiJ0YzISNhRjshJF8jRj0hJUE8RjkhJidRNUZARkFGRCs3RjBGUUY0ISM9RjVGM0Y4IiM9RjMiJDwiRjsiJCdbRj0iJTlKRjkiJiV5PEZAIic7YTZGREZBRk43I0Yu

Aisolens[3]

L0kjQTJHNiIsJComLCgqJiIiJCIiIilJI1IwR0YkIiIjRipGKiooRilGKkYsRipJInRHRiRGKkYqKiQpRi9GLUYqRipGKkYxISIiRjI=

A2v:=factor(rem(subs(R0=R0w,op(2,%)),algwv,w))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRBMnZHRigqJiwwKiYiIzYiIiIpSSJ2R0YoIiInRjJGMiomIiNDRjIpRjQiIiZGMkYyKiYiIz5GMilGNCIiJUYyRjIqJiIiKUYyKUY0IiIkRjIhIiIqJkY7RjIpRjQiIiNGMkZCKiZGP0YyRjRGMkZCRjJGQkYyKSwoKiZGRUYyRkBGMkYyKiZGPUYyRjRGMkZCRjJGQkZFRkI3I0Yu

res:=factor(resultant(numer(A2v-A2),algv,v)):nops(%); degree(%%,A2)

IiRwIg==

IiM3

algA2:=collect(res,A2,factor): Aisolens[2]

L0kjQTFHNiIsJCooIyIiIiIiJEYoLC4qKCIjYUYoSSNSMEdGJEYoSSNSMUdGJEYoRigqKCIjPUYoRi1GKEkidEdGJEYoISIiKigiI0ZGKEYuRihGMUYoRigqJiIjNUYoKUYxIiIjRihGMiomIiIqRihGLUYoRjIqJiIiJUYoRjFGKEYyRihGMUYyRjI=

A1v:=factor(subs(R0=R0w,R1=R1w,op(2,%)))

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

res:=factor(resultant(numer(A1v-A1),algv,v)):nops(%); degree(%%,A1)

IiIk

IiM3

nops(factor(res/op(1,res)/op(2,res)));

IiRaIw==

algA1:=op(3,res): Aisolens[4]

L0kjQTNHNiIsJCooIiIkIiIiLD4qKCIjQ0YoKUkjUjBHRiQiIiNGKEkidEdGJEYoISIiKioiIz1GKEYtRihJI1IxR0YkRihGL0YoRjAqKEYyRihGLUYoKUYvRi5GKEYwKigiI0ZGKClGM0YuRihGL0YoRigqKEY3RihGM0YoRjVGKEYwKiYiIiZGKClGL0YnRihGKCooRidGKEkjQjFHRiRGKEYvRihGKCooIiInRihJI0IyR0YkRihGLUYoRjAqKEYnRihGQUYoRi9GKEYwKiZGQEYoRixGKEYwKihGJ0YoRi1GKEYvRihGMCooIiIqRihGM0YoRi9GKEYwKiZGQEYoRjVGKEYoRi9GKEYoRi9GMEYw

factor(evala(Normal(subs(w=RootOf(algwv,w),factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,op(2,%)))))))

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

A3v:=factor(rem(%, algv,t))

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

res:=factor(resultant(numer(A3v-A3),algv,v)):nops(%); degree(%%,A3)

IiIk

IiM3

nops(factor(res/op(1,res)/op(2,res)));

IiQyJA==

algA3:=op(3,res): Aisolens[1]

L0kjQTBHNiIsJCooIyIiIiIiJEYoLEIqKCIjc0YoKUkjUjBHRiQiIiNGKClJInRHRiRGL0YoRigqKiIjYUYoRi5GKEkjUjFHRiRGKEYwRihGKCooRjNGKEYuRigpRjFGKUYoRigqKCIjIilGKClGNEYvRihGMEYoISIiKihGOEYoRjRGKEY2RihGKComIiImRigpRjEiIiVGKEYoKigiIz1GKEkjQjFHRiRGKEYtRihGKCoqRkFGKEZCRihGLkYoRjFGKEYoKigiIipGKEZCRihGMEYoRigqKkZBRihJI0IyR0YkRihGLkYoRjFGKEYoKihGRUYoRkdGKEYwRihGKCooRkFGKEYtRihGMUYoRigqKEZFRihGLkYoRjBGKEYoKigiI0ZGKEY0RihGMEYoRigqJiIiJ0YoRjZGKEY6KiZGL0YoRjBGKEY6RihGMEY6Rig=

factor(evala(Normal(subs(w=RootOf(algwv,w),factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,op(2,%)))))))

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

A0v:=factor(rem(%, algv,t))

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

res:=factor(resultant(numer(A0v-A0),algv,v)):nops(%); degree(%%,A0)

IiIk

IiM3

nops(factor(res/op(1,res)/op(2,res)));

IiRxJA==

algA0:=op(3,res):

e0:=eqStcatzsmall

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNlMEdGKCwsKiYsKComIiNGIiIiKUkiekdGKCIiI0YzISIiKiYsJiomIiNPRjNJInRHRihGM0YzIiM9RjdGM0Y1RjNGMyooIiIqRjMsJiomRjZGM0Y8RjNGM0YzRjNGMywmKiYiIzVGM0Y8RjNGM0YzRjNGM0YzRjMpSSNTdEdGKCIiJEYzRjMqJiwoKiYsJiomRkdGM0kjQTJHRihGM0YzRkdGM0YzRjRGM0YzKiYsKComRkdGM0kjQTFHRihGM0YzKiYiIiVGM0Y8RjNGN0Y2RjNGM0Y1RjNGM0kjQTNHRihGM0YzRkZGM0YzKiZGTUYzRjRGM0YzKiZGUUYzRjVGM0YzSSNBMEdGKEYzNyNGLg==

de1:=collect(diff(eqStcatzsmall,St),St,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZTFHRigsMCoqIiNGIiIiLCgqJiIiI0YxSSJ0R0YoRjFGMUkiekdGKEYxRjFGMUYxLCgqJiIjNUYxRjVGMUYxKiYiIiRGMUY2RjEhIiJGMUYxRjEpSSNTdEdGKEY0RjFGMSooRjtGMUkjQTJHRihGMSlGNkY0RjFGMSooRjtGMUkjQTFHRihGMUY2RjFGMSooIiIlRjFGNUYxRjZGMUY8KiZGO0YxRkFGMUYxSSNBM0dGKEYxKiZGNEYxRjZGMUYxNyNGLg==

dez:=diff(eqStcatzsmall,z)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXpHRigsKiomLCgqJiIjYSIiIkkiekdGKEYzISIiKiYiI09GM0kidEdGKEYzRjMiIz1GNUYzKUkjU3RHRigiIiRGM0YzKiYsKiooIiIjRjMsJiomRjxGM0kjQTJHRihGM0YzRjxGM0YzRjRGM0YzKiZGPEYzSSNBMUdGKEYzRjMqJiIiJUYzRjhGM0Y1RkBGM0YzRjtGM0YzKihGQEYzRkNGM0Y0RjNGM0ZFRjM3I0Yu

collect(St*de1-3*eqStcatzsmall,St,factor);

LCoqJiwuKigiIiciIiJJI0EyRzYiRicpSSJ6R0YpIiIjRichIiIqKEYmRidJI0ExR0YpRidGK0YnRi0qKCIiKUYnSSJ0R0YpRidGK0YnRicqJkYmRidGKkYnRi0qJkYsRidJI0EzR0YpRidGLSomIiIlRidGK0YnRi1GJ0kjU3RHRilGJ0YnKigiIiRGJ0YoRidGKkYnRi0qKEY6RidGL0YnRitGJ0YtKiZGOkYnSSNBMEdGKUYnRi0=

factor(resultant(de1,dez,A2))

LCQqKCwmKiYiIiQiIiJJI1N0RzYiRidGJ0YnRidGJ0kiekdGKUYnLD4qKCIlITMiRicpRigiIiNGJylJInRHRilGL0YnRicqKiIkIT1GJ0YuRidGMUYnRipGJ0YnKigiJDMiRidGLkYnKUYqRi9GJyEiIiooIiRbJ0YnRi5GJ0YxRidGJyooIiMhKkYnRi5GJ0YqRidGNyoqIiM3RidGKEYnRjFGJ0YqRidGJyooIiM9RidGKEYnRjZGJ0Y3KihGJkYnSSNBMUdGKUYnRipGJ0YnKiYiI2FGJ0YuRidGJyooIiInRidGKEYnRipGJ0Y3KigiIilGJ0YxRidGKkYnRjcqJkZFRidGNkYnRicqJkYvRidJI0EzR0YpRidGJyomIiIlRidGKkYnRidGJ0Y3

n:=8: normal(series(subs(S(x)=Sex(n),R0=R0ex(n),x=X1ser(n),StS),t,n)); normal(series(subs(S(x)=Sex(n),R0=R0ex(n),x=X3ser(n),t=s^2,StS),s,n)); normal(series(subs(S(x)=Sex(n),R0=R0ex(n),x=X5ser(n),t=s^2,StS),s,n))

KzFJInRHNiIjIiIiIiInIiIhI0YmIiIjRiojIiM4RioiIiUiIzoiIiYjIiQuJEYqRiciJD0oIiIoLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIik=

KzFJInNHNiIjISIiIiIkIiIhRiYiIiMhIiNGJyEiJiIiJSEjOCIiJiEjTyIiJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIiKA==

Ky1JInNHNiIjISIiIiIkIiIhIiIiIiIjISIkIiIlIiM3IiInLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIig=

collect(op(2,factor(resultant(de1,dez,A3))),St,factor); collect(op(4,factor(resultant(de1,dez,A2))),St,factor); collect(op(2,factor(resultant(de1,dez,A1))),St,factor);

LCoqJiwoKiYiIzciIiJJInRHNiJGJ0YnKiYiIz1GJ0kiekdGKUYnISIiIiInRi1GJylJI1N0R0YpIiIjRidGJyomLCgqJiIiJUYnRihGJ0YtKiZGLkYnRixGJ0YnRjFGJ0YnRjBGJ0YnKihGMUYnSSNBMkdGKUYnRixGJ0YnSSNBMUdGKUYn

LDAqJiwuKiYiJSEzIiIiIilJInRHNiIiIiNGJ0YnKigiJCE9RidGKUYnSSJ6R0YqRidGJyomIiQzIkYnKUYuRitGJyEiIiomIiRbJ0YnRilGJ0YnKiYiIyEqRidGLkYnRjIiI2FGJ0YnKUkjU3RHRipGK0YnRicqKiIiJ0YnRi5GJywoKiZGK0YnRilGJ0YnKiYiIiRGJ0YuRidGMkYnRjJGJ0Y5RidGJyooRj9GJ0kjQTFHRipGJ0YuRidGJyooIiIpRidGKUYnRi5GJ0YyKiZGO0YnRjFGJ0YnKiZGK0YnSSNBM0dGKkYnRicqJiIiJUYnRi5GJ0Yn

LDAqJiwuKiYiJFMmIiIiKUkidEc2IiIiI0YnISIiKigiI3NGJ0YpRidJInpHRipGJ0YsKiYiI0ZGJylGL0YrRidGJyomIiRDJEYnRilGJ0YsKiYiI09GJ0YvRidGJ0YxRixGJylJI1N0R0YqRitGJ0YnKioiIidGJ0YvRicsKComRitGJ0YpRidGJyomIiIkRidGL0YnRixGJ0YsRidGOEYnRiwqKEY+RidJI0EyR0YqRidGMkYnRicqKCIiJUYnRilGJ0YvRidGJyomRj5GJ0YyRidGLEkjQTNHRipGLComRitGJ0YvRidGLA==

res:=factor(resultant(de1,dez,St))

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

n:=6:normal(series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], z=zx/(1-2*t),x=X1ser(n),op(2,res)),t,n)); normal(series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], z=zx/(1-2*t),x=X3ser(n),t=s^2,op(2,res)),s,n)); normal(series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], z=zx/(1-2*t),x=X5ser(n),t=s^2,op(2,res)),s,n))

KzFJInRHNiIhIioiIiEhI08iIiIhIyEqIiIjISRfIyIiJCIkJHAiIiUiJSdcKSIiJi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIn

Ky1JInNHNiIhIz0iIiMiI08iIiQhJDwiIiIlIiMhKiIiJi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIiJw==

KylJInNHNiIiIz0iIiMiI2oiIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=

rem1:=collect(factor(rem(op(3,res),z^2-4*t*(1+t),z)),z,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVyZW0xR0YoLF5xKiYsYHAqKCInIW8uIiIiIilJI0EyR0YoIiIjRjMpSSJ0R0YoIiImRjNGMyoqIiZHUChGM0kjQTFHRihGM0Y1RjMpRjgiIiVGM0YzKigiJitrKUYzRjRGM0Y9RjNGMyooIiZfMiJGM0Y1RjNGN0YzISIiKigiJTdwRjMpRjxGNkYzKUY4IiIkRjNGMyoqIiZTPSZGM0Y8RjNGNUYzRkdGM0YzKigiJlNJI0YzRjxGM0Y9RjNGMyooIiY/ZiNGM0Y0RjNGR0YzRkMqKiIlXzZGM0Y1RjNJI0EzR0YoRjNGR0YzRjMqKCImKyM+RjNGNUYzRj1GM0YzKiYiJnNBI0YzRjdGM0ZDKioiJiszIkYzRjxGM0Y1RjMpRjhGNkYzRjMqKiIlTzpGM0Y8RjNGUUYzRlhGM0YzKigiJjshUUYzRjxGM0ZHRjNGMyooIiZnSCJGM0Y0RjNGWEYzRkMqKiIlRzxGM0Y1RjNGUUYzRlhGM0YzKigiJltLIkYzRjVGM0ZHRjNGMyooIiVrO0YzRlFGM0ZHRjNGQyomIiZ3XCJGM0Y9RjNGQyooIiUnSCJGM0ZGRjNGOEYzRkMqKiIlb25GM0Y8RjNGNUYzRjhGM0YzKioiJWM1RjNGPEYzRlFGM0Y4RjNGMyooIiYnKkcjRjNGPEYzRlhGM0YzKigiJT9WRjNGNEYzRjhGM0ZDKipGYm9GM0Y1RjNGUUYzRjhGM0ZDKigiJidcOUYzRjVGM0ZYRjNGQyooIiNbRjMpRlFGNkYzRjhGM0ZDKigiJCM+RjNGUUYzRlhGM0YzKiYiJVNRRjNGR0YzRjMqJiIkOyNGM0ZGRjNGQyooIiRDJEYzRjxGM0Y1RjNGMyooIiNnRjNGPEYzRlFGM0YzKigiJD8oRjNGPEYzRjhGM0ZDKigiI3NGM0Y1RjNGUUYzRjMqKCIlM0FGM0Y1RjNGOEYzRjMqJiIjQ0YzRmBwRjNGMyooRmJwRjNGUUYzRjhGM0YzKiYiJXNJRjNGWEYzRjMqJiIkMyJGM0Y8RjNGMyomIiNrRjNGUUYzRjMqJkZccUYzRjhGM0YzRmJxRjNGM0kiekdGKEYzRjMqJiIjN0YzRlFGM0YzKigiI09GM0Y8RjNGUUYzRjMqJiIjIilGM0ZGRjNGMyooRmJvRjNGNEYzRjhGM0YzKihGXHFGM0Y1RjNGOEYzRjMqKCIlKVsiRjNGPEYzRjhGM0YzKiZGPkYzRmBwRjNGMyooIidjSThGM0Y0RjNGPUYzRjMqKCImM00kRjNGNEYzRkdGM0YzKigiJ1tjSkYzRjVGM0Y9RjNGMyooIiVbZ0YzRkZGM0ZYRjNGMyooIiZrZyNGM0Y0RjNGWEYzRjMqKCInN0A3RjNGNUYzRkdGM0YzKigiJXM9RjNGRkYzRjhGM0YzKigiJTdkRjNGPEYzRlhGM0ZDKigiJSdcKUYzRjVGM0ZYRjNGQyooRmpvRjNGUUYzRlhGM0YzKigiJClHRjNGUUYzRjhGM0YzKigiJ0NVQ0YzRjRGMylGOCIiJ0YzRjMqKCInUydvJEYzRjRGM0Y3RjNGMyooIid3ODVGM0Y1RjNGXnRGM0YzKihGTEYzRkZGM0Y9RjNGMyooIiZnYCJGM0Y8RjNGN0YzRkMqKCInJ3AmR0YzRjVGM0Y3RjNGMyooIiZPMiNGM0ZGRjNGR0YzRjMqKCIkbyhGM0Y8RjNGPUYzRjMqKEZFRjNGUUYzRj1GM0YzKigiJGciRjNGYHBGM0ZYRjNGMyooIiUlKSoqRjNGUUYzRkdGM0YzKigiJEciRjNGYHBGM0Y4RjNGMyoqIicjZjUiRjNGPEYzRjVGM0Y3RjNGMyoqIiYvLiNGM0Y8RjNGNUYzRlhGM0ZDKioiJGckRjNGPEYzRlFGM0Y4RjNGQyoqIiVnZEYzRjVGM0ZRRjNGWEYzRjMqKiImQ1EiRjNGNUYzRlFGM0ZHRjNGMyoqIiR3JkYzRjxGM0ZRRjNGWEYzRjMqKkYyRjNGPEYzRjVGM0Y9RjNGMyoqIiVbJSlGM0Y1RjNGUUYzRj1GM0YzKigiJUcqKUYzRjxGM0ZHRjNGMyomIidjPTdGM0Y3RjNGMyomIicnXDkiRjNGPUYzRjMqJiImKVtaRjNGR0YzRjMqJiIlO0NGM0ZYRjNGQyomIiZjeSZGM0ZedEYzRjMqJiIkI2ZGM0Y4RjNGMyoqIiZHTCNGM0Y8RjNGNUYzRkdGM0ZDKioiJSkpUUYzRjxGM0Y1RjNGOEYzRkMqKiIkJVFGM0Y1RjNGUUYzRjhGM0YzNyNGLg==

coeff(rem1,z);indets(%);coeff(rem1,z,0);indets(%);indets(c1);indets(c0)

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

PCZJI0ExRzYiSSNBMkdGJEkjQTNHRiRJInRHRiQ=

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

PCZJI0ExRzYiSSNBMkdGJEkjQTNHRiRJInRHRiQ=

PCdJI0EwRzYiSSNBMUdGJEkjQTJHRiRJI0EzR0YkSSJ0R0Yk

PCdJI0EwRzYiSSNBMUdGJEkjQTJHRiRJI0EzR0YkSSJ0R0Yk

co1:=collect(coeff(rem1,z),A3,factor); degree(%,A2)

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

IiIj

co0:=collect(coeff(rem1,z,0),A3,factor); degree(%,A3)

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

IiIj

with(Groebner)

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

?Basis base:=factor(Basis([co0,co1,c1],plex(A1,A2,A3))):

Warning, computation interrupted

nops(base)

IiIl

map(nops,base)

NyYiJFAjIiRYIyIkQyMiJEEj

map(degree,base,[A1,A2,A3]); map(indets,base)

NyYiIiUiIiNGJEYk

NyY8JUkjQTJHNiJJI0EzR0YlSSJ0R0YlPCZJI0ExR0YlRiRGJkYnRihGKA==

op(1,base)

,fhl*("1/*fw(HPt7""")I#A2G6"""%F%)I"tGF("#=F%F%*("1%y'3ogi#['F%F&F%)F+"#<F%F%*("1wd">$Hp4MF%)F'""$F%F*F%F%*("2S!>pl*RAg"F%F&F%)F+"#;F%F%**"0Sak*HNH>F%F3F%I#A3GF(F%F7F%F%*("2SYq9KS#=<F%F3F%F/F%F%*("1sU4([GA[$F%)F'""#F%F*F%F%*("2;/Y5"*e?]#F%F&F%)F+"#:F%F%**"0W*yHBBC&)F%F3F%F;F%FDF%F%*("2;cxtuzy?%F%F3F%F7F%F%**"0#*4iP(=^RF%F@F%F;F%F7F%F%*("2k)3>^m!pu"F%F@F%F/F%F%*("1#>cW)*=ig"F%F'F%F*F%F%*("2k+G7B#G9FF%F&F%)F+"#9F%F%**"1c!*=q'4%3=F%F3F%F;F%FRF%F%*("2[%37>#[h`'F%F3F%FDF%F%**"/+W$HBi4"F%F@F%)F;FAF%FRF%F%**"1[sf))HCK<F%F@F%F;F%FDF%F%*("2#>%y>#eJgUF%F@F%F7F%F%**"0W8[*>_SFF%F'F%F;F%F7F%F%*("1G<#4"*[M1)F%F'F%F/F%F%*&"0c-3ibd#GF%F*F%F%*("23E@=<%fL@F%F&F%)F+"#8F%F%**"1sIgXj!\R#F%F3F%F;F%FaoF%F%*("2#R*\"efjbqF%F3F%FRF%F%**"/![s^ae5%F%F@F%FZF%FaoF%F%**"1G\KN'fdk$F%F@F%F;F%FRF%F%*("27ldW*3$yg'F%F@F%FDF%F%**"/g<9HlD:F%F'F%FZF%FRF%F%**"1/v2`eW*>"F%F'F%F;F%FDF%F%*("2_v+y&f'p'>F%F'F%F7F%F%*("//$=!eqWkF%F;F%F7F%F%*&"1/bS3-vF9F%F/F%F%*("2%Q#*\4'*4L7F%F&F%)F+"#7F%F%**"1K76m\In@F%F3F%F;F%FipF%F%*("2[7qj>>5^&F%F3F%FaoF%F%**"/%=@uIGD(F%F@F%FZF%FipF%F%**"1)GS(43%4"[F%F@F%F;F%FaoF%F%*("2/>4g1z>8(F%F@F%FRF%F%**"-+S1CoFF%F'F%)F;F4F%FipF%F%**"/wXQ*R!)o&F%F'F%FZF%FaoF%F%**"1g(46uWv^#F%F'F%F;F%FRF%F%*("2_NYXSCc0$F%F'F%FDF%F%*(".%y=`&fR&F%FZF%FRF%F%*("0'pdHHXMGF%F;F%FDF%F%*&"1C=%H019]$F%F7F%F%*("1)o-W)Q-R_F%F&F%)F+"#6F%F%**"1CU7Z@V&R"F%F3F%F;F%FfrF%F%*("2O.NaMB@;$F%F3F%FipF%F%**"/)3(4J>$)yF%F@F%FZF%FfrF%F%**"1c5!*HJ;SVF%F@F%F;F%FipF%F%*("2'47QU9(3d&F%F@F%FaoF%F%**"-+7&[g])F%F'F%FgqF%FfrF%F%**"//V"\()z(**F%F'F%FZF%FipF%F%**"1s5H/)R>K$F%F'F%F;F%FaoF%F%*("2K%y8$G)f7LF%F'F%FRF%F%*("-+sU$H'>F%FgqF%FipF%F%*("/'H*f30<?F%FZF%FaoF%F%*("0['R<h+nfF%F;F%FRF%F%*&"1)Gc&3`*zY&F%FDF%F%*("1?N%[[e7i"F%F&F%)F+"#5F%F%**"0SQgl"fpkF%F3F%F;F%FdtF%F%*("2[[htUOsL"F%F3F%FfrF%F%**"/?&R@hFu&F%F@F%FZF%FdtF%F%**"1_BLjG`"y#F%F@F%F;F%FfrF%F%*("2+/&4bp>'>$F%F@F%FipF%F%**".?B.:O>"F%F'F%FgqF%FdtF%F%**"03-(Qkx#3"F%F'F%FZF%FfrF%F%**"1+%)fi&*p1IF%F'F%F;F%FipF%F%*("2'pXCD!>lg#F%F'F%FaoF%F%*("+++W@EF%)F;F)F%FdtF%F%*("-SI9tHgF%FgqF%FfrF%F%*("/Oz;gXNNF%FZF%FipF%F%*("0[)ys=d+zF%F;F%FaoF%F%*&"1+KcS%pv(fF%FRF%F%*("0#fA5nJ)o$F%F&F%)F+""*F%F%**"0SMh(ods@F%F3F%F;F%FevF%F%*("1[7#3wl5=%F%F3F%FdtF%F%**"/%)R62JLHF%F@F%FZF%FevF%F%**"1%=$\Q;`'G"F%F@F%F;F%FdtF%F%*("2'p*yl\?#\8F%F@F%FfrF%F%**".%Q?v^=5F%F'F%FgqF%FevF%F%**"/gX^?H&*yF%F'F%FZF%FdtF%F%**"1++G4%pm$>F%F'F%F;F%FfrF%F%*("2ceIdP+*3:F%F'F%FipF%F%*("++gX"H'F%FjuF%FevF%F%*("-_**=)[S)F%FgqF%FdtF%F%*("/?nW7[TQF%FZF%FfrF%F%*("0!o*>/Jn?(F%F;F%FipF%F%*&"1kcu8]g]ZF%FaoF%F%*("/+w42$yb'F%F&F%)F+"")F%F%**"/+c)\muI&F%F3F%F;F%FexF%F%*("0;#HZt=(y*F%F3F%FevF%F%**"/+'\Myp1"F%F@F%FZF%FexF%F%**"0;_yfkkK%F%F@F%F;F%FevF%F%*("1'H**48-oA%F%F@F%FdtF%F%**"-+G<kTdF%F'F%FgqF%FexF%F%**"/kcQ-<ESF%F'F%FZF%FevF%F%**"0g,-h?X+*F%F'F%F;F%FdtF%F%*("1Ob)R2dJS'F%F'F%FfrF%F%*("++Cu[kF%FjuF%FexF%F%*("-#*pf%e<(F%FgqF%FevF%F%*("/C'e7Bj#GF%FZF%FdtF%F%*("0wd.`\(yYF%F;F%FfrF%F%*&"1on*G@e%pFF%FipF%F%*("/wHe:$R/"F%F&F%)F+""(F%F%**".s-(["H$**F%F3F%F;F%FezF%F%*("0'\#G%>2$z"F%F3F%FexF%F%**".))=%fvVGF%F@F%FZF%FezF%F%**"0CM]m*3y5F%F@F%F;F%FexF%F%*("0/6fCl$o**F%F@F%FevF%F%**"-/6VC%H#F%F'F%FgqF%FezF%F%**"/?V55Yt9F%F'F%FZF%FexF%F%**"0cIXh*y:IF%F'F%F;F%FevF%F%*("1oZe"fdr(>F%F'F%FdtF%F%*("+g(pG7%F%FjuF%FezF%F%*("-s)R%*z5%F%FgqF%FexF%F%*("/))==')))[9F%FZF%FevF%F%*("07(fisKx@F%F;F%FdtF%F%*&"1;W%[Hkl<"F%FfrF%F%*(".oBog`:"F%F&F%)F+""'F%F%**".K#z!etV"F%F3F%F;F%Fe\lF%F%*("/S="=TAZ#F%F3F%FezF%F%**"-;;fIJbF%F@F%FZF%Fe\lF%F%**"/cqBkQ!*>F%F@F%F;F%FezF%F%*("0S!>PT=i<F%F@F%FexF%F%**",+wdFf'F%F'F%FgqF%Fe\lF%F%**".W8)=y!)QF%F'F%FZF%FezF%F%**"/g\Yr[\tF%F'F%F;F%FexF%F%*("0?^k'\q5XF%F'F%FevF%F%*("+%=8/!=F%FjuF%Fe\lF%F%*("-?ZdcH;F%FgqF%FezF%F%*(".35&Qan_F%FZF%FexF%F%*("/++;oY]sF%F;F%FevF%F%*&"0;'z/,=$f$F%FdtF%F%*("-C9F@*R"F%F&F%)F+""&F%F%**"-wP)e2$=F%F3F%F;F%Fe^lF%F%*(".?z\zsn$F%F3F%Fe\lF%F%**",[!yx.#)F%F@F%FZF%Fe^lF%F%**".O"z*R5.$F%F@F%F;F%Fe\lF%F%*("/sa)p][v#F%F@F%FezF%F%**",!G"3]Q"F%F'F%FgqF%Fe^lF%F%**"-3]ndmwF%F'F%FZF%Fe\lF%F%**"/%=Ddg&z8F%F'F%F;F%FezF%F%*("/w@3k*)R")F%F'F%FexF%F%*("*s9[l&F%FjuF%Fe^lF%F%*(",wL@Mm%F%FgqF%Fe\lF%F%*(".w&3o7z8F%FZF%FezF%F%*("/wX-orX<F%F;F%FexF%F%*&"/CI"4(o(*zF%FevF%F%*("+/z%\N*F%F&F%)F+F)F%F%**",/jyxc"F%F3F%F;F%Fe`lF%F%*("-%y#)z$oGF%F3F%Fe^lF%F%**"+k#fy8*F%F@F%FZF%Fe`lF%F%**"-c#))eFO$F%F@F%F;F%Fe^lF%F%*("./Jmab%HF%F@F%Fe\lF%F%**"+W4Lu?F%F'F%FgqF%Fe`lF%F%**"-)3L=$=6F%F'F%FZF%Fe^lF%F%**".;3")fy*>F%F'F%F;F%Fe\lF%F%*("/35"GJ$)="F%F'F%FezF%F%*("*%ebv7F%FjuF%Fe`lF%F%*("+sY;&f*F%FgqF%Fe^lF%F%*("-7TVR#o#F%FZF%Fe\lF%F%*(".'4we@TKF%F;F%FezF%F%*&"/KoDB*fW"F%FexF%F%*("*[s$o))F%F&F%)F+F4F%F%**"+3U<a9F%F3F%F;F%FdblF%F%*(",s)>$Qt$F%F3F%Fe`lF%F%**"*)Gk6()F%F@F%FZF%FdblF%F%**",s=G4&RF%F@F%F;F%Fe`lF%F%*("-WpU!)3XF%F@F%Fe^lF%F%**"*3=^B#F%F'F%FgqF%FdblF%F%**",7*=KU8F%F'F%FZF%Fe`lF%F%**"-ObA_qEF%F'F%F;F%Fe^lF%F%*(".;?A7@q"F%F'F%Fe\lF%F%*(")[CJ?F%FjuF%FdblF%F%*("+%yqiY"F%FgqF%Fe`lF%F%*(",C'='))*QF%FZF%Fe^lF%F%*("-%eFELb%F%F;F%Fe\lF%F%*&".KgR79%>F%FezF%F%*(");(z&GF%F&F%)F+FAF%F%**")'HT*fF%F3F%F;F%FcdlF%F%*("+?jTK:F%F3F%FdblF%F%**");!Ho%F%F@F%FZF%FcdlF%F%**"+/VD/BF%F@F%F;F%FdblF%F%*(",!G6\a?F%F@F%Fe`lF%F%**");s;;F%F'F%FgqF%FcdlF%F%**"+_$[x3"F%F'F%FZF%FdblF%F%**",?^Q$GAF%F'F%F;F%Fe`lF%F%*("-Gd%p7X"F%F'F%Fe^lF%F%*("(cF3#F%FjuF%FcdlF%F%*("*CY&*f"F%FgqF%FdblF%F%*("+[w?)y%F%FZF%Fe`lF%F%*(",g04()\'F%F;F%Fe^lF%F%*&"-/nd;HMF%Fe\lF%F%*("(kd7#F%F&F%F+F%F%**"(kS4%F%F3F%F;F%F+F%F%*("*W[I["F%F3F%FcdlF%F%**"(Co&HF%F@F%FZF%F+F%F%**"*%Q6<?F%F@F%F;F%FcdlF%F%*("+cIN7HF%F@F%FdblF%F%**"'/"\*F%F'F%FgqF%F+F%F%**")?WN!*F%F'F%FZF%FcdlF%F%**"+)G;\9#F%F'F%F;F%FdblF%F%*(",%y'[!G;F%F'F%Fe`lF%F%*("'WU6F%FjuF%F+F%F%*(")_DI8F%FgqF%FcdlF%F%*("*C5?B%F%FZF%FdblF%F%*("+)36iB&F%F;F%Fe`lF%F%*&",O2M$G=F%Fe^lF%F%*("(c")f#F%F3F%F+F%F%**"('\"R%F%F@F%F;F%F+F%F%*("*/Zk5"F%F@F%FcdlF%F%**"(!eWCF%F'F%FZF%F+F%F%**"*[;H9"F%F'F%F;F%FcdlF%F%*("*O.vR*F%F'F%FdblF%F%*("'o*[%F%FgqF%F+F%F%*("))e@#GF%FZF%FcdlF%F%*("*G*)3B&F%F;F%FdblF%F%*&"+K[>!y$F%Fe`lF%F%*("&$o>F%F@F%F;F%F%*("([WT#F%F@F%F+F%F%*("&a*=F%F'F%FZF%F%**"(GP8$F%F'F%F;F%F+F%F%*(")[4XgF%F'F%FcdlF%F%*&"%jXF%FgqF%F%*("'+(e(F%FZF%F+F%F%*(")%)f!3#F%F;F%FcdlF%F%*&")sIi))F%FdblF%F%*("&AJ"F%F'F%F;F%F%*("(?g+"F%F'F%F+F%F%*&"&zG"F%FZF%F%*("'_(o)F%F;F%F+F%F%*&")C9f6F%FcdlF%F%*&"%hlF%F;F%F%*&"'o4AF%F+F%F%"$H(F%

collect(numer(factor(rem(coeff(rem1,z,0),coeff(rem1,z,1),A3))),A3,factor)

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

factor(resultant(coeff(rem1,z,0),coeff(rem1,z,1),A3))

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

This discriminant must be related to Disc3 discsmall:=factor(discrim(eqStcatzsmall,St))

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

factor(subs(Aisolens,discsmall)/Disc3)

LCQqKiIlKD0jIiIiKUkidEc2IiIiJyEiIiwoKiYiIiNGJUYnRiVGJUkiekdGKEYlRiVGJUYlLCgqJiIjNUYlRidGJUYlKiYiIiRGJUYuRiVGKkYlRiVGJUYl

Disc3small:=collect(numer(factor(discsmall/((2187*(2*t+z+1))*(10*t-3*z+1)/t^6)))/t^6,z,factor)

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

reste:=collect(factor(rem(Disc3small,z^2-4*t*(1+t),z)),z,factor)

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

c0:=collect(coeff(reste,z,0),[A0,A3,A2,A1],factor); c1:=collect(coeff(reste,z,1),A0,factor)

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

map(factor,rem(c0,c1,A1))

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

coeff(%,A1,1)

LCQqLCIkVyIiIiJJInRHNiJGJSwmRiZGJUYlRiVGJSwmKiYiIiNGJUYmRiVGJUYlISIiRiUsLiooIiNnRiVJI0EyR0YnRiUpRiZGK0YlRiUqKEYvRiVGMEYlRiZGJUYlKiYiI1tGJUYxRiVGLComIiNGRiVJI0EwR0YnRiVGJSomIiIlRiVJI0EzR0YnRiVGLComRjRGJUYmRiVGLEYlRiw=

degree(c0,A0);degree(c1,A0)

IiIj

IiIj

This polynomial is a square quotient:=collect(factor(quo(Disc3small,z^2-4*t*(1+t),z)),z,factor)

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

D4form:=add(d[i]*z^i,i=0..4);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdENGZvcm1HRigsLComKUkiekdGKCIiJSIiIiZJImRHRig2I0YyRjNGMyomKUYxIiIkRjMmRjU2I0Y5RjNGMyomKUYxIiIjRjMmRjU2I0Y+RjNGMyomRjFGMyZGNTYjRjNGM0YzJkY1NiMiIiFGMzcjRi4=

collect(D4form-(alpha*z^2+beta*z+g)^2,z,factor);

LC4qJiwmKiQpSSZhbHBoYUc2IiIiIyIiIiEiIiZJImRHRig2IyIiJUYqRiopSSJ6R0YoRi9GKkYqKiYsJiooRilGKkYnRipJJWJldGFHRihGKkYrJkYtNiMiIiRGKkYqKUYxRjhGKkYqKiYsKCooRilGKkYnRipJImdHRihGKkYrKiQpRjVGKUYqRismRi02I0YpRipGKilGMUYpRipGKiomLCYqKEYpRipGNUYqRj1GKkYrJkYtNiNGKkYqRipGMUYqRioqJClGPUYpRipGKyZGLTYjIiIhRio=

sol:=factor(solve({seq(coeff(%,z,i),i=2..4)},{alpha,beta,g}));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig8JS9JJmFscGhhR0YoLUknUm9vdE9mR0YlNiMsJiokKUkjX1pHRiUiIiMiIiJGOSZJImRHRig2IyIiJSEiIi9JJWJldGFHRigsJCoqI0Y5RjhGOSZGOzYjIiIkRjlGMUY5RjpGPkY5L0kiZ0dGKCwkKiojRjkiIilGOSwmKihGPUY5JkY7NiNGOEY5RjpGOUY5KiQpRkRGOEY5Rj5GOSlGOkY4Rj5GMUY5Rjk3I0Yu

D4formfinal:=subs(RootOf(_Z^2-d[4])=sqrt(d[4]),factor(expand(subs(sol,(alpha*z^2+beta*z+g)^2))));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSxENGZvcm1maW5hbEdGKCwkKigjIiIiIiNrRjEpJkkiZEdGKDYjIiIlIiIkISIiKSwqKigiIilGMSlJInpHRigiIiNGMSlGNEZARjFGMSoqRjdGMUY/RjEmRjU2I0Y4RjFGNEYxRjEqKEY3RjEmRjU2I0ZARjFGNEYxRjEqJClGQ0ZARjFGOUZARjFGMTcjRi4=

eqdi:=map(numer,[coeffs(collect(D4form-D4formfinal,z,factor),z)]);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcWRpR0YoNyQsKiooIiNrIiIiJkkiZEdGKDYjIiIhRjIpJkY0NiMiIiUiIiRGMkYyKigiIztGMikmRjQ2IyIiI0ZBRjIpRjhGQUYyISIiKioiIilGMkY/RjIpJkY0NiNGO0ZBRjJGOEYyRjIqJClGR0Y6RjJGQywoKihGRUYyJkY0NiNGMkYyRkJGMkYyKipGOkYyRj9GMkZHRjJGOEYyRkMqJClGR0Y7RjJGMjcjRi4=

map(factor,series(sqrt(D4form/d[4]),z=infinity,3))

LDAqJClJInpHNiIiIiMiIiJGKCoqI0YoRidGKCZJImRHRiY2IyIiJEYoJkYsNiMiIiUhIiJGJUYoRigqKEYqRigmRiw2I0YnRihGL0YyRigqKCNGKCIiKUYoKUYrRidGKClGL0YnRjJGMioqI0YoIiM7RigsKCooRjhGKCZGLDYjRihGKEY6RihGKCoqRjFGKEY0RihGK0YoRi9GKEYyKiQpRitGLkYoRihGKClGL0YuRjJGJUYyRigqKiNGKCIkRyJGKCwsKigiI2tGKCZGLDYjIiIhRihGRUYoRigqKiIjS0YoRkBGKEYrRihGOkYoRjIqKEY9RigpRjRGJ0YoRjpGKEYyKioiI0NGKEY0RihGOUYoRi9GKEYoKiYiIiZGKClGK0YxRihGMkYoKUYvRjFGMkYkRjJGKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IyokKUYlRi5GMkYo

systsmall:=numer(factor(subs(seq(d[i]=coeff(quotient,z,i),i=0..4), eqdi))):nops(%)

IiIj

op(2,systsmall)

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

systsmall:=subsop(2=op(3,op(2,systsmall)),systsmall): systsmall:=subsop(1=op(3,op(1,systsmall)),systsmall): map(nops,systsmall)

NyQiJCg+IiN6

systsmall:=[c0,c1,op(systsmall)]: map(nops,systsmall)

NyYiIzYiI1UiJCg+IiN6

systfinalsmall:=factor(systsmall): map(nops,systfinalsmall);map(indets,systfinalsmall); map(degree,systfinalsmall,A0);map(degree,systfinalsmall,A1);map(degree,systfinalsmall,A2);map(degree,systfinalsmall,A3);

NyYiI2giI1oiJCg+IiN6

NyY8J0kjQTBHNiJJI0ExR0YlSSNBMkdGJUkjQTNHRiVJInRHRiVGI0YjRiM=

NyYiIiNGI0YjIiIi

NyYiIiMiIiQiIiVGJA==

NyYiIiQiIiMiIikiIiY=

NyYiIiQiIiNGJCIiIg==

libname:="/home/bousquet/Calculs/FGB/FGblib",libname;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShsaWJuYW1lR0YoNiRRQi9ob21lL2JvdXNxdWV0L0NhbGN1bHMvRkdCL0ZHYmxpYkYoUTMvb3B0L21hcGxlMjAxOC9saWJGKDckRi9GMA==

with(FGb);

Path set to /home/bousquet/Calculs/FGB/FGblib/../libfgbunid.so FGb/Maple interface package Version 1.61 JC Faugere (Jean-Charles.Faugere@inria.fr) Type ?FGb for documentation

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

fgb_gbasis_elim([x^2+y,y^2+x],0,[x],[y]);

NyMsJiokKUkieUc2IiIiJSIiIiIiIkkieUc2IiIiIg==

fgb_gbasis([x^2+y,y^2+x],0,[x],[y]);

NyQsJiokKUkieUc2IiIiIyIiIkYpSSJ4R0YnRiksJiokKUYmIiIlRilGKUYmRik=

F:=[x+28*u-16*v-30*u*v , y-72+87*u^2-47*u*v , z+48-53*u+28*u^2]: indets(F)

PCdJInVHNiJJInZHRiRJInhHRiRJInlHRiRJInpHRiQ=

fgb_gbasis_elim(F , 0 , [u,v ] , [x,y,z ] ) ;

NyMsQiooIidHZicpIiIiKUkieEc2IiIiIyIiIkkiekc2IiIiIiIiIioqIihTYTUiIiIiSSJ4RzYiIiIiSSJ5RzYiIiIiSSJ6RzYiIiIiISIiKigiKGdaViQiIiJJInhHNiIiIiIpSSJ6RzYiIiIjIiIiIiIiKigiJytHTiIiIilJInlHNiIiIiMiIiJJInpHNiIiIiIiIiIqKCIoK0M+IyIiIkkieUc2IiIiIilJInpHNiIiIiMiIiIhIiIqJiIoXWdTJCIiIilJInpHNiIiIiQiIiIiIiIqJiIpV1hjVCIiIilJInhHNiIiIiMiIiIiIiIqKCIpc1lvbyIiIkkieEc2IiIiIkkieUc2IiIiIiEiIiooIiosIylRTSMiIiJJInhHNiIiIiJJInpHNiIiIiIiIiIqJiIpT25ySCIiIilJInlHNiIiIiMiIiIiIiIqKCIqJWY/TkMiIiJJInlHNiIiIiJJInpHNiIiIiIhIiIqJiIqLzltYCciIiIpSSJ6RzYiIiIjIiIiIiIiKiYiK19CJT1ZJSIiIkkieEc2IiIiIiIiIiomIis/Sik+SyYiIiJJInlHNiIiIiIhIiIqJiIsX2ZkZihSIiIiSSJ6RzYiIiIiIiIiIi1LY1s1Ij0nIiIi

res:=fgb_gbasis(systfinalsmall,0,[A0,A1,A2],[t,A3]):

Warning, computation interrupted

lower the degrees in A0 systa:=numer([systfinalsmall[4], op(factor(subs(isolate(systfinalsmall[4],A0),subsop(4=NULL,systfinalsmall))))]): map(nops,%)

NyYiI3oiJCh5IiQ0JyIiJQ==

op(4,systa)/op(4,op(4,systa))

LCQqKCIiIyIiIiwmKiYiIiVGJUkjQTJHNiJGJUYlRiVGJUYlKSwmRilGJUYkISIiRiRGJUYl

systb:=subsop(4=op(4,op(4,systa)),systa): map(nops,systb); map (indets, systb)

NyYiI3oiJCh5IiQ0JyIkJVs=

NyY8J0kjQTBHNiJJI0ExR0YlSSNBMkdGJUkjQTNHRiVJInRHRiU8JkYmRidGKEYpRipGKg==

map(degree,systd,A0);map(degree,systd,A1);map(degree,systd,A2);map(degree,systd,A3);

NyYiIiIiIiFGJEYk

NyYiIiQiIidGJEYk

NyYiIiYiIzZGJCIjNQ==

NyYiIiIiIiQiIiNGJQ==

res1:=factor(rem(systd[4],systd[3],A3)):nops(%)

IiIn

map(indets,[seq(op(i,res1),i=1..nops(res1))])

Nyg8IjwlSSNBMUc2IkkjQTJHRiZJInRHRiY8JkYlRidJI0EzR0YmRig8I0YnRitGJA==

for i from 2 to 6 do series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], op(i,res1)),t,n) od

KzNJInRHNiIiIioiIiEhIz0iIiIiI3MiIiMiJShHIiIiJSIlUVYiIiYiJnMnUiIiJyInP2RBIiIoLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIik=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

KzFJInRHNiIjISIiIiIkISIjIyIiI0YnRiYjIiM5RiciIiEjIiM/RiciIiIiI1FGKiMiJF0mRidGJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YwIiIl

KzNJInRHNiIjISIiIiIkIiIhIyIiIkYnIiIjI0YrRidGJyMiIzxGJyIiJSMiIyEpRiciIiYjIiROJkYnIiInIiV3NSIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YqIiIp

KzVJInRHNiIjIiIiIiRWIyIiISMiIiVGJ0YmIyEiIiIjIikiIiMjISNlRiciIiQjISRfJEYnRiojISRHJ0YtIiImIyElTjYiI0YiIicjISZnJD5GLSIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YmIiIp

res3:=op(3,res1):nops(%); degree(res3,A3)

IiRGKg==

IiIi

res4:=numer(factor(subs(isolate(res3,A3),systd[2]))): nops(%)

IiIk

map(indets,[seq(op(i,res4),i=1..nops(res4))])

NyU8JEkjQTFHNiJJInRHRiU8JUYkSSNBMkdGJUYmRic=

for i from 1 to 3 do series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], op(i,res4)),t,n) od

KzVJInRHNiIiIioiIiEiIz0iIiIiI3MiIiQiJCE9IiIlIiVbOiIiJiIld3giIiciJi9PJiIiKCInd0VMIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGJQ==

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

KzVJInRHNiIiIyIpIiIhISRDJCIiIiIlPzsiIiMhJSNmIyIiJCImXSRHIiIlIiZfPCQiIiYiJ2NLdSIiJyIoUyVmSyIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIp

res5:=op(2,res4):nops(%); indets(res5)

IiZlNCI=

PCVJI0ExRzYiSSNBMkdGJEkidEdGJA==

res6:=numer(factor(subs(isolate(res3,A3),systd[3]))): nops(%)

IiIn

map(indets,[seq(op(i,res6),i=1..nops(res6))])

Nyg8I0kjQTJHNiJGIzwkSSNBMUdGJUkidEdGJTwlRidGJEYoRilGKQ==

for i from 1 to 6 do series(subs(A1=Aiserens[2], A2=Aiserens[3], A3=Aiserens[4], op(i,res6)),t,n) od

KzFJInRHNiIhIiQiIiMhIiciIiQhI2EiIiUhJF8jIiImISVBPCIiJyEmJ1E1IiIoLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiIp

KzNJInRHNiIhIiQiIiFGJSIiIyEiJyIiJCEjYSIiJSEkXyMiIiYhJUE8IiInISYnUTUiIigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

KzVJInRHNiIiIioiIiEiIz0iIiIiI3MiIiQiJCE9IiIlIiVbOiIiJiIld3giIiciJi9PJiIiKCInd0VMIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGJQ==

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

KzVJInRHNiIiJFYjIiIhISRzKiIiIiIlPFkiIiMhJSFIKCIiJCImckAoIiIlIiYrSCgiIiYiKHUjeTwiIiciKEkkM3ciIigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiKQ==

KzVJInRHNiIiIyIpIiIhISRDJCIiIiIlPzsiIiMhJSNmIyIiJCImXSRHIiIlIiZfPCQiIiYiJ2NLdSIiJyIoUyVmSyIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIp

res7:=op(4,res6):nops(%); indets(res7)

IiVAPg==

PCVJI0ExRzYiSSNBMkdGJEkidEdGJA==

degree(res5,A1);degree(res5,A2);degree(res7,A1);degree(res7,A2);

IiNC

IiNQ

IiM4

IiM9

res8:=factor(resultant(res5,res7,A1)): nops(res8);

Warning, computation interrupted

IiIi

eqcat:=numer(factor(subs(S(x)=Sx,eqScat))):nops(%);

IiRMIw==

deqS:=factor(diff(eqcat,Sx)):nops(%);indets(deqS);

IiRVIg==

PClJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSNTeEdGJEkidEdGJEkieEdGJA==

At t=0 n:=4: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n),deqS),t,n));

KylJInRHNiIsJCooIiIkIiIiKUkieEdGJCIiJUYoLCYqJClGKiIiI0YoRihGKEYoRihGKEYvLCQqKCIiJ0YoKUYqRidGKClGLEYvRighIiJGJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRis=

Since the first coefficient has degree 6 in x, 6 series in t (or in power of t) will be solutions A closer look n:=6: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n),deqS),t,n));

Ky1JInRHNiIsJCooIiIkIiIiKUkieEdGJCIiJUYoLCYqJClGKiIiI0YoRihGKEYoRihGKEYvLCQqKCIiJ0YoKUYqRidGKClGLEYvRighIiJGJywyKiZGMkYoKUYqIiIoRihGNSomIiM6RigpRipGMkYoRjUqJiIjT0YoKUYqIiImRihGNSomIiNGRihGKUYoRjUqJiIjQ0YoRjNGKEY1KiZGO0YoRi5GKEY1KiZGMkYoRipGKEY1RidGNUYrLCQqKCIjN0YoRjNGKCwmKiZGJ0YoRi5GKEYoRihGKEYoRjVGQC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRjI=

with(gfun):map(allvalues,algeqtoseries(convert(%%,polynom),t,x,3,true));

NygrKUkidEc2Il4jIiIiIiIhIiIjRiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGJyIiJCspRiQsJEYmISIiRihGKUYpRipGMCwqKiQpRiQjRidGKUYnRidGJEYnKiYjRjBGKUYnKUYkRjlGJ0YnLUYrNiMqJClGJEYpRidGJywoKiZGJkYnRjZGJ0YnKiYsJEYmRidGJ0Y6RidGM0Y7RicsKkY1RjNGJEYnRjhGM0Y7RicsKComRkJGJ0Y2RidGMyomRiZGJ0Y6RidGJ0Y7Ric=

This means that one solution has I and one -I as constant term, the others four vanish at t=0 We compute them inductively using the first few coefficients of S, R, .... We start with the series with non-zero constant terms unassign('x1'): X1ser := proc(N) add(x1[n]*t^n,n=0..N): end: n:=2: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X1ser(n),deqS),t,n+1));

KydJInRHNiIsJCooIiIkIiIiKSZJI3gxR0YkNiMiIiEiIiVGKCwmKiQpRioiIiNGKEYoRihGKEYoRihGMi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRic=

x1[0]:=I: n:=n+1: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X1ser(n),deqS),t,n+1));

KydJInRHNiIqJiomIiInIiIiXiNGKEYoRigmSSN4MUdGJDYjRihGKCIiJC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRGLCIiJQ==

solve(convert(%,polynom),x1[n-2]):x1[n-2]:=%;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkjeDFHRig2IyIiIiIiITcjRjE=

for i from 1 to 10 do n:=n+1: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X1ser(n),deqS),t,n+1)):solve(convert(%,polynom),x1[n-2]): x1[n-2]:=%; od: X1ser(n);

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

The other solution with non-zero constant term must be obtained by replacing I by -I. We conjecture that X1*X2 = 1series(X1ser(n)*subs(I=-I,X1ser(n)),t,n-1);

KydJInRHNiIiIiIiIiEtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjNw==

The other roots are expected to be series in s=sqrt(t) unassign('x3'): X3ser := proc(N) add(x3[n]*s^n,n=0..N): end: n:=4: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X3ser(n),t=s^2,deqS),s,n+1));

KydJInNHNiIsJCooIiIkIiIiKSZJI3gzR0YkNiMiIiEiIiVGKCwmKiQpRioiIiNGKEYoRihGKEYoRihGLi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIm

x3[0]:=0: n:=8: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X3ser(n),t=s^2,deqS),s,n+1));

KydJInNHNiIsJCoqIiIkIiIiLCYmSSN4M0dGJDYjRihGKEYoISIiRigsJkYqRihGKEYoRigsJiokKUYqIiIjRihGKEYoRihGKEYoIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJEYsIiIq

x3[1]:=1: for i from 1 to 10 do n:=n+1: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X3ser(n),t=s^2,deqS),s,n+1));isolate(convert(%,polynom),x3[n-7]): assign(%); od: X3ser(6);

LC5JInNHNiIiIiIqJClGIyIiI0YlRiUqJiMiIiRGKEYlKUYjRitGJUYlKiZGK0YlKUYjIiIlRiVGJSomIyIjXiIiKUYlKUYjIiImRiVGJSomIiM5RiUpRiMiIidGJUYl

Another series (called X4) is obtained by replacing s by -s Next we compute X5 unassign('x5'): X5ser := proc(N) add(x5[n]*s^n,n=0..N): end: n:=4: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X5ser(n),t=s^2,deqS),s,n+1));

KydJInNHNiIsJCooIiIkIiIiKSZJI3g1R0YkNiMiIiEiIiVGKCwmKiQpRioiIiNGKEYoRihGKEYoRihGLi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIm

x5[0]:=0: n:=8: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X5ser(n),t=s^2,deqS),s,n+1));

KydJInNHNiIsJCoqIiIkIiIiLCYmSSN4NUdGJDYjRihGKEYoISIiRigsJkYqRihGKEYoRigsJiokKUYqIiIjRihGKEYoRihGKEYoIiIpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJEYsIiIq

x5[1]:=I: for i from 1 to 10 do n:=n+1: factor(series(subs(Sx=Sex(n),B1=B1ex(n),B2=B2ex(n),R0=R0ex(n),R1=R1ex(n), x=X5ser(n),t=s^2,deqS),s,n+1));isolate(convert(%,polynom),x5[n-7]): assign(%); od: X5ser(10);

LDIqJl4jIiIiRiVJInNHNiJGJUYlKiYsJEYkRiVGJSlGJiIiJEYlISIiKiYqJiIiI0YlRiRGJUYlKUYmIiImRiVGJSokKUYmIiInRiVGJSomLCQqJiIiJUYlRiRGJUYlRiUpRiYiIihGJUYsKiZGL0YlKUYmIiIpRiVGJSomKiYiIztGJUYkRiVGJSlGJiIiKkYlRiUqJiIjQEYlKUYmIiM1RiVGJQ==

The 6th root is obtained by replacing s by -s, or equivalently i by -i. Now we have the first terms of our 6 roots X_i JSFH

factor(diff(eqcat,x)): nops(%);

IiRHIw==

deqx:=collect(diff(eqcat,x),[Sx,R0,R1,B1,B2],factor); indets(%);

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

PClJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSNTeEdGJEkidEdGJEkieEdGJA==

degree(eqcat,B1);degree(deqS,B1);degree(deqx,B1); degree(eqcat,B2);degree(deqS,B2);degree(deqx,B2);

IiIi

IiIi

IiIi

IiIi

IiIi

IiIi

coeff(eqcat,B1);coeff(deqS,B1);coeff(deqx,B1);

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

LCwqKCIiJCIiIilJInRHNiIiIiNGJSlJInhHRigiIidGJSEiIiooRixGJUYmRiUpRisiIiZGJUYtKigiIipGJUYmRiUpRisiIiVGJUYtKihGLEYlRiZGJSlGK0YkRiVGLSooRiRGJUYmRiUpRitGKUYlRi0=

LCoqLiIiJyIiIkkieEc2IkYlKUkidEdGJyIiI0YlLCgqJClGJkYqRiVGJUYmRiVGJUYlRiUsKComIiIkRiVGLUYlRiUqJkYqRiVGJkYlRiVGJUYlRiVJI1N4R0YnRiUhIiIqKkYqRiVGJkYlLCoqJkYkRiUpRiYiIiVGJUYlKiYiIiZGJSlGJkYwRiVGJSomRjBGJUYmRiVGM0YqRjNGJSlJI1IwR0YnRipGJUYlKipGKUYlRiZGJSwsKiYiIzdGJUY3RiVGJSomIiNERiVGO0YlRiUqJkZCRiVGLUYlRiVGPEYlRjhGM0YlRj5GJUYlKihGJkYlRihGJSwsRjZGJUY5RiVGRUYlKiZGJEYlRiZGJUYlRjhGJUYlRjM=

We take a linear combination of the 3 equations to eliminate B1 and B2 e1:=numer(factor(subs(isolate(deqS,B1),eqcat))): nops(%);

IiQtJQ==

e2:=numer(factor(subs(isolate(deqS,B1),deqx))): nops(%);

IiR5Jg==

degree(e1,B2); degree(e2,B2);

IiIi

IiIi

e3:=numer(factor(subs(isolate(e1,B2),e2))): nops(%);

IiIn

seq(indets(op(i,e3)),i=1..6);

Nig8IjwjSSJ4RzYiPCRJInRHRiZGJTwmSSNSMEdGJkkjU3hHRiZGKEYlPCdGKkkjUjFHRiZGK0YoRiU8I0Yo

We want to decide which factor vanishes, for each value of x=X_i. Only 3 factors are likely to be cancelled e3a:=op(3,e3): e3b:=op(4,e3): e3c:=op(5,e3): collect(e3a,t,factor);

LCYqKCwmKiQpSSJ4RzYiIiIjIiIiRipGKkYqRiopLCZGJ0YqRipGKkYpRipJInRHRihGKkYqRiUhIiI=

n:=6: normal(series(subs(x=X1ser(n),e3a),t,4)); normal(series(subs(x=X3ser(n),t=s^2,e3a),s,4)); normal(series(subs(x=X5ser(n),t=s^2,e3a),s,4));

KytJInRHNiIiIiIiIiEsJComIiIlRiVeI0YlRiUhIiIiIiMsJiIiKUYrKiZGLkYlRipGJUYrIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiVGKQ==

KyVJInNHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiU=

KylJInNHNiIiIiNGJSomRiUiIiJeI0YnRiciIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIiJQ==

n:=6: normal(series(subs(R0=R0ex(n),Sx=Sex(n),x=X1ser(n),e3b),t,4)); normal(series(subs(R0=R0ex(n),Sx=Sex(n),x=X3ser(n),t=s^2,e3b),s,n)); normal(series(subs(R0=R0ex(n),Sx=Sex(n),x=X5ser(n),t=s^2,e3b),s,n));

KylJInRHNiIiIiJGJSwmRiVGJSomIiIjRiVeI0YlRiUhIiIiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJQ==

KylJInNHNiIhIiIiIiUhIiMiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIic=

KydJInNHNiIiIiIiIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==

n:=8: normal(series(subs(R0=R0ex(n),R1=R1ex(n),Sx=Sex(n),x=X1ser(n),e3c),t,n)); normal(series(subs(R0=R0ex(n),R1=R1ex(n),Sx=Sex(n),x=X3ser(n),t=s^2,e3c),s,n)); normal(series(subs(R0=R0ex(n),R1=R1ex(n),Sx=Sex(n),x=X5ser(n),t=s^2,e3c),s,n));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

KylJInNHNiIiIiUiIidGJSIiKC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIiKQ==

KyVJInNHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

Hence X3 and X4 satisfy e3a, and the other four roots satisfy e3c In particular, we have found the minimal equation satisfied by X3 and its twin X4 (obtained by replacing sqrt(t) by -sqrt(t)). Genus zero algX3:=e3a;collect(%,t,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdYM0dGKCwuKiZJInRHRigiIiIpSSJ4R0YoIiIlRjFGMSooIiIjRjFGMEYxKUYzIiIkRjFGMSooRjZGMUYwRjEpRjNGNkYxRjEqKEY2RjFGMEYxRjNGMUYxKiRGOkYxISIiRjBGMTcjRi4=

LCYqKCwmKiQpSSJ4RzYiIiIjIiIiRipGKkYqRiopLCZGJ0YqRipGKkYpRipJInRHRihGKkYqRiUhIiI=

factor(isolate(algX3,t));

L0kidEc2IiooKUkieEdGJCIiIyIiIiwmKiRGJkYpRilGKUYpISIiKSwmRidGKUYpRilGKEYs

with(algcurves): genus(algX3,t,x)

IiIh

An equation for X1 and X5 --- which we will not use, in fact eqX15:=collect(e3c,[Sx,R0,R1],factor);

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

The discriminant factor(coeff(eqcat,Sx,3));

LCQqLCIiJCIiIilJInRHNiIiIiNGJSksKCokKUkieEdGKEYpRiVGJUYuRiVGJUYlRilGJSwqKiZGJ0YlRi1GJUYlKihGKUYlRidGJUYuRiVGJUYnRiVGLkYlRiUsKiooRiRGJUYnRiVGLUYlRiVGMUYlKiZGJEYlRidGJUYlRi4hIiJGJUY1

Disc0:=factor(discrim(eqcat,Sx)): nops(Disc0);

IiIn

map(indets,[seq(op(i,Disc0),i=1..nops(Disc0))]);

Nyg8IjwjSSJ4RzYiPCRJInRHRiZGJUYnPChJI0IxR0YmSSNCMkdGJkkjUjBHRiZJI1IxR0YmRihGJTwjRig=

factor(Disc0/op(5,Disc0)/Delta);

LCQqKiIjRiIiIilJInRHNiIiIiNGJSlJInhHRihGKUYlKSwoKiRGKkYlRiVGK0YlRiVGJUYpRiVGJQ==

Let us check that the two simple factors coming from Delta do not cancel at X_i op(3,Disc0); op(4,Disc0);

LCoqJkkidEc2IiIiIilJInhHRiUiIiNGJkYmKihGKUYmRiRGJkYoRiZGJkYkRiZGKEYm

LCoqKCIiJCIiIkkidEc2IkYlKUkieEdGJyIiI0YlRiUqKEYqRiVGJkYlRilGJUYlKiZGJEYlRiZGJUYlRikhIiI=

n:=6: normal(series(subs(x=X1ser(n),op(3,Disc0)),t,4)); normal(series(subs(x=X3ser(n),t=s^2,op(3,Disc0)),s,4)); normal(series(subs(x=X5ser(n),t=s^2,op(3,Disc0)),s,4));

Ky1JInRHNiJeIyIiIiIiISomIiIjRiZGJUYmRiZGKUYpLCYiIilGJiomIiIlRiZGJUYmRiYiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJkYt

KytJInNHNiIiIiJGJSIiI0YmIyIiKEYmIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiU=

KytJInNHNiJeIyIiIkYmRiYiIiNGJSIiJC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YmIiIl

n:=6: normal(series(subs(x=X1ser(n),op(4,Disc0)),t,4)); normal(series(subs(x=X3ser(n),t=s^2,op(4,Disc0)),s,4)); normal(series(subs(x=X5ser(n),t=s^2,op(4,Disc0)),s,4));

Ky1JInRHNiIsJF4jIiIiISIiIiIhKiYiIiNGJ0YmRidGJyEiI0YrKiYiIzdGJ0YmRiciIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIiJQ==

KytJInNHNiIhIiIiIiIiIiNGJyNGJkYnIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIiU=

KytJInNHNiIsJF4jIiIiISIiRiciIiQiIiMqJkYpRidGJkYnRiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIiJQ==

Hence all X_i's are double roots of Disc1:=op(5,Disc0): degree(Disc1,x);

IiND

This one is symmetric in x and 1/x factor(subs(x=1/x,Disc1)/Disc1);

KiQpSSJ4RzYiIiNDISIi

We want to write Disc1/x^12 as a polynomial in 1+x+1/x=y res:=Disc1/x^(12):discy:=0: for i from 0 to 12 do discy:=discy+y^(12-i)*coeff(res,x,12-i): res:= expand(res-(1+x+1/x)^(12-i)*coeff(res,x,12-i)) od: factor(subs(y=1+x+1/x,discy)/Disc1);

KiQpSSJ4RzYiIiM3ISIi

Disc2:=discy: degree(Disc2,y);

IiM3

Let us examine the series Y_i =1+X_i+1/X_i. Could it be that Y_1=Y_2 ? n:=6: normal(series(subs(x=X1ser(n),1+x+1/x),t,4)); subs(I=-I,%); normal(series(subs(x=X3ser(n),1+x+1/x),s,4)); subs(s=-s,%); normal(series(subs(x=X5ser(n),1+x+1/x),s,4)); subs(I=-I,%);

KytJInRHNiIiIiIiIiEiIiUiIiMiIikiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJUYn

KytJInRHNiIiIiIiIiEiIiUiIiMiIikiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJUYn

KylJInNHNiIiIiIhIiIjRiUiIiNGJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlRig=

KyksJEkic0c2IiEiIiIiIkYmI0YnIiIjRictSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGJ0Yp

KylJInNHNiIsJF4jIiIiISIiRihGJyIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YnIiIk

KylJInNHNiJeIyIiIiEiIkYmIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIiQ=

This is indeed real, and we suspect that X1*X2=1 n:=10: normal(series(subs(x=X1ser(n),1+x+1/x),t,n));

KzdJInRHNiIiIiIiIiEiIiUiIiMiIikiIiQiI3NGJyIkRyQiIiYiJWdBIiInIiY3TSIiIigiJnMqKilGKSInaykpZSIiKi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiM1

collect(algX3/x^2,t,expand);

LCYiIiIhIiIqJiwsKiQpSSJ4RzYiIiIjRiNGIyomRitGI0YpRiNGI0YrRiMqJkYrRiNGKUYkRiMqJEYoRiRGI0YjSSJ0R0YqRiNGIw==

expand(%-t*(x+1/x+1)^2);

LCYiIiIhIiJJInRHNiJGJA==

We know the series Y3 and Y4 n:=10: factor(series((X3ser(n)+1/X3ser(n)+1)^2,s,n))

KylJInNHNiIiIiIhIiNGJSIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIo

Expansion of the other series n:=6: factor(series(X1ser(n)+1/X1ser(n)+1,t,n))

Ky9JInRHNiIiIiIiIiEiIiUiIiMiIikiIiQiI3NGJyIkRyQiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==

n:=8: factor(series(X5ser(n)+1/X5ser(n)+1,s,n))

Ky1JInNHNiIsJF4jIiIiISIiRihGJyIiIUYnIiIlRiYiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJyIiJw==

Now D2(z) has 5 double roots (at least). It is also almost symmetric in y seq(factor(coeff(Disc2,y,12-i)/coeff(Disc2,y,i)),i=0..5);

NigqJilJInRHNiIiIiciIiIpLCZGJUYoRihGKEYnISIiKiYpRiUiIiZGKClGKkYuRisqJilGJSIiJUYoKUYqRjJGKyomKUYlIiIkRigpRipGNkYrKiYpRiUiIiNGKClGKkY6RisqJkYlRihGKkYr

Let us write D2 as a polynomial in ty+(t+1)/y res:=Disc2/y^(6):discz:=0: for i from 0 to 6 do discz:=discz+(z/t)^(6-i)*coeff(res,y,6-i): res:= expand(res-(y+(t+1)/t/y)^(6-i)*coeff(res,y,6-i)) od: factor(subs(z=t*y+(t+1)/y,discz)/Disc2);

KiQpSSJ5RzYiIiInISIi

Disc3:=discz: degree(%,z);

IiIn

What are the series Z_i, for i=2... 5 ? n:=4: series(subs(y=X1ser(n)+1/X1ser(n)+1, t*y+(t+1)/y),t,n+1);

Ky9JInRHNiIiIiIiIiEiIiNGJSEiJUYnISIpIiIkISNjIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiY=

We have determined Z3= 2sqrt(t(1+t)) n:=12: series(subs(y=X3ser(n)+1/X3ser(n)+1,t=s^2, t*y+(t+1)/y),s,n+1);

KzFJInNHNiIiIiMiIiJGJiIiJCMhIiIiIiUiIiYjRiYiIikiIigjISImIiNrIiIqI0YuIiRHIiIjNi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YmIiM4

n:=12: series(subs(y=X3ser(n)+1/X3ser(n)+1,t=s^2, %%^2),s,n+1);

KylJInNHNiIiIiUiIiNGJUYlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiM5

This is a series in t, not just in s, which suggests that Z5=Z6, ie Y5*Y6=1+1/t n:=12: series(subs(y=X5ser(n)+1/X5ser(n)+1,t=s^2, t*y+(t+1)/y),s,n+1);

Ky9JInNHNiIiIiNGJUYlIiInIiM1IiIpIiNfRicsJiIjVSIiIiomLCQqJkYlRixeI0YsRixGLEYsLCYqJkYwRiwmSSN4NUdGJDYjIiM3RixGLComIiNTRixGMEYsRixGLCEiIkY2LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiwiIzg=

Let us check : seems OK. That is, Y5*Y6=1+1/t series((X5ser(n)+1/X5ser(n)+1)*subs(I=-I,X5ser(n)+1/X5ser(n)+1),s,n);

KylJInNHNiIiIiIhIiNGJSIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIq

We know two roots of D3, and that there are in addition two double roots D3form:=add(d[i]*z^i,i=0..6);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdEM2Zvcm1HRigsMComKUkiekdGKCIiJyIiIiZJImRHRig2I0YyRjNGMyomKUYxIiImRjMmRjU2I0Y5RjNGMyomKUYxIiIlRjMmRjU2I0Y+RjNGMyomKUYxIiIkRjMmRjU2I0ZDRjNGMyomKUYxIiIjRjMmRjU2I0ZIRjNGMyomRjFGMyZGNTYjRjNGM0YzJkY1NiMiIiFGMzcjRi4=

collect(D3form-(z^2-4*t*(1+t))*(alpha*z^2+beta*z+g)^2,z,factor);

LDQqJiwmKiQpSSZhbHBoYUc2IiIiIyIiIiEiIiZJImRHRig2IyIiJ0YqRiopSSJ6R0YoRi9GKkYqKiYsJiooRilGKkYnRipJJWJldGFHRihGKkYrJkYtNiMiIiZGKkYqKUYxRjhGKkYqKiYsLCooIiIlRipGJkYqKUkidEdGKEYpRipGKiooRj1GKkYmRipGP0YqRioqKEYpRipGJ0YqSSJnR0YoRipGKyokKUY1RilGKkYrJkYtNiNGPUYqRiopRjFGPUYqRioqJiwqKioiIilGKkYnRipGNUYqRj5GKkYqKipGS0YqRidGKkY1RipGP0YqRioqKEYpRipGNUYqRkJGKkYrJkYtNiMiIiRGKkYqKUYxRlBGKkYqKiYsLioqRktGKkYnRipGQkYqRj5GKkYqKihGPUYqRkRGKkY+RipGKioqRktGKkYnRipGQkYqRj9GKkYqKihGPUYqRkRGKkY/RipGKiokKUZCRilGKkYrJkYtNiNGKUYqRiopRjFGKUYqRioqJiwoKipGS0YqRjVGKkZCRipGPkYqRioqKkZLRipGNUYqRkJGKkY/RipGKiZGLTYjRipGKkYqRjFGKkYqKihGPUYqRj5GKkZZRipGKiooRj1GKkY/RipGWUYqRiomRi02IyIiIUYq

sol:=factor(solve({seq(coeff(%,z,i),i=4..6)},{alpha,beta,g}));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRig8JS9JJmFscGhhR0YoLUknUm9vdE9mR0YlNiMsJiokKUkjX1pHRiUiIiMiIiJGOSZJImRHRig2IyIiJyEiIi9JJWJldGFHRigsJCoqI0Y5RjhGOSZGOzYjIiImRjlGMUY5RjpGPkY5L0kiZ0dGKCwkKiojRjkiIilGOSwqKigiIztGOSlJInRHRihGOEY5KUY6RjhGOUY5KihGT0Y5RlFGOUZSRjlGOSooIiIlRjkmRjs2I0ZVRjlGOkY5RjkqJClGREY4RjlGPkY5RlJGPkYxRjlGOTcjRi4=

D3formfinal:=subs(RootOf(_Z^2-d[6])=sqrt(d[6]),factor(expand(subs(sol,(z^2-4*t*(1+t))*(alpha*z^2+beta*z+g)^2))));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSxEM2Zvcm1maW5hbEdGKCwkKiojIiIiIiNrRjEpJkkiZEdGKDYjIiInIiIkISIiLCgqJiIiJUYxKUkidEdGKCIiI0YxRjEqJClJInpHRihGP0YxRjkqJkY8RjFGPkYxRjFGMSksLiooIiM7RjFGPUYxKUY0Rj9GMUYxKigiIilGMUZBRjFGSEYxRjEqKEZHRjFGPkYxRkhGMUYxKipGPEYxRkJGMSZGNTYjIiImRjFGNEYxRjEqKEY8RjEmRjU2I0Y8RjFGNEYxRjEqJClGTUY/RjFGOUY/RjFGOTcjRi4=

factor(%/(z^2-4*t*(1+t)));

LCQqKCMiIiIiI2tGJSksLiooIiM7RiUpSSJ0RzYiIiIjRiUpJkkiZEdGLTYjIiInRi5GJUYlKigiIilGJSlJInpHRi1GLkYlRi9GJUYlKihGKkYlRixGJUYvRiVGJSoqIiIlRiVGN0YlJkYxNiMiIiZGJUYwRiVGJSooRjpGJSZGMTYjRjpGJUYwRiVGJSokKUY7Ri5GJSEiIkYuRiUpRjAiIiRGQ0Yl

coeffs(collect(D3form-D3formfinal,z,factor),z);

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

syst:=factor(subs(seq(d[i]=coeff(Disc3,z,i),i=0..6), {%})): nops(syst);

IiIl

Removing some factors nops(op(1,syst));indets(op(1,op(1,syst)));

IiIj

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

op(1,syst)/op(1,op(1,syst));

KiQpSSJ0RzYiIiIjIiIi

nops(op(2,syst));indets(op(2,op(2,syst)));

IiIk

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

op(2,syst)/op(2,op(2,syst));

LCQqJiIiJyIiIilJInRHNiIiIiNGJUYl

nops(op(3,syst));indets(op(2,op(3,syst)));

IiIk

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

op(3,syst)/op(2,op(3,syst));

LCQqJiIiIyIiIilJInRHNiJGJEYlRiU=

nops(op(4,syst));indets(op(2,op(4,syst)));

IiIk

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

op(4,syst)/op(2,op(4,syst));

LCQqJiIiIyIiIilJInRHNiJGJEYlISIi

systfinal:=factor({op(1,op(1,syst)),op(2,op(2,syst)),op(2,op(3,syst)),op(2,op(4,syst))}): map(nops,systfinal);map(indets,systfinal); map(degree,systfinal,R0);map(degree,systfinal,R1);map(degree,systfinal,B1);map(degree,systfinal,B2);

PCYiI3MiJEsiIiQjPiIkdyM=

PCM8J0kjQjFHNiJJI0IyRzYiSSNSMEc2IkkjUjFHNiJJInRHNiI=

PCQiIiYiIic=

PCYiIiQiIiUiIiYiIic=

PCUiIiIiIiMiIiQ=

PCUiIiIiIiMiIiQ=

The smallest equation systfinal[1];

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

Checking the system n:=10: for i from 1 to 4 do normal(series(subs(R0=R0ex(n),R1=R1ex(n),B1=B1ex(n),B2=B2ex(n),op(i,systfinal)),t,n+1)):od;

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

save(systfinal,systfinalR0R1B1B2):

map(degree,[op(systfinal)],B1);map(degree,[op(systfinal)],B2);

NyYiIiIiIiNGJCIiJA==

NyYiIiIiIiNGJCIiJA==

Let us eliminate B1 and B2 factor(coeff(systfinal[1],B1,1)); factor(coeff(systfinal[1],B2,1))

KiYsJiomIiIjIiIiSSNSMEc2IkYmRiZJInRHRihGJkYmLDYqKCIjN0YmKUYnIiIkRiZGKUYmRiYqKiIjT0YmKUYnRiVGJkkjUjFHRihGJkYpRiZGJiooIiInRiZGMUYmKUYpRiVGJkYmKipGMEYmRidGJkYyRiZGNUYmRiYqKEYlRiZGJ0YmKUYpRi5GJiEiIiomRiVGJilGKSIiJUYmRiYqJkY0RiZGLUYmRjkqKCIjOkYmRjFGJkYpRiZGOSooIiM2RiZGJ0YmRjVGJkY5KiRGOEYmRjlGJg==

LCQqJiwoKiQpSSNSMEc2IiIiIyIiIkYqKiZGJ0YqSSJ0R0YoRipGKiokKUYsRilGKkYqRiosMiooIiNPRipGJkYqSSNSMUdGKEYqRioqKCIjN0YqRiZGKkYsRiohIiIqKkYxRipGJ0YqRjJGKkYsRipGKiooIiM7RipGJ0YqRi5GKkY1KiZGKUYqKUYsIiIkRipGNSomIiInRipGJkYqRjUqKCIiJUYqRidGKkYsRipGNUYtRipGKkY1

syst2:=map(numer,factor(subs(isolate(systfinal[1],B2),[systfinal[2], systfinal[3], systfinal[4]]))): map(nops,%);

NyUiJCNbIiRmKCIlKCk9

map(degree,syst2,B1);

NyUiIiNGIyIiJA==

res1:=factor(resultant(syst2[1],syst2[2],B1)): nops(res1);

IiIn

map(indets,[seq(op(i,res1),i=1..nops(res1))]); map(nops,[seq(op(i,res1),i=1..nops(res1))]);

Nyg8IjwjSSJ0RzYiPCRJI1IxR0YmRiU8JEkjUjBHRiZGJTwlRipGKEYlRis=

NygiIiIiIiMiIiRGJCIlM0xGJA==

The factor(s) that vanish n:=8: series(subs(R0=R0ex(n),R1=R1ex(n),op(3,res1)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(4,res1)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(5,res1)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(6,res1)),t,n+1);

KzVJInRHNiIhIiIiIiEhIiMiIiIiIiNGKSIjPSIiJSIjWyIiJiIkQyUiIiciJW9AIiIoIiY/XyIiIiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiKg==

Ky1JInRHNiIiIiIiIiUiIiMiIidGJiIiKCIjUCIiKS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIq

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiI0s=

KydJInRHNiIiIiIiIiktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiKg==

A first equation between R0 and R1 res2:=op(5,res1): res3:=factor(resultant(syst2[1],syst2[3],B1)): nops(res3);

IiIn

map(indets,[seq(op(i,res3),i=1..nops(res3))]); map(nops,[seq(op(i,res3),i=1..nops(res3))]);

Nyg8IjwjSSJ0RzYiPCRJI1IxR0YmRiU8JEkjUjBHRiZGJTwlRipGKEYlRis=

NygiIiIiIiMiIiRGJCIlI1EoRiQ=

The factor(s) that vanish n:=12: series(subs(R0=R0ex(n),R1=R1ex(n),op(3,res3)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(4,res3)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(5,res3)),t,n+1); series(subs(R0=R0ex(n),R1=R1ex(n),op(6,res3)),t,n+1);

Kz1JInRHNiIhIiIiIiEhIiMiIiIiIiNGKSIjPSIiJSIjWyIiJiIkQyUiIiciJW9AIiIoIiY/XyIiIikiJm9fKiIiKiInSU1sIiM1IihHTFMlIiM2IilpWmlJIiM3LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIzg=

KzFJInRHNiIiIiIiIiciIiQiIilGJiIiKiIjZCIjNSIkayMiIzYiJVY9IiM3LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIzg=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiI1c=

KydJInRHNiIiIiIiIzctSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIjOA==

Another equation between R0 and R1 res4:=op(5,res3): degree(res2,R0);degree(res2,R1);degree(res4,R0);degree(res4,R1);

IiNL

IiM4

IiNX

IiM8

res5:=factor(resultant(res2,res4,R1)): nops(res5):

Error, (in resultant) invalid arguments

n:=4:R0ex(n); R1ex(n); B1ex(n); B2ex(n);

KiYpSSJ0RzYiIiIjIiIiLCoqJiIjISlGJylGJCIiJUYnRicqJiIjPEYnKUYkIiIkRidGJyomRiZGJ0YjRidGJ0YkRidGJw==

KiYpSSJ0RzYiIiIjIiIiLCoqJiMiJDcjIiIkRicpRiQiIiVGJ0YnKiYiIilGJylGJEYsRidGJyomRixGJ0YjRidGJyNGJ0YsRidGJw==

LCYqJiMiIiQiIiMiIiIpSSJ0RzYiRiZGJyEiIiomRiVGJylGKSIiJUYnRis=

LCgqJiIiJiIiIilJInRHNiIiIiVGJSEiIiomIiIjRiUpRiciIiRGJUYqKiYjRiVGLEYlKUYnRixGJUYq

Here we prove that there exists a unique solution with R1, B1, B2 multiples of t^2 and R0 multiple of t^3 eqensn:=factor(subs(R0=t^3*R0n, R1=t^2*R1n, B1=t^2*B1n, B2=t^2*B2n,[op(systfinal)])): map(nops, eqensn);

NyYiIiNGI0YjRiM=

op(1, eqensn[1]);op(1, eqensn[2]);op(1, eqensn[3]);op(1, eqensn[4]);

KiQpSSJ0RzYiIiInIiIi

KiQpSSJ0RzYiIiInIiIi

KiQpSSJ0RzYiIiInIiIi

KiQpSSJ0RzYiIiInIiIi

eqensn:=map(Z->factor(Z/t^6),eqensn): indets(eqensn);map(nops, eqensn);

PCdJJEIxbkc2IkkkQjJuR0YkSSRSMG5HRiRJJFIxbkdGJEkidEdGJA==

NyYiI3MiJEsiIiQjPiIkdyM=

We would like something like a diagonal system, alowing us to compute the coefficients of t^n in each series, in turn, assuming we know all previous coefficients factor(subs(t=0,eqensn));

NyYsKkkkQjFuRzYiISIiSSRCMm5HRiVGJiomIiIkIiIiSSRSMW5HRiVGKkYqRilGJiwqKiYiIzhGKkYkRipGKiomRilGKkYnRipGJiomIiIqRipGK0YqRiYiI0BGKiwmKiYiIztGKkYkRipGKiIjQ0YqLCYqJiIiKUYqRiRGKkYqIiM3Rio=

res:=factor(2*eqensn[4]-eqensn[3]):nops(res);

IiIj

op(1,res);

SSJ0RzYi

subs(t=0,op(2,res));

LCwqJiIkTSIiIiJJJEIxbkc2IkYlRiUqJiIjYUYlSSRCMm5HRidGJUYlKiYiIidGJUkkUjBuR0YnRiUhIiIqJiIkMyJGJUkkUjFuR0YnRiVGJSIkKT5GJQ==

eqensn1:=subsop(4=op(2,res),eqensn): subs(t=0,%);

NyYsKkkkQjFuRzYiISIiSSRCMm5HRiVGJiomIiIkIiIiSSRSMW5HRiVGKkYqRilGJiwqKiYiIzhGKkYkRipGKiomRilGKkYnRipGJiomIiIqRipGK0YqRiYiI0BGKiwmKiYiIztGKkYkRipGKiIjQ0YqLCwqJiIkTSJGKkYkRipGKiomIiNhRipGJ0YqRioqJiIiJ0YqSSRSMG5HRiVGKkYmKiYiJDMiRipGK0YqRioiJCk+Rio=

factor((op(1,eqensn1)*3-op(2,eqensn1))): subs(t=0,%);

LCgqJiIjOyIiIkkkQjFuRzYiRiUhIiIqJiIjPUYlSSRSMW5HRidGJUYlIiNJRig=

Here is a diagonal system, proving that the four series R0n, R1n, B1n, B2n are uniquely defined. And hence algebraic. eqens2:=subsop(1=op(1,eqensn1)*3-op(2,eqensn1),eqensn1): subs(t=0,%);

NyYsKComIiM7IiIiSSRCMW5HNiJGJiEiIiomIiM9RiZJJFIxbkdGKEYmRiYiI0lGKSwqKiYiIzhGJkYnRiZGJiomIiIkRiZJJEIybkdGKEYmRikqJiIiKkYmRixGJkYpIiNARiYsJkYkRiYiI0NGJiwsKiYiJE0iRiZGJ0YmRiYqJiIjYUYmRjNGJkYmKiYiIidGJkkkUjBuR0YoRiZGKSomIiQzIkYmRixGJkYmIiQpPkYm

JSFH

The system of 4 equations obtained for R0 R1 B1 and B2 read(systfinalR0R1B1B2): indets(systfinal[1]);

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

systfinal:=[op(systfinal)]: map(degree,systfinal,R0);map(degree,systfinal,R1);map(degree,systfinal,B1);map(degree,systfinal,B2);map(degree,systfinal,t);

NyYiIiYiIidGI0Yk

NyYiIiQiIiUiIiYiIic=

NyYiIiIiIiNGJCIiJA==

NyYiIiIiIiNGJCIiJA==

NyYiIihGIyIiKiIjNQ==

map(Z->nops(expand(Z)),systfinal);

NyYiI3MiJEsiIiQjPiIkdyM=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

with(algcurves): A quartic series u algu:= (1-3*u)^3*(1+u)*t^2+(1+18*u^2-27*u^4)*t-u; genus(%,t,u);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGd1R0YoLCgqKCksJiIiIkYyKiYiIiRGMkkidUdGKEYyISIiRjRGMiwmRjJGMkY1RjJGMilJInRHRigiIiNGMkYyKiYsKComIiNGRjIpRjUiIiVGMkY2KiYiIz1GMilGNUY6RjJGMkYyRjJGMkY5RjJGMkY1RjY3I0Yu

IiIj

collect(algu/(t*(t+1)),u,factor);

LCoiIiJGIyomIiNGRiMpSSJ1RzYiIiIlRiMhIiIqJiIjPUYjKUYnIiIjRiNGIyoqLCYqJiIiKUYjKUkidEdGKEYuRiNGI0YjRiNGI0Y0RiosJkY0RiNGI0YjRipGJ0YjRio=

A cubic series over Q(u) algvu:=u*(1+3*v-v^3)- v*(v^2+v+1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd2dUdGKCwmKiZJInVHRigiIiIsKCokKUkidkdGKCIiJEYxISIiKiZGNkYxRjVGMUYxRjFGMUYxRjEqJkY1RjEsKCokKUY1IiIjRjFGMUY1RjFGMUYxRjFGNzcjRi4=

uvsol:=solve(%,u);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ1dnNvbEdGKCwkKihJInZHRigiIiIsKCokKUYwIiIjRjFGMUYwRjFGMUYxRjEsKCokKUYwIiIkRjFGMSomRjlGMUYwRjEhIiJGMUY7RjtGOzcjRi4=

algv:=collect(factor(resultant(algvu,algu,u)),v,factor);

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

And finally a quadratic series over Q(v) algwv := 4*v^4+4*v^3-4*v-1+w^2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd3dkdGKCwsKiYiIiUiIiIpSSJ2R0YoRjBGMUYxKiZGMEYxKUYzIiIkRjFGMSokKUkid0dGKCIiI0YxRjEqJkYwRjFGM0YxISIiRjFGPDcjRi4=

genus(algwv,v,w);

IiIi

Series expansions user:=proc(n) option remember: if n=0 then 0 else series(subs(u=user(n-1),algu+u),t,n+1);fi: end: user(4);

Ky1JInRHNiIiIiJGJUYlIiIjIiM1IiIkIiNZIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiY=

algvu;

LCYqJkkidUc2IiIiIiwoKiQpSSJ2R0YlIiIkRiYhIiIqJkYrRiZGKkYmRiZGJkYmRiZGJiomRipGJiwoKiQpRioiIiNGJkYmRipGJkYmRiZGJkYs

vser:=proc(n) option remember: if n=0 then 0 else series(subs(u=user(n), v=vser(n-1), u*(-v^3+3*v+1)/(v^2+v+1)),t,n+1): fi: end: vser(5);

Ky9JInRHNiIiIiJGJSIiJCIiIyIjOkYmIiMiKSIiJSIkKlsiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==

wser:=proc(n) series(sqrt(subs(w=0,v=vser(n),-algwv)),t,1+n): end: wser(5);

KzFJInRHNiIiIiIiIiEiIiNGJSIiJUYnIiM/IiIkIiMlKkYoIiRVJiIiJi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIn

Expressions of the series (derived later from the guessed minimal polynomials) R0w:=t/2*(w*(1+2*v)/(1+4*v-2*v^3)-1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSMHdHRigsJCooIyIiIiIiI0YxSSJ0R0YoRjEsJiooSSJ3R0YoRjEsJkYxRjEqJkYyRjFJInZHRihGMUYxRjEsKComRjJGMSlGOSIiJEYxISIiKiYiIiVGMUY5RjFGMUYxRjFGPkYxRjFGPkYxRjE3I0Yu

n:=12: series(subs(v=vser(n),w=wser(n),R0w-R0ex(n)),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=

R1w:=1/6*(1+2*t+(1+2*v)*(1-2*t)*(16*v^6+24*v^5+7*v^4-24*v^3-30*v^2-10*v-1)/w/(1+4*v-2*v^3)/(1+2*v+6*v^2+8*v^3+v^4));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSMXdHRigsKCMiIiIiIidGMComI0YwIiIkRjBJInRHRihGMEYwKjBGL0YwLCZGMEYwKiYiIiNGMEkidkdGKEYwRjBGMCwmRjBGMComRjlGMEY1RjAhIiJGMCwwKiYiIztGMClGOkYxRjBGMComIiNDRjApRjoiIiZGMEYwKiYiIihGMClGOiIiJUYwRjAqJkZDRjApRjpGNEYwRj0qJiIjSUYwKUY6RjlGMEY9KiYiIzVGMEY6RjBGPUYwRj1GMEkid0dGKEY9LCgqJkY5RjBGS0YwRj0qJkZJRjBGOkYwRjBGMEYwRj0sLCokRkhGMEYwKiYiIilGMEZLRjBGMComRjFGMEZORjBGMEY4RjBGMEYwRj1GMDcjRi4=

n:=12: series(subs(v=vser(n),w=wser(n),R1w-R1ex(n)),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=

This one does not require w B1v:=3*v^2*(1+4*v+v^2)*(v^2-1)*(1+2*v)*(1-8*t)/2/(1-3*v^2-4*v^3)^3/(1+4*v-2*v^3);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRCMXZHRigsJCoyIyIiJCIiIyIiIilJInZHRihGMkYzLCgqJEY0RjNGMyomIiIlRjNGNUYzRjNGM0YzRjMsJkY3RjNGMyEiIkYzLCZGM0YzKiZGMkYzRjVGM0YzRjMsJiomIiIpRjNJInRHRihGM0Y7RjNGM0YzKSwoKiZGOUYzKUY1RjFGM0Y7KiZGMUYzRjRGM0Y7RjNGM0YxRjssKComRjJGM0ZFRjNGO0Y4RjNGM0YzRjtGMzcjRi4=

n:=12: series(subs(v=vser(n),B1v-B1ex(n)),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=

The final one B2w:=((1+2*v)*(1-2*t))/(2*w*(v^4+8*v^3+6*v^2+2*v+1)^2*(2*v^3-4*v-1)) *(4*t*v^12+68*t*v^11+16*(22*t+1)*v^10 +12*(67*t+2)*v^9+5*(192*t-5)*v^8+8*(61*t-10)*v^7-286*t*v^6-41*v^6-788*t*v^5 +66*v^5-738*t*v^4+113*v^4-4*(97*t-17)*v^3-126*t*v^2+19*v^2-24*t*v+2*v-2*t ) ;

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

n:=12: series(subs(v=vser(n),w=wser(n),B2w-B2ex(n)),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzg=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

algu:= (1-3*u)^3*(1+u)*t^2+(1+18*u^2-27*u^4)*t-u; algvu:=u*(1+3*v-v^3)- v*(v^2+v+1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGd1R0YoLCgqKCksJiIiIkYyKiYiIiRGMkkidUdGKEYyISIiRjRGMiwmRjJGMkY1RjJGMilJInRHRigiIiNGMkYyKiYsKComIiNGRjIpRjUiIiVGMkY2KiYiIz1GMilGNUY6RjJGMkYyRjJGMkY5RjJGMkY1RjY3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd2dUdGKCwmKiZJInVHRigiIiIsKCokKUkidkdGKCIiJEYxISIiKiZGNkYxRjVGMUYxRjFGMUYxRjEqJkY1RjEsKCokKUY1IiIjRjFGMUY1RjFGMUYxRjFGNzcjRi4=

Another way of writing algu alias(trootu=RootOf(algu,t))

SSd0cm9vdHVHNiI=

Rewriting of algu Equation (28) factor(evala(Normal(subs(t=trootu,t*(1+t)/(1-8*t))))); factor(evala(Normal(subs(t=trootu,(1-2*t)^2/(1-8*t)))))

LCQqKEkidUc2IiIiIiwmRiZGJkYkRiYhIiIpLCYqJiIiJEYmRiRGJkYmRiZGKEYsRihGKA==

KigsKiomIiNGIiIiKUkidUc2IiIiJUYmRiYqJiIjPUYmKUYoIiIjRiYhIiIqJkYqRiZGKEYmRiZGJkYvRiYsJkYmRiZGKEYmRi8pLCYqJiIiJEYmRihGJkYmRiZGL0Y1Ri8=

algv:=collect(factor(resultant(algvu,algu,u)),v,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGd2R0YoLDwqJiwmIiIiRjEqJiIiKUYxSSJ0R0YoRjEhIiJGMSlJInZHRigiIzdGMUYxKiYsKComIiNrRjEpRjQiIiNGMUY1KiYiI3NGMUY0RjFGNUYxRjFGMSlGNyIjNkYxRjEqJiwoKiYiJCslRjFGPUYxRjUqJiIkTyRGMUY0RjFGNUYzRjVGMSlGNyIjNUYxRjEqJiwoKiYiJFsoRjFGPUYxRjUqJiIkXydGMUY0RjFGNUY4RjVGMSlGNyIiKkYxRjEqJiwoKiYiJGImRjFGPUYxRjUqJiIkdidGMUY0RjFGNSIjOkYxRjEpRjdGM0YxRjEqJiwoKiYiI1tGMUY9RjFGMSomIiQpR0YxRjRGMUY1IiNVRjFGMSlGNyIiKEYxRjEqKCIjQEYxKSwmKiYiIiVGMUY0RjFGMUYxRjFGPkYxKUY3IiInRjFGMSomLCgqJiIkbyJGMUY9RjFGMSomIiRLJUYxRjRGMUYxIiNMRjVGMSlGNyIiJkYxRjEqJiwoKiYiI0lGMUY9RjFGNSomIiRdJUYxRjRGMUYxIiNnRjVGMSlGN0Zjb0YxRjEqJiwoRmduRjUqJiIkWyNGMUY0RjFGMSIjUEY1RjEpRjciIiRGMUYxKiYsKComRjNGMUY9RjFGNUY/RjFGSkY1RjEpRjdGPkYxRjEqJiwoKiZGY29GMUY9RjFGMSomRjhGMUY0RjFGMUYxRjVGMUY3RjFGMSomRjRGMSwmRjRGMUYxRjFGMUYxNyNGLg==

algwv := 4*v^4+4*v^3-4*v-1+w^2;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd3dkdGKCwsKiYiIiUiIiIpSSJ2R0YoRjBGMUYxKiZGMEYxKUYzIiIkRjFGMSokKUkid0dGKCIiI0YxRjEqJkYwRjFGM0YxISIiRjFGPDcjRi4=

alias(troot=RootOf(algv,t))

NiRJJ3Ryb290dUc2IkkmdHJvb3RHRiQ=

map(series,[solve(algv,t)],v,4)

NyQrLUkidkc2IiEiIiIiISEiKiIiIiEjWCIiIyEkciIiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGKSIiJSsrRiRGKUYpISIkRitGLUYtRi5GNA==

tv:=op(2,[solve(algv,t)]): Rewriting of algv Equation (30) factor(evala(Normal(subs(t=troot,t*(1+t)/(1-8*t))))); factor(evala(Normal(subs(t=troot,(1-8*t)/(1-2*t)^2))))

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKEYnRiUqJiIiJUYlRiNGJUYlRiVGJUYwKSwoKiZGM0YlRi1GJUYlKiZGLkYlRihGJUYlRiVGMEYuRjA=

KiosKCokKUkidkc2IiIiIyIiIkYpKiYiIiVGKUYmRilGKUYpRilGKSksKComRitGKSlGJiIiJEYpRikqJkYwRilGJUYpRilGKSEiIkYwRiksKiomRitGKSlGJkYrRilGKUYuRilGKkYyRilGMkYyKSwsKiRGNUYpRikqJiIiKUYpRi9GKUYpKiYiIidGKUYlRilGKSomRihGKUYmRilGKUYpRilGKEYy

Series expansions user:=proc(n) option remember: if n=0 then 0 else series(subs(u=user(n-1),algu+u),t,n+1);fi: end: user(4);

Ky1JInRHNiIiIiJGJUYlIiIjIiM1IiIkIiNZIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiY=

vser:=proc(n) option remember: if n=0 then 0 else series(subs(u=user(n), v=vser(n-1), u*(-v^3+3*v+1)/(v^2+v+1)),t,n+1): fi: end: vser(5);

Ky9JInRHNiIiIiJGJSIiJCIiIyIjOkYmIiMiKSIiJSIkKlsiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJw==

wser:=proc(n) series(sqrt(subs(w=0,v=vser(n),-algwv)),t,1+n): end: wser(5);

KzFJInRHNiIiIiIiIiEiIiNGJSIiJUYnIiM/IiIkIiMlKkYoIiRVJiIiJi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlIiIn

R0w:=(1/2)*t*(w*(2*v+1)/(-2*v^3+4*v+1)-1); R1w:=1/6+(1/3)*t+(2*v+1)*(1-2*t)*(16*v^6+24*v^5+7*v^4-24*v^3-30*v^2-10*v-1)/(6*w*(-2*v^3+4*v+1)*(v^4+8*v^3+6*v^2+2*v+1));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSMHdHRigsJCooIyIiIiIiI0YxSSJ0R0YoRjEsJiooSSJ3R0YoRjEsJiomRjJGMUkidkdGKEYxRjFGMUYxRjEsKComRjJGMSlGOSIiJEYxISIiKiYiIiVGMUY5RjFGMUYxRjFGPkYxRjFGPkYxRjE3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSMXdHRigsKCMiIiIiIidGMComI0YwIiIkRjBJInRHRihGMEYwKjBGL0YwLCYqJiIiI0YwSSJ2R0YoRjBGMEYwRjBGMCwmRjBGMComRjlGMEY1RjAhIiJGMCwwKiYiIztGMClGOkYxRjBGMComIiNDRjApRjoiIiZGMEYwKiYiIihGMClGOiIiJUYwRjAqJkZDRjApRjpGNEYwRj0qJiIjSUYwKUY6RjlGMEY9KiYiIzVGMEY6RjBGPUYwRj1GMEkid0dGKEY9LCgqJkY5RjBGS0YwRj0qJkZJRjBGOkYwRjBGMEYwRj0sLCokRkhGMEYwKiYiIilGMEZLRjBGMComRjFGMEZORjBGMEY4RjBGMEYwRj1GMDcjRi4=

B1v:=3*v^2*(v^2+4*v+1)*(v^2-1)*(2*v+1)*(-8*t+1)/(2*(-4*v^3-3*v^2+1)^3*(-2*v^3+4*v+1)); B2w:=(2*v+1)*(1-2*t)*(4*t*v^12+68*t*v^11+(16*(22*t+1))*v^10+(12*(67*t+2))*v^9+(5*(192*t-5))*v^8+(8*(61*t-10))*v^7-286*t*v^6-41*v^6-788*t*v^5+66*v^5-738*t*v^4+113*v^4-(4*(97*t-17))*v^3-126*t*v^2+19*v^2-24*t*v+2*v-2*t)/(2*w*(v^4+8*v^3+6*v^2+2*v+1)^2*(2*v^3-4*v-1));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRCMXZHRigsJCoyIyIiJCIiIyIiIilJInZHRihGMkYzLCgqJEY0RjNGMyomIiIlRjNGNUYzRjNGM0YzRjMsJkY3RjNGMyEiIkYzLCYqJkYyRjNGNUYzRjNGM0YzRjMsJkYzRjMqJiIiKUYzSSJ0R0YoRjNGO0YzKSwoKiZGOUYzKUY1RjFGM0Y7KiZGMUYzRjRGM0Y7RjNGM0YxRjssKComRjJGM0ZFRjNGO0Y4RjNGM0YzRjtGMzcjRi4=

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

rem(R0w*(t+R0w),algwv,w)

LCQqKilJInRHNiIiIiMiIiIpSSJ2R0YmRidGKCwsKiYiIiZGKClGKiIiJUYoRigqJiIiKUYoKUYqIiIkRihGKCokRilGKEYoKiZGL0YoRipGKCEiIkYoRjZGKCksKComRidGKEYyRihGKEY1RjZGKEY2RidGNkY2

We start with R0 numer(factor(resultant(R0-R0w,algwv,w)));

LEQqKCIiJSIiIilJI1IwRzYiIiIjRiUpSSJ2R0YoIiInRiVGJSoqRiRGJUYnRiVJInRHRihGJUYqRiVGJSooIiImRiUpRi5GKUYlRipGJUYlKigiIilGJUYxRiUpRitGMEYlRiUqKCIjO0YlRiZGJSlGK0YkRiUhIiIqKkY2RiVGJ0YlRi5GJUY3RiVGOComRjFGJUY3RiVGJSooRiRGJUYmRiUpRisiIiRGJUY4KipGJEYlRidGJUYuRiVGPEYlRjgqKEYkRiVGMUYlRjxGJUY4KihGNkYlRiZGJSlGK0YpRiVGJSoqRjZGJUYnRiVGLkYlRkFGJUYlKiZGMUYlRkFGJUY4KihGM0YlRiZGJUYrRiVGJSoqRjNGJUYnRiVGLkYlRitGJUYlKiRGJkYlRiUqJkYnRiVGLkYlRiU=

res:=factor(resultant(%,algv,v)): nops(res);

IiRCJA==

algR0:=collect(res,R0,factor): degree(algR0,R0);degree(algR0,t);

IiND

IiNP

nops(expand(algR0));

IiRCJA==

R1w;

LCgjIiIiIiInRiQqJiNGJCIiJEYkSSJ0RzYiRiRGJCowRiNGJCwmRiRGJComIiIjRiRJInZHRipGJEYkRiQsJkYkRiQqJkYuRiRGKUYkISIiRiQsMComIiM7RiQpRi9GJUYkRiQqJiIjQ0YkKUYvIiImRiRGJComIiIoRiQpRi8iIiVGJEYkKiZGOEYkKUYvRihGJEYyKiYiI0lGJClGL0YuRiRGMiomIiM1RiRGL0YkRjJGJEYyRiRJIndHRipGMiwoKiZGLkYkRkBGJEYyKiZGPkYkRi9GJEYkRiRGJEYyLCwqJEY9RiRGJComIiIpRiRGQEYkRiQqJkYlRiRGQ0YkRiRGLUYkRiRGJEYyRiQ=

numer(factor(resultant(numer(R1-R1w),algwv,w))): res:=factor(resultant(%,algv,v)): nops(res);

IiIk

indets(op(3,res));

PCRJI1IxRzYiSSJ0R0Yk

nops(op(3,res)); factor(res/op(3,res))

IiRCJw==

LCQqJiI7Q1VXVmMhM1BeNWBqRSMiIiIpLCYqJiIiI0YlSSJ0RzYiRiVGJUYlISIiIiNDRiVGLA==

algR1:=collect(op(3,res),R1,factor): degree(algR1,R1); degree(algR1,t); nops(expand(algR1));

IiND

IiNP

IiRCJw==

B1v;

LCQqMiMiIiQiIiMiIiIpSSJ2RzYiRiZGJywoKiRGKEYnRicqJiIiJUYnRilGJ0YnRidGJ0YnLCZGLEYnRichIiJGJywmRidGJyomRiZGJ0YpRidGJ0YnLCYqJiIiKUYnSSJ0R0YqRidGMEYnRidGJyksKComRi5GJylGKUYlRidGMComRiVGJ0YoRidGMEYnRidGJUYwLCgqJkYmRidGOkYnRjBGLUYnRidGJ0YwRic=

res:=op(3,numer(factor(resultant(numer(B1-B1v),algv,v)))): nops(res);

IiRIIw==

algB1:=collect(res,B1,factor): degree(algB1,B1); degree(algB1,t); nops(expand(algB1));

IiM3

IiND

IiRIIw==

Finally B2 res:=numer(factor(resultant(numer(B2-B2w),algwv,w))):nops(%);

IiRgIg==

res:=factor(resultant(res,algv,v)): nops(res);

IiIk

op(1,res);op(2,res);

IT0qby47I1wkW0NZc3BHLHIl

KiQpLCYqJiIiIyIiIkkidEc2IkYnRidGJyEiIiIjU0Yn

nops(op(3,res));

IiR4JQ==

algB2:=collect(op(3,res),B2,factor): degree(algB2,B2); degree(algB2,t); nops(expand(algB2));nops(algB2)

IiND

IiNn

IiR4JQ==

IiM4

Oh ? Only 13 terms in an equation of degree 24? seq(coeff(algB2,B2,2*i+1),i=0..11);

Ni4iIiFGI0YjRiNGI0YjRiNGI0YjRiNGI0Yj

save(algR0,algR1,algB1,algB2,guessedeqs):

The guessed equations read(guessedeqs): degree(algR0,R0);degree(algR1,R1);degree(algB1,B1);degree(algB2,B2);

IiND

IiND

IiM3

IiND

nops(algR0);nops(algR1);nops(algB1);nops(algB2);

IiNE

IiNE

IiM4

IiM4

nops(algB2)

IiM4

JSFH

map(nops,systfinal);

NyYiI3MiJEsiIiQjPiIkdyM=

We begin with the first and smallest equation res:=numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,systfinal[1]))): nops(res);indets(res);

IiIm

PCVJInRHNiJJInZHRiRJIndHRiQ=

seq(nops(op(i,res)),i=1..nops(res)); seq(indets(op(i,res)),i=1..nops(res));

NiciIiIiIiNGJEYkIiQ4JQ==

Nic8IjwjSSJ0RzYiPCNJInZHRiZGJDwlRiVGKEkid0dGJg==

res1:=factor(rem(op(5,res),algwv,w)): nops(res1);

IiIo

seq(nops(op(i,res1)),i=1..nops(res1)); seq(indets(op(i,res1)),i=1..nops(res1));

NikiIiIiIiNGJCIiJCIjPkYkIiNQ

Nik8IjwjSSJ2RzYiRiRGJEYkRiQ8JEkidEdGJkYl

res2:=numer(factor(rem(op(7,res1),algv,v)));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVyZXMyR0YoIiIhNyNGLg==

The second one res:=numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,systfinal[2]))): nops(res);indets(res);

IiIl

PCVJInRHNiJJInZHRiRJIndHRiQ=

seq(nops(op(i,res)),i=1..nops(res)); seq(indets(op(i,res)),i=1..nops(res));

NiYiIiIiIiNGJCIlTTg=

NiY8IjwjSSJ0RzYiPCNJInZHRiY8JUYlRihJIndHRiY=

res1:=factor(rem(op(4,res),algwv,w)): nops(res1);

IiIn

seq(nops(op(i,res1)),i=1..nops(res1)); seq(indets(op(i,res1)),i=1..nops(res1));

NigiIiIiIiNGJCIiJCIjUCIkQiI=

Nig8IjwjSSJ2RzYiRiRGJDwkSSJ0R0YmRiVGJw==

Two choices here: one factor at least should be zero! res2a:=numer(factor(rem(op(5,res1),algv,v))); res2b:=numer(factor(rem(op(6,res1),algv,v))): nops(res2b);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyZXMyYUdGKCIiITcjRi4=

IiIk

The third one res:=numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,systfinal[3]))): nops(res);indets(res);

IiIm

PCVJInRHNiJJInZHRiRJIndHRiQ=

seq(nops(op(i,res)),i=1..nops(res)); seq(indets(op(i,res)),i=1..nops(res));

NiciIiIiIiNGJEYkIiUjRyI=

Nic8IjwjSSJ0RzYiPCNJInZHRiZGJDwlRiVGKEkid0dGJg==

res1:=factor(rem(op(5,res),algwv,w)): nops(res1);

IiIk

seq(nops(op(i,res1)),i=1..nops(res1)); seq(indets(op(i,res1)),i=1..nops(res1));

NiUiIiIiI1AiJFki

NiU8IjwkSSJ0RzYiSSJ2R0YmRiQ=

Two choices here: one factor at least should be zero! res2a:=numer(factor(rem(op(2,res1),algv,v))): nops(res2a);; res2b:=numer(factor(rem(op(3,res1),algv,v))): nops(res2b);

IiIi

IiIk

One of the above two results is zero (depending on Maple's mood, this may change!) res2a

IiIh

The fourth one res:=numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,systfinal[4]))): nops(res);indets(res);

IiIl

PCVJInRHNiJJInZHRiRJIndHRiQ=

seq(nops(op(i,res)),i=1..nops(res)); seq(indets(op(i,res)),i=1..nops(res));

NiYiIiIiIiNGJCIlckg=

NiY8IjwjSSJ0RzYiPCNJInZHRiY8JUYlRihJIndHRiY=

res1:=factor(rem(op(4,res),algwv,w)): nops(res1);

IiIk

seq(nops(op(i,res1)),i=1..nops(res1)); seq(indets(op(i,res1)),i=1..nops(res1));

NiUiIiIiI1AiJEck

NiU8IjwkSSJ0RzYiSSJ2R0YmRiQ=

Two choices here: one factor at least should be zero! res2a:=numer(factor(rem(op(2,res1),algv,v))): nops(res2a);; res2b:=numer(factor(rem(op(3,res1),algv,v))): nops(res2b);

IiIi

IiIk

res2a;

IiIh

DONE! JSFH

nops(algB1);

IiM4

We compute subfields for various values of t, avoiding t=2 for which algB1 factors factor(subs(t=2,algB1));

LCQqKCIoUWZjKiIiIiwqKiYiJ2NwYkYlKUkjQjFHNiIiIiRGJUYlKiYiKF1QZihGJSlGKiIiI0YlRiUqJiIpdiRSKUdGJUYqRiVGJSIpXTdgPkYlRiUsNiomIi9fUkRfOFNTRiUpRioiIipGJUYlKiYiMWsvQjokXGMsIkYlKUYqIiIpRiVGJSomIjIvWmE+UyhcSjVGJSlGKiIiKEYlRiUqJiIyKW9lbXMpPTZQJkYlKUYqIiInRiVGJSomIjMhWyk9ekEib2xdIkYlKUYqIiImRiVGJSomIjMpKWUkejkxXiUqPiNGJSlGKiIiJUYlRiUqJiIzL0g5cFVvNys6RiVGKUYlRiUqJiIyR1M8ZyRbWmRMRiVGL0YlRiUqJiIuI1xXQkFVO0YlRipGJSEiIiInWnI8RiVGJUYl

For t=1 for instance, we find a subfield of degree 4 t0:=1: evala(Subfields(subs(t=t0,algB1), 2)); evala(Subfields(subs(t=t0,algB1), 3)); evala(Subfields(subs(t=t0,algB1), 4)); evala(Subfields(subs(t=t0,algB1), 6));

PCI=

PCI=

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywsKiYiKlRaKCoqPiIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIlIiIiIiIiKiYiKT9wOnciIiIpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiEiIiomIixFUCkpKmVNIiIiKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiMiIiIhIiIqJiItW2tGVSdbIyIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIiIiIiLVZcaSFRQCYhIiI=

PCI=

pol:=199974741*_Z^4-76156920*_Z^3-34589883726*_Z^2+248642276448*_Z-521380624943;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRwb2xHRigsLComIipUWigqKj4iIiIpSSNfWkdGJSIiJUYxRjEqJiIpP3A6d0YxKUYzIiIkRjEhIiIqJiIsRVApKSplTUYxKUYzIiIjRjFGOSomIi1ba0ZVJ1sjRjFGM0YxRjEiLVZcaSFRQCZGOTcjRi4=

We tried in vain to factor algB1 over Q(t,B1) for a generic value of t (to avoid time wasting, do not execute !) res:=subs(RootOf(algB1,B1)=B1,factor(subs(B1=F,algB1),RootOf(algB1,B1))): nops(res);

Warning, computation interrupted

IiIl

We factor over Q(t,B1), but for specific values of t res:=numer(subs(RootOf(subs(t=3,algB1),B1)=B1,factor(subs(B1=F,t=3,algB1),RootOf(subs(t=3,algB1),B1)))): nops(res);

IiIl

map(degree,[seq(op(i,res),i=1..4)],F);

NyYiIiEiIioiIiMiIiI=

Here is the calculation of the minimal polynomial M2 of p2 for two values of t for t0 from 3 to 4 do res:=subs(RootOf(subs(t=t0,algB1),B1)=B1,factor(subs(B1=F,t=t0,algB1),RootOf(subs(t=t0,algB1),B1))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-B1) fi: od: # minimal polynomial of p2 (the cube of a polynomial of degree 4) M:=factor(resultant(numer(coeff(P3, F,2)-p),subs(t=t0,algB1),B1)): M:=simplify((M/lcoeff(M,p))^(1/3),symbolic): Mlist[t0]:=M; print(M): od:

LCwqJClJInBHNiIiIiUiIiJGKComIyIuNypwOStEXSIsTE56WEAnRigpRiUiIiRGKCEiIiomIyIxJlFBZCR6WF1DIi4lZiRHQyc9NkYoKUYlIiIjRihGKComIyIzQnN5X3p4dFxJIi8+Jkd5VSxeIkYoRiVGKEYvIyIzQEwpKlJ0VlA+biIvbyg9JVs0YSEpRig=

LCwqJClJInBHNiIiIiUiIiJGKComIyIvY0NYaVRAOSItLkhlUEY1RigpRiUiIiRGKCEiIiomIyIxZEE9eFlNWFIiLT11XERraEYoKUYlIiIjRihGKComIyIzdDghWyUpZjBBeCMiLiJRUVoiUngjRihGJUYoRi8jIjU0KVIuVCpSJT0kPTwiMGtvS0FQVypSRig=

We repeat with more values of t0, so as to reconstruct the complete value of M2 (which seems a bit smaller than M0 and M1). We try various values of tmax until the reconstructed coefficients of M2 look compact tmax:=30: for t0 from 3 to tmax do res:=subs(RootOf(subs(t=t0,algB1),B1)=B1,factor(subs(B1=F,t=t0,algB1),RootOf(subs(t=t0,algB1),B1))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-B1) fi: od: # minimal polynomial of p2 (the cube of a polynomial of degree 4) M:=factor(resultant(numer(coeff(P3, F,2)-p),subs(t=t0,algB1),B1)): M:=simplify((M/lcoeff(M,p))^(1/3),symbolic): Mlist[t0]:=M; od: with(CurveFitting): Mlist[3];

LCwqJClJInBHNiIiIiUiIiJGKComIyIuNypwOStEXSIsTE56WEAnRigpRiUiIiRGKCEiIiomIyIxJlFBZCR6WF1DIi4lZiRHQyc9NkYoKUYlIiIjRihGKComIyIzQnN5X3p4dFxJIi8+Jkd5VSxeIkYoRiVGKEYvIyIzQEwpKlJ0VlA+biIvbyg9JVs0YSEpRig=

We try to reconstruct the coefficients of M2, which should be rational functions of t c0:=RationalInterpolation([seq([t0, coeff(Mlist[t0],p,0)],t0=3..tmax)],t);

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

c1:=RationalInterpolation([seq([t0, coeff(Mlist[t0],p,1)],t0=3..tmax)],t);

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

c2:=RationalInterpolation([seq([t0, coeff(Mlist[t0],p,2)],t0=3..tmax)],t);

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

c3:=RationalInterpolation([seq([t0, coeff(Mlist[t0],p,3)],t0=3..tmax)],t);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjM0dGKComLDQqJiIqd0RGIlEiIiIpSSJ0R0YoIiIpRjIhIiIqJiIqQ3E8ISkpRjIpRjQiIihGMkY2KiYiKjMhcGtxRjIpRjQiIidGMkY2KiYiKitbdi0kRjIpRjQiIiZGMkY2KiYiKls2YDkiRjIpRjQiIiVGMkY2KiYiKVdKQUJGMilGNCIiJEYyRjYqJiIoZyRbUkYyKUY0IiIjRjJGNiomIiZXTyJGMkY0RjJGNkY1RjZGMiwwKiYiKVtXWFxGMkY9RjJGMiomIil3VGMiKkYyRkFGMkYyKiYiKW94IlIlRjJGRUYyRjIqJiIob1JRKUYyRklGMkYyKiYiKCl5QW1GMkZNRjJGMiomIiZzOiRGMkY0RjJGMiIjQEYyRjY3I0Yu

M2conj:=collect(numer(factor(c0+c1*p+c2*p^2+c3*p^3+p^4)),p,factor);

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

degree(M2conj,t);

IiM3

nops(expand(M2conj));

IiNg

Now we want to find a smaller description of the field K generated by p with(algcurves): genus(M2conj, t,p); is_hyperelliptic(M2conj,t,p)

IiIj

SSV0cnVlRyUqcHJvdGVjdGVkRw==

param:=Weierstrassform(M2conj,t,p,f,g): op(1,param);

LDAqJClJImdHNiIiIiMiIiJGKComIyI6X2piUl5VRj53IXkpPSQiLEQxIVFNQ0YoKUkiZkdGJiIiJkYoRigqJiMiODMpPkBuQ00pSFFfbCYiKXZmSzdGKClGLiIiJUYoISIiKiYjIjdXdFhlVS4wOVdnPCImMDckRigpRi4iIiRGKEYoKiYjIjU7W3IlNExOJD1XRCIjekYoKUYuRidGKEY2KiYiM2dQYVQwYXY1KClGKEYuRihGKCIzJmU0IzMjXFclNCEqRjY=

Let us check numer(factor(subs(f=op(2,param), g=op(3, param),op(1,param)))):factor(rem(%,M2conj,p));

IiIh

We take as a new choice for u2 the value of f. What is its minimal polynomial? u2expr:=op(2,param);

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

Its minimal polynomial res:=factor(resultant(numer(u2-u2expr),M2conj,p));

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

map(indets,[seq(op(i,res),i=1..nops(res))]);

Nyc8IjwjSSJ0RzYiRiRGJDwkRiVJI3UyR0Ym

already better than M2 algu2:=collect(op(nops(res),res),u2,factor);

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

igcd(coeffs(expand(algu2)));

IiIi

If we take g instead u2expr:=op(3,param): Its minimal polynomial res:=factor(resultant(numer(u2-u2expr),M2conj,p));

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

map(indets,[seq(op(i,res),i=1..nops(res))]);

Nyg8IjwjSSJ0RzYiRiRGJEYkPCRGJUkjdTJHRiY=

even better. The coefficients have many factors in common algu2:=collect(op(nops(res),res),u2,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd1MkdGKCwsKiYpLCYqJiIiJSIiIkkidEdGKEY0RjRGNEY0IiImRjQpSSN1MkdGKEYzRjRGNCosIiorJj5sQ0Y0LCYqJiIiI0Y0RjVGNEY0RjQhIiJGNCwoKiYiJDciRjQpRjVGPUY0RjQqJiIkPyJGNEY1RjRGNEY0Rj5GNCwoKiYiIztGNEZCRjRGNComIiNzRjRGNUY0RjQiIihGPkY0KUY4IiIkRjRGPioqIjRdKD0jekg/RGItIkY0KUY7Rj1GNClGMUZMRjQpRjhGPUY0RjQqKiI8K0Rjd1wnPkRbVXdJdkFGNClGMUY9RjQpRjtGTEY0RjhGNEY+KigiRERjXi5PVzJ2PHljWD4lPnFeNUY0RjFGNClGO0YzRjRGNDcjRi4=

ifactor([246519500,102552520297921875,227530764248251964976562500,10517019419455678177507443603515625]);

NyYqKCktSSFHNiI2IyIiI0YpIiIiKS1GJjYjIiImIiIkRiopLUYmNiMiI3pGL0YqKigpLUYmNiNGL0YvRiopRiwiIidGKilGMUY5RioqKkYkRiopRjZGLkYqKUYsIiIqRiopRjFGPkYqKigpRjZGOUYqKUYsIiM3RiopRjFGQ0Yq

With this transformation, only one of the coefficients depends on t algu3:=map(factor,collect(subs(u2=79^3*5^3*3*(2*t-1)*3*u3/(1+4*t), algu2/79^(12)/27/5^12/3^3/(2*t-1)^4/(1+4*t)),u3,factor));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd1M0dGKCwsIiIiRi8qJiIiKkYvKUkjdTNHRigiIiVGL0YvKixGNEYvLCgqJiIkNyJGLylJInRHRigiIiNGL0YvKiYiJD8iRi9GOkYvRi9GLyEiIkYvLCgqJiIjO0YvRjlGL0YvKiYiI3NGL0Y6Ri9GLyIiKEY+Ri8pLCYqJkY0Ri9GOkYvRi9GL0YvRjRGPilGMyIiJEYvRj4qJiIjSUYvKUYzRjtGL0YvKiYiIzdGL0YzRi9GPjcjRi4=

a new variable T:=coeff(algu3,u3,3);;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJUR0YoLCQqKiIiJSIiIiwoKiYiJDciRjEpSSJ0R0YoIiIjRjFGMSomIiQ/IkYxRjZGMUYxRjEhIiJGMSwoKiYiIztGMUY1RjFGMSomIiNzRjFGNkYxRjEiIihGOkYxKSwmKiZGMEYxRjZGMUYxRjFGMUYwRjpGOjcjRi4=

factor(resultant(numer(T+a),numer(diff(T,t)),t));solve(%,a);

LCQqKCI6JVEleWc4KD4sbV5nVU0iIiIsJiomIiIqRiVJImFHNiJGJUYlIiV3NyEiIkYlKSwmRilGJSIjT0YlIiIjRiVGJQ==

NiUjIiV3NyIiKiEjT0Ym

factor(T-36);

LCQqKCIjayIiIiksKComIiM7RiUpSSJ0RzYiIiIjRiVGJSomIiNDRiVGK0YlRiVGJSEiIkYtRiUpLCYqJiIiJUYlRitGJUYlRiVGJUY0RjBGMA==

Still another (smaller) variable T:=(16*t^2+24*t-1)/(1+4*t)^2; factor(T-1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJUR0YoKiYsKComIiM7IiIiKUkidEdGKCIiI0YyRjIqJiIjQ0YyRjRGMkYyRjIhIiJGMiksJiomIiIlRjJGNEYyRjJGMkYyRjVGODcjRi4=

LCQqKCIiIyIiIiwmKiYiIilGJUkidEc2IkYlRiVGJSEiIkYlKSwmKiYiIiVGJUYpRiVGJUYlRiVGJEYrRiU=

factor(2/%+1);

LCQqKiIjOyIiIkkidEc2IkYlLCZGJkYlRiVGJUYlLCYqJiIiKUYlRiZGJUYlRiUhIiJGLEYl

algu3;

LCwiIiJGIyomIiIqRiMpSSN1M0c2IiIiJUYjRiMqLEYpRiMsKComIiQ3IkYjKUkidEdGKCIiI0YjRiMqJiIkPyJGI0YvRiNGI0YjISIiRiMsKComIiM7RiNGLkYjRiMqJiIjc0YjRi9GI0YjIiIoRjNGIyksJiomRilGI0YvRiNGI0YjRiNGKUYzKUYnIiIkRiNGMyomIiNJRiMpRidGMEYjRiMqJiIjN0YjRidGI0Yz

A new way to write algu3 e1:=9*4*u3^3+collect(algu3-9*4*u3^3,u3,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNlMUdGKCwuKiYiI08iIiIpSSN1M0dGKCIiJEYxRjFGMUYxKiYiIipGMSlGMyIiJUYxRjEqKiIja0YxKSwoKiYiIztGMSlJInRHRigiIiNGMUYxKiYiI0NGMUZARjFGMUYxISIiRkFGMSksJiomRjhGMUZARjFGMUYxRjFGOEZERjJGMUZEKiYiI0lGMSlGM0ZBRjFGMSomIiM3RjFGM0YxRkQ3I0Yu

factor(e1-op(4,e1));

KiQpLCgqJiIiJCIiIilJI3UzRzYiIiIjRidGJyomIiInRidGKUYnRidGJyEiIkYrRic=

algu3new:=%/u3^3+op(4,e1)/u3^3;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlhbGd1M25ld0dGKCwmKiYpLCgqJiIiJCIiIilJI3UzR0YoIiIjRjRGNComIiInRjRGNkY0RjRGNCEiIkY3RjQpRjZGM0Y6RjQqKCIja0Y0KSwoKiYiIztGNClJInRHRihGN0Y0RjQqJiIjQ0Y0RkNGNEY0RjRGOkY3RjQpLCYqJiIiJUY0RkNGNEY0RjRGNEZJRjpGOjcjRi4=

factor(algu3new/algu3);

KiQpSSN1M0c2IiIiJCEiIg==

subs(u3=u4^2,algu3new);

LCYqJiksKComIiIkIiIiKUkjdTRHNiIiIiVGKEYoKiYiIidGKClGKiIiI0YoRihGKCEiIkYwRigpRipGLkYxRigqKCIja0YoKSwoKiYiIztGKClJInRHRitGMEYoRigqJiIjQ0YoRjpGKEYoRihGMUYwRigpLCYqJkYsRihGOkYoRihGKEYoRixGMUYx

algu4:=simplify(sqrt(op(1,%)),symbolic)- factor(simplify(sqrt(-op(2,%)),symbolic));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd1NEdGKCwmKiYsKComIiIkIiIiKUkjdTRHRigiIiVGM0YzKiYiIidGMylGNSIiI0YzRjNGMyEiIkYzKUY1RjJGO0YzKigiIilGMywoKiYiIztGMylJInRHRihGOkYzRjMqJiIjQ0YzRkNGM0YzRjNGO0YzKSwmKiZGNkYzRkNGM0YzRjNGM0Y6RjtGOzcjRi4=

algu4a:=factor(op(1,algu4)-8)+factor(op(2,algu4)+8);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGd1NGFHRigsJiooLCYqJiIiJCIiIkkjdTRHRihGM0YzRjNGM0YzKSwmRjRGM0YzISIiRjJGMylGNEYyRjdGMyooIiM7RjMsJiomIiIpRjNJInRHRihGM0YzRjNGN0YzKSwmKiYiIiVGM0Y+RjNGM0YzRjMiIiNGN0Y3NyNGLg==

factor(%/algu4);

IiIi

algu4b:=map(Z->1/Z,algu4a);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGd1NGJHRigsJiooLCYqJiIiJCIiIkkjdTRHRihGM0YzRjNGMyEiIiksJkY0RjNGM0Y1RjJGNSlGNEYyRjNGMyooI0YzIiM7RjMsJiomIiIpRjNJInRHRihGM0YzRjNGNUY1KSwmKiYiIiVGM0Y/RjNGM0YzRjMiIiNGM0Y1NyNGLg==

algu4c:=factor(op(1,algu4b)+1/16)+factor(op(2,algu4b)-1/16)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdhbGd1NGNHRigsJiosIyIiIiIjO0YxLCYqJiIiJEYxSSN1NEdGKEYxRjFGMSEiIkYxKSwmRjZGMUYxRjFGNUYxLCZGNEYxRjFGMUY3KSwmRjZGMUYxRjdGNUY3RjEqKEkidEdGKEYxLCZGPkYxRjFGMUYxLCYqJiIiKUYxRj5GMUYxRjFGN0Y3Rjc3I0Yu

algufinal:=map(factor,subs(u4=(1+3*u)/3/(1-u), algu4c));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSphbGd1ZmluYWxHRigsJiooSSJ1R0YoIiIiKSwmKiYiIiRGMUYwRjFGMUYxISIiRjVGNiwmRjFGMUYwRjFGNkYxKihJInRHRihGMSwmRjlGMUYxRjFGMSwmKiYiIilGMUY5RjFGMUYxRjZGNkY2NyNGLg==

algu;

LCgqKCksJiIiIkYmKiYiIiRGJkkidUc2IkYmISIiRihGJiwmRiZGJkYpRiZGJilJInRHRioiIiNGJkYmKiYsKComIiNGRiYpRikiIiVGJkYrKiYiIz1GJilGKUYvRiZGJkYmRiZGJkYuRiZGJkYpRis=

factor(resultant(numer(algufinal),algu,t));

IiIh

solve(u4=(1+3*u)/3/(1-u),u)

LCQqKCMiIiIiIiRGJSwmKiZGJkYlSSN1NEc2IkYlRiVGJSEiIkYlLCZGKUYlRiVGJUYrRiU=

The description that we would like to simply M2conj

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

read(`../../Calculs/Hoeij/NormalBasis`); n := degree(M2conj,p);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJuR0YoIiIlNyNGLg==

alpha := RootOf(M2conj,p): V := Candidates(M2conj,t,p): select(has,V,p): nops(%);

IiIi

beta := select(has,V,p)[1]: beta := subs(p=alpha, beta): m_beta := collect(evala(Norm(u2 - beta)),u2,factor);

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

nops(m_beta); degree(m_beta,u2);degree(m_beta,t);

IiIp

IiIl

IiIk

numer(op(2,m_beta))

LCQqKCIrW09bWkAiIiIsJiomImlbbDNJZz4ieStFcVxPd18qW0BHWUxFUlQ1UjtyRlQjeUclW3JaNmIiSCJHTDhcVFgmXGpxKEg/TyI0ZSZvJyo0dCxkSTJAMCZlcSU+YUtkJ1tJJyk9KTMuSTpXS1pYTlBeYkFLeVktZU8qW2AnR2Nsa21geHpdTylvJTQjbzE2NyFSQjlkWjx5P0wxLEJxIUgvMVpqNCRGJUkidEc2IkYlRiUiYVxsKEghKkhpSzUmMyxkSjsqZmNjQFM+KEgiekQ1Vyc+YmFJT0RKJFtxIykqKSpwJEdSRnohZkwsdiRSWGttPTtLNndRWCI9KGYkeUg8V2woKmZOdnIpUSpca01eQF9yP0c4IiozSk5UV2JEMSU+JSpIPGdMLjlWTiIpUWhpYXFrQ0lhOiU9OFFHeVA9PyNwYl8/O1RwYGMnNCE0Ty1iIiEiIkYlKUkjdTJHRioiIiRGJUYs

nops(algB1);

IiM4

It seems that the "factor" command only works correctly when in RootOf(pol,_Z), the polynomial Pol is monic in Z factor(lcoeff(algu,u));

LCQqKCIjRiIiIkkidEc2IkYlLCZGJkYlRiVGJUYlISIi

algumonic:=-collect(numer(factor(subs(u=up/lcoeff(algu,u),algu))),up,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSphbGd1bW9uaWNHRigsKiokKUkjdXBHRigiIiUiIiJGMyoqIiQnW0YzKUYxIiIjRjMpSSJ0R0YoRjdGMyksJkY5RjNGM0YzRjdGMyEiIiosIiRIKEYzRjhGMywmKiYiIilGM0Y4RjNGM0YzRjNGM0Y6RjNGMUYzRjwqKCImJG8+RjMpRjlGMkYzKUY7RjJGM0Y8NyNGLg==

res:=subs(RootOf(algumonic,up)=up,factor(algB1,RootOf(algumonic,up))): nops(res);

IiIn

map(indets, [seq(op(i,res),i=1..nops(res))]);

Nyg8IjwlSSNCMUc2IkkidEdGJkkjdXBHRiZGJDwjRidGKUYp

map(degree, [seq(op(i,res),i=1..nops(res))],B1);

NygiIiEiIioiIiRGI0YjRiM=

algB1upt:=collect(op(3,res),[B1,up],factor);

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

Back to the series u rather than up algB1ut:=collect(op(4,factor(subs(up=u*lcoeff(algu,u),algB1upt))),[B1,u],factor);

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

degree(algB1ut,u);

IiIk

What is the correct value of u? with(gfun): usolser:=map(allvalues,algeqtoseries(algu,t,u,3));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSh1c29sc2VyR0YoNyYrK0kidEdGKCIiIkYxRjEiIiMiIzUiIiQtSSJPR0YlNiNGMSIiJSwoKiYsJiNGMSIiJ0YxKiYqJkY8RjFeI0YxRjFGMSlGNCNGMUYyRjFGMUYxKUYwI0YxRjQhIiJGMSooRj1GMSlGO0YyRjFGQ0YxRkUtRjY2IyokKUYwI0YyRjRGMUYxLCgqJkZERjFGQ0ZFRkUqJkZMRjFGQ0YxRkVGSEYxLCgqJiwmRjxGMSomLCRGP0YxRjFGQUYxRkVGMUZDRkVGMSooRj1GMSlGUkYyRjFGQ0YxRkVGSEYxNyNGLg==

series(subs(B1=B1ex(5), u=op(1,usolser), algB1ut),t,5)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=

simplify(series(subs(B1=B1ex(n), u=op(2,usolser), algB1ut),t,5))

LC4jIiIoIiIqIiIiKiYiIzlGJilJInRHNiIjRiYiIiRGJkYmKigsJComRihGJl4jRiZGJkYmRiZGKUYmKUYtI0YmIiIjRiYhIiIqJiMiJFImRjRGJilGKiNGNEYtRiZGNSooLCQqJkY3RiZGMUYmRiZGJkY5RiZGMkYmRjUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YrNiNGKkYm

With the other choice of u, the factor of degree 9 vanishes series(subs(up=u*lcoeff(algu,u),B1=B1ex(5), u=op(1,usolser),op(2,res)),t,5); simplify(series(subs(up=u*lcoeff(algu,u),B1=B1ex(5), u=op(2,usolser),op(2,res)),t,5))

KytJInRHNiIiJS5eIiIjIScnNDQkIiIkIik3XCdcIiIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIiJg==

LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiQpSSJ0R0YnIiIkIiIi

Now we have 3 variables, B1, u and t... how can we find a simple series in Q(t,B_1)? algB1ut;

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

Equation of B1 over Q(u) res:=factor(resultant(algB1ut,algu,t)): nops(res);

IiIl

map(indets,[seq(op(i,res),i=1..nops(res))]);

NyY8IjwjSSJ1RzYiRiQ8JEkjQjFHRiZGJQ==

nops(op(4,res));

IiRwIg==

Now we have two variables only, u and B1 algB1u:=collect(op(4,res),B1,factor);

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We can repeat what we did before for the equation in t and B1, but this time over Q(u) rather than Q(t) with(algcurves): genus(algB1u,u,B1);

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We find between Q(u) and Q(u,B1) a subfield of degree 2 over Q(u), which is Q(t,u), and one of degree 3, which we want to explore further for u0 from 2 to 6 do : evala(Subfields(subs(u=u0,algB1u), 2)); evala(Subfields(subs(u=u0,algB1u), 3));od;

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIlcEQhIiI=

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIiVZWiIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIhIiIiJ1YiPSIhIiI=

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PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIilNKWZJIiIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIhIiIiLE5edGZDIiEiIg==

We factor algB1u over Q(u,B1) for various values of u Let us try for a generic value of u (did not work - do not execute) lcoeff(algB1u,B1);

LCQqKCIkIz4iIiIpLCoqJClJInVHNiIiIiRGJUYlKiYiIiZGJSlGKiIiI0YlISIiKiZGLEYlRipGJUYlIiIoRiVGMEYlKSwmRjJGJUYlRjEiIz1GJUYl

algB1p:=collect(numer(factor(subs(B1=B1p/lcoeff(algB1u,B1),algB1u))),B1p,factor);

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

Do not execute this res:=numer(subs(RootOf(algB1p,B1p)=B1p,factor(subs(B1=F,u=u,algB1u),RootOf(algB1p,B1p))));map(degree,[seq(op(i,%),i=1..nops(%))],F);

Warning, computation interrupted

NykiIiFGI0YjRiNGI0YjRiM=

Resume here Now for special values of u u0:=2:res:=numer(subs(RootOf(subs(u=u0,algB1u),B1)=B1,factor(subs(B1=F,u=u0,algB1u),RootOf(subs(u=u0,algB1u),B1)))): map(degree,[seq(op(i,%),i=1..nops(%))],F);

NyciIiEiIiNGJCIiIkYl

One element C1 of Q(u,B1), distinct from B1, is also a root of algB1u. B1->C1 must be an involution The minimal polynomial of B1 over the field tilde K should be (F-B1)(F-C1) Let us reconstruct this other root

nops(res);

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umax:=20:for u0 from 3 to umax do res:=subs(RootOf(subs(u=u0,algB1u),B1)=B1,factor(subs(B1=F,u=u0,algB1u),RootOf(subs(u=u0,algB1u),B1))): for i from 1 to nops(res) do if degree(op(i,res),F)=1 then P1:= op(i,res); sol:=solve(P1,F): if sol<>B1 then sollist[u0]:=sol: fi: fi: od: od: at u=21, the equation factors factor(subs(u=21,algB1u));

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We skip u0=21 umax:=100:for u0 from 22 to umax do res:=subs(RootOf(subs(u=u0,algB1u),B1)=B1,factor(subs(B1=F,u=u0,algB1u),RootOf(subs(u=u0,algB1u),B1))): for i from 1 to nops(res) do if degree(op(i,res),F)=1 then P1:= op(i,res); sol:=solve(P1,F): if sol<>B1 then sollist[u0]:=sol: fi: fi: od: od: with(CurveFitting): c0:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,0)],u0=3..20), seq([u0, coeff(sollist[u0],B1,0)],u0=22..umax)],u));

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c1:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,1)],u0=3..20), seq([u0, coeff(sollist[u0],B1,1)],u0=22..umax)],u));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNjMUdGKCwkKiwjIiIiIiIqRjEsZnAqJiI1LHY6WyR5V209VSdGMSlJInVHRigiI1dGMUYxKiYiNi8lb19VTjkjNE0oKSpGMSlGNyIjVkYxISIiKiYiN3lzXGs3WTZDN25nRjEpRjciI1VGMUYxKiYiOGcwJypRX3JQJCkzbHkiRjEpRjciI1RGMUY9KiYiOChlPDc1cm5nKD4nKSo9RjEpRjciI1NGMUYxKiYiOF8qKWVUJSpRKVtpLEFGRjEpRjciI1JGMUYxKiYiODd1Oi5QMUhGayNHISpGMSlGNyIjUUYxRj0qJiI4Z2wuMk11Iz0hKjNrX0YxKUY3IiNQRjFGMSomIjhGJm9HZDglZVMqZWxqRjEpRjciI09GMUYxKiYiODNmJykpPiRlOz1MZkApRjEpRjciI05GMUY9KiYiOHVsRSFcLVFkYFBaUUYxKUY3IiNNRjFGMSomIjh3NCZmVywvTC5LbGxGMSlGNyIjTEYxRj0qJiI4MFZbRzVUI1JeUFRDRjEpRjciI0tGMUYxKiYiOUdYKlw7dE1qXmYjKlEiRjEpRjciI0pGMUYxKiYiOVdkbzkrJmVLN2RbYSJGMSlGNyIjSUYxRj0qJiI4Iz4vckZZSCQzc1deI0YxKUY3IiNIRjFGPSomIjk5Kkd4Yil6aSIqZTgqPSJGMSlGNyIjR0YxRjEqJiI4LyRSKjMlKTRAJUdcISpbRjEpRjciI0ZGMUY9KiYiOCtMdWhNby08cm0mPkYxKUY3IiNFRjFGPSomIjhTWSFlXUlLXEwmeT0jRjEpRjciI0RGMUYxKiYiNyFIKTRwNnJAbHg5d0YxKUY3IiNDRjFGPSomIjc7W0d0WDxWQXhNNkYxKUY3IiNCRjFGMSomIjZzO3EsQkIicHVJKilGMSlGNyIjQUYxRjEqJiI2d0BlZSM9QjVqJioqKUYxKUY3IiNARjFGPSomIjYhKlw8aVs3JCoqZWtVRjEpRjciIz9GMUYxKiYiNitRZlYqcFhHJCpIPEYxKUY3IiM+RjFGPSomIjVfSVlNXDwsOyRHJkYxKUY3IiM9RjFGMSomIjVPVkBXNjxIYihHIkYxKUY3IiM8RjFGPSomIjQ1XSU0PGdGcVxKRjEpRjciIztGMUYxKiYiM2srJSp5KlJOZDYkRjEpRjciIzpGMUY9KiYiMjszeWZLZkFdKkYxKUY3IiM5RjFGMSomIjJDQTRtaDYwayJGMSlGNyIjOEYxRjEqJiIxJCpwVnA+YCdlIkYxKUY3IiM3RjFGMSomIjE/TVdIX1g5O0YxKUY3IiM2RjFGMSomIi9VdiRmTFNeJUYxKUY3IiM1RjFGMSomIi8lUSVSIjMoXGtGMSlGN0YyRjFGMSomIi42UD52NmAjRjEpRjciIilGMUYxKiYiLl84eE93WyJGMSlGNyIiKEYxRjEqJiIsIT1oOnJtRjEpRjciIidGMUYxKiYiLDc8JSopKT0jRjEpRjciIiZGMUYxKiYiKngjZikqW0YxKUY3IiIlRjFGPSomIipLTmZoI0YxKUY3IiIkRjFGMSomIilFZ0hRRjEpRjciIiNGMUY9KiYiJ182T0YxRjdGMUYxIiZSQiJGPUYxLGJvKiYiLzwiKUheeFQ1RjFGam5GMUYxKiYiL015U14wcGNGMUZeb0YxRj0qJiIwZj07JkdcJnojRjFGYm9GMUY9KiYiMU80UzZtJnp3I0YxRmZvRjFGMSomIjFjcyJ6N2s4NihGMUZqb0YxRj0qJiIxZ0JCWTUqKVFXRjFGXnBGMUYxKiYiMicqWyE0Kkg8eisiRjFGYnBGMUYxKiYiMkdKPT5JJjRTPUYxRmZwRjFGPSomIjEvcWR1YE1TdEYxRmpwRjFGMSomIjFXLE4tWixoTUYxRl5xRjFGMSomIjEnenFEZldhJFFGMUZicUYxRj0qJiIySycpcEFLcnJJIkYxRmZxRjFGMSomIjJDXyNcNjdnNUJGMUZqcUYxRj0qJiIxQ3NEbnpnZVFGMUZeckYxRjEqJiIyOyE9K0dBWEhBRjFGYnJGMUYxKiYiMldaZldQSmVUIkYxRmZyRjFGPSomIjEpSDRlJmVfV15GMUZqckYxRj0qJiIxK3pdM15PTVxGMUZec0YxRjEqJiIwWUJMKzhQJT1GMUZic0YxRj0qJiIwd143UnRgUSJGMUZmc0YxRjEqJiIvIz46X2whUVlGMUZqc0YxRj0qJiIvbzRHJ1s2JVtGMUZedEYxRj0qJiIvM3VwYEJiOkYxRmJ0RjFGPSomIi4zM01ZIWZnRjFGZnRGMUY9KiYiLid6ckNVZzxGMUZqdEYxRj0qJiItUz1VeXVTRjFGXnVGMUY9KiYiLCdSRShwXylGMUZhdUYxRj0qJiIsYyVvbWw6RjFGZXVGMUY9KiYiK0diKTRHI0YxRml1RjFGPSomIiopW1MlbyNGMUZddkYxRj0qJiIpT0ZGREYxRmF2RjFGPSomIicrQWNGMUZldkYxRjEqJiInOFlQRjFGaXZGMUYxKiYiJW0qKkYxRjdGMUYxIiVyOEY9Rj0sKiomRmdwRjFGYXZGMUYxKiZGW3NGMUZpdkYxRj0qJkZidkYxRjdGMUYxRjFGPUY9KSwmKiZGZnZGMUY3RjFGMUYxRj1GanVGPUYxNyNGLg==

c2:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,2)],u0=3..20), seq([u0, coeff(sollist[u0],B1,2)],u0=22..umax)],u));

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

c3:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,3)],u0=3..20), seq([u0, coeff(sollist[u0],B1,3)],u0=22..umax)],u));

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

c4:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,4)],u0=3..20), seq([u0, coeff(sollist[u0],B1,4)],u0=22..umax)],u));

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

c5:=factor(RationalInterpolation([seq([u0, coeff(sollist[u0],B1,5)],u0=3..20), seq([u0, coeff(sollist[u0],B1,5)],u0=22..umax)],u));

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

Let us check factor(rem(subs(B1=c0+c1*B1+c2*B1^2+c3*B1^3+c4*B1^4+c5*B1^5,algB1u),algB1u,B1));

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Why didn't we see this root when factoring algB1 ocer Q(t,B1) ? invB1:=c0+c1*B1+c2*B1^2+c3*B1^3+c4*B1^4+c5*B1^5: user(4);

Ky1JInRHNiIiIiJGJUYlIiIjIiM1IiIkIiNZIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiY=

with(gfun):allvalues(op(2,algeqtoseries(algB1u,u,B1,4,true)));

NiQrLUkidUc2IiMhIiQiIiNGKCIiJEYpIyIjUkYoIiIlISM6IiImLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjIiIiIiInKy1GJCMhI0ZGKEYoISQqPUYpIyElUE5GKEYsISY2TCJGLkYvRjY=

n:=10: normal(series(subs(u=user(n), B1=B1ex(n),invB1),t,n));

KzVJInRHNiIjISNGIiIjRichJDsjIiIkISU+RSIiJSEmTSJHIiImISdvSUciIichKCcqNHQjIiIoISlddGZEIiIpISpkMylbQiIiKi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIjNQ==

series(subs(B1=%,algB1),t,n);

KzVJInRHNiIhI0MiIiMiJGspIiIkIScpMzwkIiIlISp3RFRXJCIiJiEsJypHdzFpIyIiJyItITNBKlFfXiIiKCEwY2UkZXFgMT8iIikhMkNJczY6KSo+OyQiIiotSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

series(subs(B1=%%,u=user(n),algB1u),t,n);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

The reason is that the following resultant has TWO factors of degree 12: one is algB1, but the other is not, and is the one that is cancelled by invB1 res:=factor(resultant(algB1u,algu,u)): nops(res);degree(res,B1);

IiIk

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The factor of degree 2 in the factorization of the minimal polynomial of B1 must be P2:=(F-B1)*(F-invB1): Let us compute the minimal polynomial of each coefficient of P2 with the constant term first res:=factor(resultant(co0-coeff(P2,F,0), algB1u,B1)): nops(res);

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seq(indets(op(i,res)),i=1..nops(res))

NiY8IjwjSSJ1RzYiRiQ8JEkkY28wR0YmRiU=

nops(op(4,res));

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algco0:=collect(op(1,op(4,res)),co0,factor);

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

With the coefficient of F res:=factor(resultant(co1-coeff(P2,F,1), algB1u,B1)): nops(res);

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seq(indets(op(i,res)),i=1..nops(res))

NiY8IjwjSSJ1RzYiRiQ8JEkkY28xR0YmRiU=

nops(op(4,res));

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algco1:=collect(op(1,op(4,res)),co1,factor);

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

degree(algco1,u)

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Hence Q(u,co1) is a subextension of Q(u,B1) of degree 3 over Q(u). We now want to simplify this algv1:=collect(op(4,numer(factor(subs(co1=v1/(1-3*u)^6*(135*u^4-90*u^2+8*u-5)*(1-u),algco1)))),v1,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd2MUdGKCwqKiYsKiomIiIkIiIiKUkidUdGKEYyRjNGMyomIiM6RjMpRjUiIiNGMyEiIiomIiIqRjNGNUYzRjMiI0BGM0YzKUkjdjFHRihGMkYzRjMqJiwsKiZGPEYzKUY1IiIlRjNGMyomIiNzRjNGNEYzRjoqJiIkRSJGM0Y4RjNGMyomIiNPRjNGNUYzRjNGPEYzRjMpRj9GOUYzRjMqJiwuKiYiIz1GMylGNSIiJkYzRjoqJkZKRjNGQ0YzRjMqJiIjKipGM0Y0RjNGMyomIiNgRjNGOEYzRjMqJiIiKEYzRjVGM0YzRjNGM0YzRj9GM0YzKihGMkYzRjhGMyksJkYzRjNGNUYzRkRGM0YzNyNGLg==

degree(algv1,u);

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genus(algv1,u,v1);

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param:=factor(parametrization(algv1,u,v1,P)): op(1,param); op(2,param):

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

An alternative with van Hoeij's NormalBasis package read(`../../Calculs/Hoeij/NormalBasis`); n := degree(algv1,v1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJuR0YoIiIkNyNGLg==

alpha := RootOf(algv1,v1): V := Candidates(algv1,u,v1): select(has,V,v1): nops(%);

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beta := select(has,V,v1)[1]: beta := subs(v1=alpha, beta): m_beta := collect(evala(Norm(v2 - beta)),v2,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdtX2JldGFHRigsKiokKUkjdjJHRigiIiQiIiJGMyomLCYqJiMiJjwtIiIlQExGM0kidUdGKEYzRjNGMkYzRjMpRjEiIiNGM0YzKiYsKComIyIqc0ZBRiIiKUJyM0xGMylGOkY8RjMhIiIqJiMiJltFI0Y5RjNGOkYzRjMjIiIoRjJGM0YzRjFGM0YzKigjRjMiLVokPjUlKikpKkYzRjpGMywoKiYiLlp3J3o+aWpGM0ZDRjNGMyomIi9iakhZIVwrIkYzRjpGM0YzIi4hKVwqcClRbiVGREYzRkQ3I0Yu

We have not obtained a rational parametrization, algv2:=collect(numer(m_beta),v2,factor):degree(algv2,v2); degree(algv2,u);

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But we can retry the Maple command param:=factor(parametrization(algv2,u,v2,P));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZwYXJhbUdGKDckLCQqKiMiIiIiI1BGMiwmIiVqKipGMiomIiZAKiopRjJJIlBHRihGMkYyRjIsKComIitAMXhgQ0YyKUY4IiIjRjJGMiomIitqKltWXyJGMkY4RjJGMiIqJGVIW3BGMkYyLCoqJiIuWncnej5pakYyKUY4IiIkRjJGMiomIi4zQlZoRCFRRjJGPEYyRjIqJiIuPjdBZ0MvJEYyRjhGMiEiIiItWiQ+NSUqKSkqRkpGSkZKLCQqKiNGMiInSidvJEYyRjRGMiwoKiYiL0hOeCZRTlglRjJGPEYyRjIqJiIvekpzWVsxXkYyRjhGMkYyIi5rLCRHODVoRkpGMkZBRkpGSjcjRi4=

We try varous things to simplify this param1:=factor(subs(P=P/89921,P=P-9963,param));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwYXJhbTFHRig3JCwkKiojIiZAKiopIiNQIiIiSSJQR0YoRjQsKComIitAMXhgQ0Y0KUY1IiIjRjRGNComIi94eXFccjwpKUY0RjVGNEY0IjQuKVsicCUzKnBoXCVGNEY0LCoqJiIuWncnej5pakY0KUY1IiIkRjRGNComIjMmW20mKlwiUnE8OkY0RjlGNEY0KiYiOD1ULFhkKm9EQCU+JkhGNEY1RjQhIiIiPDI4XF1XU183UCEpZkhZJUZHRkdGRywkKiojRjIiJ0onbyRGNEY1RjQsKComIi9ITngmUU5YJUY0RjlGNEY0KiYiNDAra3JfKSoqUS9QRjRGNUY0RjQiOFNYJUdVMkh2M0Z0ISpGR0Y0Rj5GR0ZHNyNGLg==

ifactor([2453770621,88177149707877, 4496169908469148803 ])

NyUqJi1JIUc2IjYjIiNKIiIiLUYlNiMiKSIqUTp6RikqLCktRiU2IyIiJCIjNkYpLUYlNiMiI1BGKSktRiU2IyIjVCIiI0YpLUYlNiMiI2BGKS1GJTYjIiReIkYpKigpRi8iIz5GKSlGM0Y6RikpRjciIiVGKQ==

param2:=factor(subs(P=P*41^2*37*3^10,P=1/P,param1));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwYXJhbTJHRig3JCwkKigiJkAqKikiIiIsKCokKUkiUEdGKCIiI0YyRjIqJiImRj8oRjJGNkYyRjIiK2o9Smh0RjJGMiwqKiQpRjYiIiRGMkYyKiYiJ0FIQ0YyRjVGMkYyKiYiKyZwIypwZSVGMkY2RjIhIiIiMDwpM1coUj8xKEZDRkNGMiwkKigjRjEiJWoqKkYyLCgqJiImIT0/RjJGNUYyRjIqJiIrYig0Zi0kRjJGNkYyRkMiMChlP3Q6MU84RkNGMkY7RkNGQzcjRi4=

ifactor([89921,242922,4586992695,706203974408817])

NyYqJi1JIUc2IjYjIiM4IiIiLUYlNiMiJTxwRikqKC1GJTYjIiIjRiktRiU2IyIiJEYpLUYlNiMiJihbU0YpKiwpRjFGMEYpLUYlNiMiIiZGKS1GJTYjIiNCRiktRiU2IyIkKlFGKS1GJTYjIiYkUjZGKSosRjFGKS1GJTYjIiM+RiktRiU2IyIjUEYpLUYlNiMiIyopRiktRiU2IyIrPHpRaVBGKQ==

param3:=factor(subs(P=P-2*40487,param2))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwYXJhbTNHRig3JCwkKigiJkAqKikiIiIsKCokKUkiUEdGKCIiI0YyRjIqJkYxRjJGNkYyISIiIitUaXkmMylGMkYyLCgqJClGNiIiJEYyRjIqJiIsQihldERDRjJGNkYyRjkiMGhwZCUpPjNGKEYyRjlGMiwkKigjRjEiJWoqKkYyLCgqJiImIT0/RjJGNUYyRjIqJiIrJlI/U0gnRjJGNkYyRjkiMGpDbWEpSFBDRjJGMkY7RjlGOTcjRi4=

ifactor([24257358723,727081984576961])

NyQqKC1JIUc2IjYjIiIkIiIiKS1GJTYjIiM4IiIjRikpLUYlNiMiJTxwRi5GKSomKUYrRihGKSlGMEYoRik=

Here is something nice param4:=factor(subs(P=P*13*6917,P=-1/P,param3))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdwYXJhbTRHRig3JCooLCgqJClJIlBHRigiIiMiIiJGNUYzRjVGNUY1RjVGM0Y1LCgqJClGMyIiJEY1RjUqJkY5RjVGMkY1RjVGNSEiIkY7LCQqKiNGNSIlaioqRjUsKComIiZWLCRGNUYyRjVGNSomIiYmKipwRjVGM0Y1RjUiJiE9P0Y1RjVGM0Y1RjZGO0Y7NyNGLg==

isolate(algvu,u)

L0kidUc2IiooSSJ2R0YkIiIiLCgqJClGJiIiI0YnRidGJkYnRidGJ0YnLCgqJClGJiIiJEYnISIiKiZGL0YnRiZGJ0YnRidGJ0Yw

factor(param4[1]-op(2,%))

KiosKComSSJQRzYiIiIiSSJ2R0YmRidGJ0YlRidGKEYnRicsNCooIiIjRicpRiVGK0YnKUYoRitGJ0YnKiZGLEYnRihGJyEiIiooRitGJ0YlRidGLUYnRicqJEYsRidGLyooRitGJ0YlRidGKEYnRicqJEYtRidGL0YlRi9GKEYvRidGL0YnLCgqJClGJSIiJEYnRicqJkY3RidGLEYnRidGJ0YvRi8sKCokKUYoRjdGJ0YnKiZGN0YnRihGJ0YvRidGL0Yv

we can now factor the equation for B1 over Q(v) uv:=solve(algvu,u)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1dkdGKCwkKihJInZHRigiIiIsKCokKUYwIiIjRjFGMUYwRjFGMUYxRjEsKCokKUYwIiIkRjFGMSomRjlGMUYwRjEhIiJGMUY7RjtGOzcjRi4=

res:=numer(factor(subs(u=uv,algB1u))): nops(%);

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We want the factor of degree 2 map(indets,[seq(op(i,res),i=1..nops(res))]); map(degree,[seq(op(i,res),i=1..nops(res))],B1)

NyQ8JEkjQjFHNiJJInZHRiVGIw==

NyQiIiMiIiU=

algB1v:=collect(op(1,res),B1,factor);

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Which v should we choose ? The one with no constant term vusolens:=map(allvalues,algeqtoseries(algvu,u,v,3));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSl2dXNvbGVuc0dGKDclKytJInVHRigsJiMiIiIiIiMhIiIqJiomRjJGM14jRjNGM0YzKSIiJEYyRjNGMyIiISwkKiYsJEY4RjNGM0Y5RjNGNUYzLCYjRjpGNEY1RjZGM0Y0LUkiT0dGJTYjRjNGOisrRjAsJkYyRjUqJiwkRjdGM0YzRjlGM0Y1RjsqJkY4RjNGOUYzRjMsJkZARjVGRkY1RjRGQUY6KytGMEYzRjNGNEY0RjNGOkZBIiIlNyNGLg==

series(subs(v=vusolens[3], u=user(5), B1=B1ex(5),algB1v),t,4);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiU=

factor(series(subs(v=vusolens[1], u=user(5), B1=B1ex(5),algB1v),t,1));

KydJInRHNiIsJiMiJWhsIiIjISIiKiYsJComRiYiIiJeI0YtRi1GLUYtKSIiJCNGLUYoRi1GKSIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YtRi0=

Let us check the factor of degree 4 series(subs(v=vusolens[3], u=user(5), B1=B1ex(5),op(2,res)),t,4); simplify(series(subs(v=vusolens[1], u=user(5), B1=B1ex(5),op(2,res)),t,5));

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KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiQ=

Now we want to factor the quadratic polynomial of B1 over Q(t,v). Again, we need to give to Maple a monic equation algvp:=collect(-numer(factor(subs(t=tp/lcoeff(algv,t),algv))),tp,factor);

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res:=factor(numer(subs(RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t),factor(algB1v,RootOf(algvp,tp)))));nops(res);

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algB1vta:=op(1,res):algB1vtb:=op(3,res): n:=4: series(subs(v=vser(n), B1=B1ex(n), algB1vta),t,n);

KylJInRHNiIhI0MiIiMhJEcmIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiIl

series(subs(v=vser(n), B1=B1ex(n), algB1vtb),t,n);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiU=

algB1vt:=collect(algB1vtb,B1,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShhbGdCMXZ0R0YoLCYqKiIiIyIiIiwoKiZGMEYxKUkidkdGKCIiJEYxRjEqJiIiJUYxRjVGMSEiIkYxRjlGMSksKComRjhGMUY0RjFGMSomRjZGMSlGNUYwRjFGMUYxRjlGNkYxSSNCMUdGKEYxRjEqMEY2RjFGPkYxLCZGNUYxRjFGOUYxLCZGMUYxKiZGMEYxRjVGMUYxRjEsJkY1RjFGMUYxRjEsKCokRj5GMUYxRjdGMUYxRjFGMSwmKiYiIilGMUkidEdGKEYxRjFGMUY5RjFGMTcjRi4=

B1vtsol:=solve(%,B1);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShCMXZ0c29sR0YoLCQqNCMiIiQiIiMiIiIpSSJ2R0YoRjJGMywmRjVGM0YzISIiRjMsJkYzRjMqJkYyRjNGNUYzRjNGMywmRjVGM0YzRjNGMywoKiRGNEYzRjMqJiIiJUYzRjVGM0YzRjNGM0YzLCYqJiIiKUYzSSJ0R0YoRjNGM0YzRjdGMywoKiZGMkYzKUY1RjFGM0YzRj1GN0YzRjdGNyksKComRj5GM0ZFRjNGMyomRjFGM0Y0RjNGM0YzRjdGMUY3Rjc3I0Yu

nops(algR0);

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We first compute an equation in R0 and v res:=factor(resultant(algR0,algv,t)): nops(%);

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seq(indets(op(i,res)),i=1..4)

NiY8IjwkSSNSMEc2IkkidkdGJkYkRiQ=

n:=20: series(subs(R0=R0ex(n),v=vser(n),op(2,res)),t,n); series(subs(R0=R0ex(n),v=vser(n),op(3,res)),t,n); series(subs(R0=R0ex(n),v=vser(n),op(4,res)),t,n);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIz8=

K0VJInRHNiIiIzsiIiUiJWM1IiImIiZTcyQiIiciJyVRTyoiIigiKSdcIykpPSIiKSIqT2tURCQiIioiK014QSYpXCIjNSIsPyQpei0ocCIjNiItOFMuM2khKiIjNyIvSChvJXpmNTYiIzgiMCdcTj86TidIIiIjOSIxWy1CcVx2XzkiIzoiMiE9STtQLylHZCJGJSIzaT1fbnQpW05sIiIjPCI0SzwkPXNrZyRbcCIiIz0iNSIzMil5PEhQTSpwIiIjPi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIjPw==

KylJInRHNiIiKSIpZS9aIiM9IixtYDVXQyIiIz4tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIz8=

algR0v:=collect(op(2,res),R0,factor); nops(%);

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degree(algR0v,R0);

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factorization over Q(t,v) res:=factor(numer(subs(RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t),factor(algR0v,RootOf(algvp,tp))))):nops(res);

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map(indets,[seq(op(i,res),i=1..nops(res))]);

NyY8I0kidkc2IkYjPCVJI1IwR0YlSSJ0R0YlRiRGJg==

n:=15: series(subs(R0=R0ex(n),v=vser(n),op(3,res)),t,n); series(subs(R0=R0ex(n),v=vser(n),op(4,res)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=

Kz9JInRHNiIhIiIiIiMhI1AiIiQhJGEoIiIlISZEOSIiIiYhJ0dfOSIiJyEoKVxaOyIiKCEpcFRHPCIiKSEqQ0NXciIiIiohKyIqUkZKOyIjNSEsSjlxUF0iIiM2IS1KKWYoW184IiM3IS52MkowSD4iIiM4IS94QiskZWQuIiIjOS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIjOg==

nops(op(3,res));

IiNw

algR0vt:=collect(op(3,res),[R0,t],factor); degree(%,t)

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

IiIi

Looking at the coefficients of t^0 and t^1 suggests to consider R0/t map(factor,subs(t=0,algR0vt));

LCYqKiwoKiQpSSJ2RzYiIiIjIiIiRioqJiIiJUYqRidGKkYqRipGKkYqKSwoKiZGKUYqKUYnIiIkRipGKkYrISIiRipGMkYpRiopLCgqJkYsRipGMEYqRioqJkYxRipGJkYqRipGKkYyRjFGKilJI1IwR0YoRilGKkYqKipGMEYqLCwqJiIiJkYqKUYnRixGKkYqKiYiIilGKkYwRipGKkYlRipGK0YyRipGMkYqLChGJUYqRidGKkYqRipGKiksKCokRjBGKkYqKiZGMUYqRidGKkYyRipGMkYxRipGKg==

map(factor,coeff(algR0vt,t));

LCYqKkkjUjBHNiIiIiIpLCgqJiIiJUYmKUkidkdGJSIiJEYmRiYqJkYtRiYpRiwiIiNGJkYmRiYhIiJGLUYmKSwoKiZGMEYmRitGJkYmKiZGKkYmRixGJkYxRiZGMUYwRiYsKCokRi9GJkYmRjVGJkYmRiZGJkYmKihGL0YmLDwqJiIiKUYmKUYsIiM3RiZGJiomIiNzRiYpRiwiIzZGJkYmKiYiJE8kRiYpRiwiIzVGJkYmKiYiJF8nRiYpRiwiIipGJkYmKiYiJHYnRiYpRixGO0YmRiYqJiIkKUdGJilGLCIiKEYmRiYqJiIkbyJGJilGLCIiJ0YmRjEqJiIkSyVGJilGLCIiJkYmRjEqJiIkXSVGJilGLEYqRiZGMSomIiRbI0YmRitGJkYxKiZGP0YmRi9GJkYxKiZGPUYmRixGJkYxRiZGMUYmLCwqJkZYRiZGZW5GJkYmKiZGO0YmRitGJkYmRjdGJkY1RjFGJkYxRiZGMQ==

algR0stvt:=collect(subs(R0=t*R0st,algR0vt/t^2),R0st,factor);

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

We want to simplify the constant term factor(evala(Normal(subs(R0st=0,t=troot,algR0stvt))))

KiopSSJ2RzYiIiIjIiIiLCgqJEYjRidGJyomIiIlRidGJEYnRidGJ0YnRicpLCgqJkYrRicpRiQiIiRGJ0YnKiZGMEYnRiNGJ0YnRichIiJGMEYnLCwqJiIiJkYnKUYkRitGJ0YnKiYiIilGJ0YvRidGJ0YpRidGKkYyRidGMkYn

algR0stv:=collect(op(3,factor(subsop(3=%,algR0stvt))),R0st,factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlhbGdSMHN0dkdGKCwoKiYpLCgqJiIiIyIiIilJInZHRigiIiRGNEY0KiYiIiVGNEY2RjQhIiJGNEY6RjNGNClJJVIwc3RHRihGM0Y0RjQqJkYwRjRGPEY0RjQqJiwsKiYiIiZGNClGNkY5RjRGNComIiIpRjRGNUY0RjQqJClGNkYzRjRGNEY4RjpGNEY6RjRGRkY0RjQ3I0Yu

factor(discrim(algR0stv,R0st))

LCQqKCksKComIiIjIiIiKUkidkc2IiIiJEYoRigqJiIiJUYoRipGKCEiIkYoRi9GJ0YoLCoqJkYuRigpRipGLkYoRigqJkYuRihGKUYoRihGLUYvRihGL0YoKSwmRihGKComRidGKEYqRihGKEYnRihGLw==

map(simplify,factor([solve(algR0stv,R0st)]),symbolic)

NyQqJiwsKiYiIiMiIiIpSSJ2RzYiIiIkRichIiIqKEYmRicpLCoqJiIiJUYnKUYpRjFGJ0YsKiZGMUYnRihGJ0YsKiZGMUYnRilGJ0YnRidGJyNGJ0YmRidGKUYnRicqJEYuRidGJ0Y0RidGJ0YnRicsKEYzRicqJiIiKUYnRilGJ0YsRiZGLEYsKiYsKiomLCYqJkYmRidGKUYnRixGJ0YsRidGLkYnRidGJUYsRjRGJ0YnRidGJ0Y3Riw=

map(series,%,v,3)

NyQrKUkidkc2IiEiIiIiIUYmIiIjLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjIiIiIiIkKydGJEYvRihGKUYw

R0ex(4);

KiYpSSJ0RzYiIiIjIiIiLCoqJiIjISlGJylGJCIiJUYnRicqJiIjPEYnKUYkIiIkRidGJyomRiZGJ0YjRidGJ0YkRidGJw==

R0stsolv:=op(2,%%%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlSMHN0c29sdkdGKComLCoqJiwmKiYiIiMiIiJJInZHRihGNCEiIkY0RjZGNCksKiomIiIlRjQpRjVGOkY0RjYqJkY6RjQpRjUiIiRGNEY2KiZGOkY0RjVGNEY0RjRGNCNGNEYzRjRGNComRjNGNEY9RjRGNkY/RjRGNEY0RjQsKEY8RjQqJiIiKUY0RjVGNEY2RjNGNkY2NyNGLg==

n:=8:series(subs(v=vser(n),R0stsolv-R0ex(n)/t),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

Version of the paper R0stpap:=1/2*(w*(1+2*v)/(1+4*v-2*v^3)-1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShSMHN0cGFwR0YoLCYqKiMiIiIiIiNGMUkid0dGKEYxLCZGMUYxKiZGMkYxSSJ2R0YoRjFGMUYxLCgqJkYyRjEpRjYiIiRGMSEiIiomIiIlRjFGNkYxRjFGMUYxRjtGMUYwRjs3I0Yu

factor(R0stpap-R0stsolv)

LCQqKiMiIiIiIiNGJSwmRiVGJSomRiZGJUkidkc2IkYlRiVGJSwmKiQpLCoqJiIiJUYlKUYpRjBGJSEiIiomRjBGJSlGKSIiJEYlRjIqJkYwRiVGKUYlRiVGJUYlRiRGJUYlSSJ3R0YqRjJGJSwoKiZGJkYlRjRGJUYlRjZGMkYlRjJGMkYl

nops(algR1);

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res:=factor(resultant(algR1,algv,t)): nops(%);

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seq(indets(op(i,res)),i=1..4)

NiY8IjwkSSNSMUc2IkkidkdGJkYkRiQ=

n:=5: series(subs(R1=R1ex(n),v=vser(n),op(2,res)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=

series(subs(R1=R1ex(n),v=vser(n),op(3,res)),t,n); series(subs(R1=R1ex(n),v=vser(n),op(4,res)),t,n)

Ky9JInRHNiIiJDciIiIhIiYhWzUiIiIiJ29AXSIiIyIpW2daOyIiJCIqZyZIIj0lIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiY=

Ky9JInRHNiIiNUgmZUk4V1Z3KSlHIiIiISI3d2EkM2pzIz5bJj1gIyIiIiI5VS1oLSoqR1F1VDY2OSIiIyE6M3JkInBAKVJSQ2daJyoqIiIkIT0ib0UmeTZ2MmA2USEqXGI9IiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiY=

An equation of degree 4 over Q(v) algR1v:=op(2,res): nops(%);

IiR6Ig==

degree(algR1v,R1);

IiIl

We try to use t and w, and obtain an equation of degree 1 res:=numer(subs(RootOf(algwv,w)=w,RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t),factor(algR1v,{RootOf(algvp,tp),RootOf(algwv,w)}))): nops(res)

IiIl

map(indets,[seq(op(i,res),i=1..nops(res))])

NyY8JkkjUjFHNiJJInRHRiVJInZHRiVJIndHRiVGI0YjRiM=

n:=15: series(subs(R1=R1ex(n),v=vser(n),w=wser(n),op(1,res)),t,n); series(subs(R1=R1ex(n),v=vser(n),w=wser(n),op(2,res)),t,n); series(subs(R1=R1ex(n),v=vser(n),w=wser(n),op(3,res)),t,n); series(subs(R1=R1ex(n),v=vser(n),w=wser(n),op(4,res)),t,n);

K0NJInRHNiIiIiMiIiEiI0siIiIiJHcjRiUiJWs9IiIkIiZtOCIiIiUiJldiJyIiJiInLzNPIiInIihLdyg9IiIoIig3MiQqKSIiKSIpMzc3TiIiKiIpKUctaCciIzUhKiFbXEd0IiM2ISxXImYnM0siIiM3IS07ZUBgejkiIzghLk9WPy1JVSIiIzktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIjOg==

K0NJInRHNiIiIiMiIiEiI1MiIiIiJCFbRiUiJW9aIiIkIiZpTCUiIiUiJzNfUCIiJiIoL3Y5JCIiJyIpWydvZSMiIigiKjdnazQjIiIpIitHUkkjbyIiIioiLEczKy9NIiIjNSItd2QpZkMxIiIjNiItR1tWVSpRKSIjNyIuKzlocGRnJyIjOCIvP2opW0gvPiYiIzktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIjOg==

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=

K0NJInRHNiIhIiUiIiEhJC8iIiIiISUrOiIiIyEma20iIiIkIScjPmkiIiIlIShjZVkiIiImISk/TW03IiInISpTO0QxIiIiKCEqRyUzVCgpIiIpISs7XzQkNCgiIiohLCk9KlwoKnAmIiM1IS03ZlluWlgiIzYhLlc3P1ImNE8iIzchL0coSFFBUSZHIiM4ITAncEhna3lcQSIjOS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiM6

algR1vwt:=collect(op(3,res),[R1,w],factor)

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

collect(solve(algR1vwt,R1),[w],factor);

LCgqMiMiIiIiIidGJSwmRiVGJSomIiIjRiVJInZHNiJGJUYlRiUsMComIiM7RiUpRipGJkYlRiUqJiIjQ0YlKUYqIiImRiVGJSomIiIoRiUpRioiIiVGJUYlKiZGMUYlKUYqIiIkRiUhIiIqJiIjSUYlKUYqRilGJUY7KiYiIzVGJUYqRiVGO0YlRjtGJSwmKiZGKUYlSSJ0R0YrRiVGJUYlRjtGJSwsKiRGNkYlRiUqJiIiKUYlRjlGJUYlKiZGJkYlRj5GJUYlRihGJUYlRiVGOywqKiZGN0YlRjZGJUYlKiZGN0YlRjlGJUYlKiZGN0YlRipGJUY7RiVGO0Y7LCgqJkYpRiVGOUYlRiVGTEY7RiVGO0Y7SSJ3R0YrRiVGO0YkRiUqJiNGJUY6RiVGQ0YlRiU=

R1pap:=1/6*(1+2*t+(1+2*v)*(1-2*t)*(16*v^6+24*v^5+7*v^4-24*v^3-30*v^2-10*v-1)/w/(1+4*v-2*v^3)/(1+2*v+6*v^2+8*v^3+v^4));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZSMXBhcEdGKCwoIyIiIiIiJ0YwKiYjRjAiIiRGMEkidEdGKEYwRjAqMEYvRjAsJkYwRjAqJiIiI0YwSSJ2R0YoRjBGMEYwLCZGMEYwKiZGOUYwRjVGMCEiIkYwLDAqJiIjO0YwKUY6RjFGMEYwKiYiI0NGMClGOiIiJkYwRjAqJiIiKEYwKUY6IiIlRjBGMComRkNGMClGOkY0RjBGPSomIiNJRjApRjpGOUYwRj0qJiIjNUYwRjpGMEY9RjBGPUYwSSJ3R0YoRj0sKComRjlGMEZLRjBGPSomRklGMEY6RjBGMEYwRjBGPSwsKiRGSEYwRjAqJiIiKUYwRktGMEYwKiZGMUYwRk5GMEYwRjhGMEYwRjBGPUYwNyNGLg==

factor(%-%%);

LCQqNCMiIiIiIidGJSwmRiVGJSomIiIjRiVJInZHNiJGJUYlRiUsMComIiM7RiUpRipGJkYlRiUqJiIjQ0YlKUYqIiImRiVGJSomIiIoRiUpRioiIiVGJUYlKiZGMUYlKUYqIiIkRiUhIiIqJiIjSUYlKUYqRilGJUY7KiYiIzVGJUYqRiVGO0YlRjtGJSwmKiZGKUYlSSJ0R0YrRiVGJUYlRjtGJSwsKiZGN0YlRjZGJUYlKiZGN0YlRjlGJUYlKiQpSSJ3R0YrRilGJUYlKiZGN0YlRipGJUY7RiVGO0YlRklGOywoKiZGKUYlRjlGJUYlRkpGO0YlRjtGOywsKiRGNkYlRiUqJiIiKUYlRjlGJUYlKiZGJkYlRj5GJUYlRihGJUYlRiVGOywqRkVGJUZGRiVGSkY7RiVGO0Y7RiU=

res:=factor(resultant(algB2,algv,t)): nops(%);

IiIl

seq(indets(op(i,res)),i=1..4)

NiY8IjwkSSNCMkc2IkkidkdGJkYkRiQ=

n:=5: series(subs(B2=B2ex(n),v=vser(n),op(2,res)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=

series(subs(B2=B2ex(n),v=vser(n),op(3,res)),t,n); series(subs(B2=B2ex(n),v=vser(n),op(4,res)),t,n)

Ky9JInRHNiIiIyIpIiIhIiVzISoiIiIiJztLXiIiIyIpa0FtPiIiJCIqQzFmeCYiIiUtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJg==

Ky9JInRHNiIiNUhiR0tgaz42W1MiIiEiN2NhSVE4UyEpPWNFSSIiIiE5Sy1lSDsjZUQqR09saiIiIyE7UzFLdS0iKlJCUyU9XUcqIiIkIjtvI1xoUWVnZT1BOFltKSIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoIiIm

algB2v:=op(2,res): nops(%);

IiR2Ig==

degree(algB2v,B2);

IiIl

An equation of degree 4 (biquadratic) over Q(v) collect(algB2v,B2,factor);

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

coeff(algB2v,B2,1); coeff(algB2v,B2,3);

IiIh

IiIh

We try to use t and w, and obtain an equation of degree 1 res:=factor(numer(subs(RootOf(algwv,w)=w,RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t),factor(algB2v,{RootOf(algvp,tp),RootOf(algwv,w)})))): nops(res)

IiIn

map(indets,[seq(op(i,res),i=1..nops(res))])

Nyg8JkkjQjJHNiJJInRHRiVJInZHRiVJIndHRiU8I0YnRilGI0YjRiM=

n:=15: series(subs(B2=B2ex(n),v=vser(n),w=wser(n),op(1,res)),t,n); series(subs(B2=B2ex(n),v=vser(n),w=wser(n),op(4,res)),t,n); series(subs(B2=B2ex(n),v=vser(n),w=wser(n),op(5,res)),t,n); series(subs(B2=B2ex(n),v=vser(n),w=wser(n),op(6,res)),t,n);

K0NJInRHNiIiIiciIiEiJEcjIiIiIiVPWiIiIyImR0YoIiIkIidJSiQqIiIlIilvYGw1IiImIiohKXlKNyJGJSIrY3ItPTYiIigiLFkmPXNtNSIiKSIsT3MxYCYpKiIiKiItP2Q/XSEpKSkiIzUiLjM0WkJjJXkiIzYiLy0qKW9SS0FvIiM3IjApeV0kMyVbY2UiIzgiMUswYCQqKT5WKFwiIzktSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIjOg==

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzo=

K0NJInRHNiIhIiciIiEhJEcjIiIiISVRWiIiIyEmc0YoIiIkISdRTyQqIiIlISlLJ2YxIiIiJiEqI1taQjYiIichK3dmPz02IiIoISx1IWYibzEiIiIpISxnejJkJikqIiIqIS0nZTEkZiEpKSkiIzUhLlN6NWJiJXkiIzYhLycqSEFxPUFvIiM3ITBPOVQ2SGomZSIjOCExIXllUV1zVChcIiM5LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIzo=

Kz9JInRHNiIiIiNGJSIjTyIiJCIkYyQiIiUiJW9GIiImIiYtJD4iIiciJ3NwNyIiKCInS1UhKSIiKSIoQ0wlXCIiKiIpM1VdSCIjNSIqXz8vcSIiIzYiKl1rNUwqIiM3IitzM0JEWiIjOCIsMS9SXS4jIiM5LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiM6

algB2vwt:=collect(op(4,res),[B2,w],factor)

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

B2soltvw:=factor(solve(algB2vwt,B2));

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

Some attempts to find a nice expression. This one is better subs(troot=t,evala(Normal(subs(t=troot,B2soltvw/(1-2*t)))))

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

B2soltvw2:=(1-2*t)*%: This is the expression given in the paper factor(B2w-B2soltvw2); rem(numer(%),algwv,w)

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

IiIh

We start from the equation in St and the 4 univariate series that we have now determined eqStcatz:=27*t^2*(2*t+z+1)*(10*t-3*z+1)*St^3+((216*t^2-27*z^2+54*t)*R0^2+27*t*(6*R1*t-6*R1*z+6*t^2+2*t*z-z^2+2*B2+t+z)*R0-9*t^2*(27*R1^2-27*R1*t+9*R1*z+5*t^2-2*t*z+3*B1-3*B2-9*R1+6*t-2*z+1))*St+(72*t^2-9*z^2+18*B1+18*t)*R0^2+9*t*(6*R1*t-6*R1*z+6*t^2+2*t*z-z^2+2*B1+2*B2+t+z)*R0+t^2*(-81*R1^2+81*R1*t-27*R1*z+5*t^2+10*t*z-3*z^2+9*B1+9*B2+27*R1-6*t+4*z-2)

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

zx:=t*(x+1/x+1)+(t+1)/(x+1/x+1); StS:=((x+1/x+1)*S(x)-R0/t+2*x*(1/3)+1/(3*x))/(x-1/x)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN6eEdGKCwmKiZJInRHRigiIiIsKEkieEdGKEYxKiRGMyEiIkYxRjFGMUYxRjEqJiwmRjBGMUYxRjFGMUYyRjVGMTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRTdFNHRigqJiwmSSJ4R0YoIiIiKiRGMCEiIkYzRjMsKiomLChGMEYxRjJGMUYxRjFGMS1JIlNHRig2I0YwRjFGMSomSSNSMEdGKEYxSSJ0R0YoRjNGMyomIyIiIyIiJEYxRjBGMUYxKiYjRjFGQEYxRjBGM0YxRjE3I0Yu

Now we replace the 4 univariate series by their expressions res:=numer(factor(subs(R0=R0w, R1=R1w,B1=B1v,B2=B2w,eqStcatz))): nops(res)

IiIj

op(1,res)

KiQpSSJ0RzYiIiIjIiIi

nops(op(2,res))

IiQtKQ==

degree(res,w); coeff(res,w,1); coeff(res,w,3);

IiIl

IiIh

IiIh

We use the defining equation of w: after taking a remainder, no w is left res1:=numer(factor(rem(res,algwv,w))): nops(res1)

IiIk

seq(indets(op(i,res1)),i=1..nops(res1));

NiU8IjwmSSNTdEc2IkkidEdGJkkidkdGJkkiekdGJjwjRic=

nops(op(2,res1));

IiRjJg==

res2:=op(2,res1): degree(res2,t); degree(res2,v);

IiIj

IiNJ

We lower the degree in t res3:=factor(rem(res2,algv,t)): nops(res3)

IiIm

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyc8IjwjSSJ2RzYiRiQ8JkkjU3RHRiZJInRHRiZGJUkiekdGJkYk

res4:=op(4,res3): nops(%);

IiR6JA==

Here is an equation for St with coefficients in Q(t,v,z), of degree 1 in t algStv:=collect(res4,[St,z],factor);indets(%)

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

PCZJI1N0RzYiSSJ0R0YkSSJ2R0YkSSJ6R0Yk

We now look at the coefficients of z^i. They depend on t in a very simple fashion degree(algStv,z)

IiIj

coeff(algStv,z,2); indets(%)

LCgqLiIjIikiIiIsKCokKUkidkc2IiIiI0YlRiUqJiIiJUYlRilGJUYlRiVGJUYlLCwqJClGKUYtRiVGJSomIiIpRiUpRikiIiRGJUYlKiYiIidGJUYoRiVGJSomRitGJUYpRiVGJUYlRiVGJSksKComRi1GJUYzRiVGJSomRjRGJUYoRiVGJUYlISIiRjRGJSksKComRitGJUYzRiVGJUYsRjxGJUY8RjRGJSlJI1N0R0YqRjRGJUYlKjIiI0ZGJUYoRiVGJkYlRj5GJUYuRiUsLComIiImRiVGMEYlRiVGMUYlRidGJUYsRjxGJUY8RiVGOEYlRkFGJUY8Ki5GNEYlRiZGJUY+RiVGLkYlLDAqJiIjNkYlKUYpRjZGJUYlKiYiI0NGJSlGKUZGRiVGJSomIiM+RiVGMEYlRiVGMUY8KiZGUEYlRihGJUY8KiZGMkYlRilGJUY8RiVGPEYlRjhGJUY8

PCRJI1N0RzYiSSJ2R0Yk

coeff(algStv,z,1): subs(t=1/2,%); indets(factor(coeff(algStv,z,1)/(1-2*t)))

IiIh

PCRJI1N0RzYiSSJ2R0Yk

coeff(algStv,z,0): subs(t=1/8,%); indets(factor(coeff(algStv,z,0)/(1-8*t)))

IiIh

PCRJI1N0RzYiSSJ2R0Yk

Recall the following identity, obtained from the minimal polynomial of v factor(evala(Normal(subs(t=troot,(1-8*t)/(1-2*t)^2))))

KiosKCokKUkidkc2IiIiIyIiIkYpKiYiIiVGKUYmRilGKUYpRilGKSksKComRitGKSlGJiIiJEYpRikqJkYwRilGJUYpRilGKSEiIkYwRiksKiomRitGKSlGJkYrRilGKUYuRilGKkYyRilGMkYyKSwsKiRGNUYpRikqJiIiKUYpRi9GKUYpKiYiIidGKUYlRilGKSomRihGKUYmRilGKUYpRilGKEYy

We introduce zt=z/(1-2t). Then we have an equation with no t algStvzt:=collect(op(3,numer(factor(evala(Normal(subs(t=troot,subs(z=zt*(1-2*t), algStv/(1-2*t)^2))))))), [St,zt],factor)

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

indets(%)

PCVJI1N0RzYiSSJ2R0YkSSN6dEdGJA==

Which has, moreover, genus 0 with(algcurves): genus(algStvzt,zt,St)

IiIh

zx;StS

LCYqJkkidEc2IiIiIiwoSSJ4R0YlRiYqJEYoISIiRiZGJkYmRiZGJiomLCZGJEYmRiZGJkYmRidGKkYm

KiYsJkkieEc2IiIiIiokRiQhIiJGKEYoLCoqJiwoRiRGJkYnRiZGJkYmRiYtSSJTR0YlNiNGJEYmRiYqJkkjUjBHRiVGJkkidEdGJUYoRigqJiMiIiMiIiRGJkYkRiZGJiomI0YmRjVGJkYkRihGJkYm

St is not well defined at x=1 n:=2: factor(series(subs(S(x)=Sex(n),R0=R0ex(n),StS),t,n))

KydJInRHNiIsJCoqIyIiIiIiJEYoLCYqJiIiI0YoKUkieEdGJEYsRihGKEYoRihGKCwmRi5GKEYoISIiRjAsJkYuRihGKEYoRjBGKCIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRiw=

The degree of S(x), at x=2. We first eliminate w res:=factor(resultant(numer(factor(subs(St=StS,S(x)=S,R0=R0w,zt=zx/(1-2*t),x=2,algStvzt))),algwv,w)): nops(res)

IiUvOg==

indets(res);degree(res,S);degree(res,t)

PCVJIlNHNiJJInRHRiRJInZHRiQ=

IiIn

IiIl

We lower the degree in t res0:=factor(rem(res,algv,t)): nops(%)

IiIn

map(indets,[seq(op(i,res0),i=1..nops(res0))])

Nyg8IjwjSSJ2RzYiRiQ8JUkiU0dGJkkidEdGJkYlRiRGJA==

algSof2vt:=op(4,res0): nops(%)

IiREKQ==

Now we eliminate v res1:=factor(resultant(op(4,res0),algv,v)): nops(res1)

IiIl

map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyY8IjwjSSJ0RzYiRiQ8JEkiU0dGJkYl

res2:=op(4,res1): nops(%)

IiUuaQ==

degree(res2,S)

IiNz

n:=18:series(subs(S=subs(x=2,Sex(n)),res2),t,n);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIz0=

algSof2:=res2: Later we have a special section for x=1

NB: the parametrizing series P0, P1, P2 below are called U0, U1, U2 in the paper

with(algcurves): algStvzt

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

We first examine the parametrization given by Maple for various values of v (only one example is given here) v0:=2: factor(parametrization(subs(v=v0,algStvzt),zt,St,P)): This suggest to look for a parametrization of the following form for zt ztparam:=(1+add(a[i]*P^i,i=1..3))/P/(1+ add(b[i]*P^i,i=1..2));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSh6dHBhcmFtR0YoKigsKiomKUkiUEdGKCIiJCIiIiZJImFHRig2I0YzRjRGNComKUYyIiIjRjQmRjY2I0Y6RjRGNComRjJGNCZGNjYjRjRGNEY0RjRGNEY0RjIhIiIsKComRjlGNCZJImJHRihGPEY0RjQqJkYyRjQmRkRGP0Y0RjRGNEY0RkA3I0Yu

At the end we'll replace P by 1/P... factor(subs(P=1/P,ztparam))

KiYsKiokKUkiUEc2IiIiJCIiIkYpKiYpRiYiIiNGKSZJImFHRic2I0YpRilGKSomRiZGKSZGLjYjRixGKUYpJkYuNiNGKEYpRiksKCokRitGKUYpKiZGJkYpJkkiYkdGJ0YvRilGKSZGOUYyRikhIiI=

An Ansatz on the parametrization unassign('alpha','beta'): Stparam:=add(alpha[i]*P^i,i=0..2)/(1+ add(beta[i]*P^i,i=1..2))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShTdHBhcmFtR0YoKiYsKComKUkiUEdGKCIiIyIiIiZJJmFscGhhR0YoNiNGM0Y0RjQqJkYyRjQmRjY2I0Y0RjRGNCZGNjYjIiIhRjRGNCwoKiZGMUY0JkklYmV0YUdGKEY3RjRGNComRjJGNCZGQUY6RjRGNEY0RjQhIiI3I0Yu

res:=factor(parametrization(algStvzt,zt,St,P)):

read(`../../Calculs/Hoeij/NormalBasis`); n := degree(algStvzt,St);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJuR0YoIiIkNyNGLg==

v0:=2: alpha := RootOf(subs(v=v0,algStvzt),St): V := Candidates(subs(v=v0,algStvzt),zt,St): select(has,V,St): nops(%);

IiIi

beta := select(has,V,St)[1]: beta := subs(St=alpha, beta): m_beta := collect(evala(Norm(P - beta)),P,factor);

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

We plug these expressions of zt and St in the equation, and cancel the coefficients of P.Depending on the order in which we determine the 10 unknowns, we get stucki, or not... maybe a Gr\303\266bner basis would do better res:=numer(factor(subs(zt=ztparam,St=Stparam,algStvzt))): nops(res)

IiZbSSM=

indets(res);degree(res,P)

PC5JIlBHNiJJInZHRiQmSSJhR0YkNiMiIiImRic2IyIiIyZGJzYjIiIkJkkmYWxwaGFHRiQ2IyIiISZGMUYoJkYxRismSSJiR0YkRigmRjdGKyZJJWJldGFHRiRGKCZGOkYr

IiM3

res:=collect(res,P,factor): co:=coeff(res,P,0);indets(%);

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

PCRJInZHNiImSSZhbHBoYUdGJDYjIiIh

collect(op(6,co),alpha[0],factor)

LDQqKCIiKiIiIiksKComIiIjRiUpSSJ2RzYiIiIkRiVGJSomIiIlRiVGK0YlISIiRiVGMEYpRiUpJkkmYWxwaGFHRiw2IyIiIUYpRiVGJSooRi1GJUYmRiVGMkYlRjAqJiIjNkYlKUYrIiInRiVGMComIiNDRiUpRisiIiZGJUYwKiYiIz5GJSlGK0YvRiVGMComIiIpRiVGKkYlRiUqJkZARiUpRitGKUYlRiUqJkZDRiVGK0YlRiVGJUYl

The only rational solution alpha0sol:=alpha[0]=-1/3: res1:=factor(subs(alpha[0]=-1/3,res/P)): nops(res1)

IiZncSI=

factor(coeff(res1,P,0));indets(%);

LCQqMiIiKiIiIiwmSSJ2RzYiRiVGJSEiIkYlLCZGJ0YlRiVGJUYlLCoqJiIiJUYlKUYnRi1GJUYlKiZGLUYlKUYnIiIkRiVGJSomRi1GJUYnRiVGKUYlRilGJSwoKiYiIiNGJUYwRiVGJUYyRilGJUYpRiUpLCgqJClGJ0Y1RiVGJUYyRiVGJUYlRjVGJSksLCokRi5GJUYlKiYiIilGJUYwRiVGJSomIiInRiVGOUYlRiUqJkY1RiVGJ0YlRiVGJUYlRjVGJSwmJkklYmV0YUdGKDYjRiVGJSomRjFGJSZJJmFscGhhR0YoRkVGJUYlRiVGKQ==

PCVJInZHNiImSSZhbHBoYUdGJDYjIiIiJkklYmV0YUdGJEYn

beta1sol:=isolate(%%,beta[1])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSliZXRhMXNvbEdGKC8mSSViZXRhR0YoNiMiIiIsJComIiIkRjImSSZhbHBoYUdGKEYxRjIhIiI3I0Yu

res2:=factor(subs(beta1sol,res1/P)): nops(res2)

IiUzJSo=

factor(coeff(res2,P,0));indets(%);

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

PCVJInZHNiImSSZhbHBoYUdGJDYjIiIjJkklYmV0YUdGJEYn

collect(op(5,%%),[alpha[2],beta[2]],factor)

LCgqLCIiJCIiIiwqKiYiIiVGJSlJInZHNiJGKEYlRiUqJkYoRiUpRipGJEYlRiUqJkYoRiVGKkYlISIiRiVGL0YlLCgqJiIiI0YlRi1GJUYlRi5GL0YlRi9GJSksLCokRilGJUYlKiYiIilGJUYtRiVGJSomIiInRiUpRipGMkYlRiUqJkYyRiVGKkYlRiVGJUYlRjJGJSZJJmFscGhhR0YrNiNGMkYlRiUqKkYmRiVGMEYlRjNGJSZJJWJldGFHRitGPkYlRiUqLkYkRiVGOkYlLCZGKkYlRiVGL0YlLCZGO0YlRiVGJUYlLCZGKkYlRiVGJUYlKSwoKiRGOkYlRiVGLkYlRiVGJUYyRiVGLw==

alpha2sol:=collect(isolate(%,alpha[2]),beta[2],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSphbHBoYTJzb2xHRigvJkkmYWxwaGFHRig2IyIiIywmKiYjIiIiIiIkRjYmSSViZXRhR0YoRjFGNiEiIioyKUkidkdGKEYyRjYsJkY9RjZGNkY6RjYsJiomRjJGNkY9RjZGNkY2RjZGNiwmRj1GNkY2RjZGNiksKCokRjxGNkY2KiYiIiVGNkY9RjZGNkY2RjZGMkY2LCoqJkZGRjYpRj1GRkY2RjYqJkZGRjYpRj1GN0Y2RjZGRUY6RjZGOkY6LCgqJkYyRjZGS0Y2RjZGRUY6RjZGOkY6KSwsKiRGSUY2RjYqJiIiKUY2RktGNkY2KiYiIidGNkY8RjZGNkZARjZGNkY2RjJGOkY2NyNGLg==

res3:=factor(subs(%,res2/P)): nops(res3)

IiIq

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nys8IjwjSSJ2RzYiRiRGJEYkPCtJIlBHRiZGJSZJImFHRiY2IyIiIiZGKjYjIiIjJkYqNiMiIiQmSSZhbHBoYUdGJkYrJkkiYkdGJkYrJkY2Ri4mSSViZXRhR0YmRi5GJEYkRiQ=

res4:=op(6,res3): nops(%)

IiYmKTQi

co:=factor(coeff(res4,P,0)): nops(%);indets(%%);

IiIk

PCZJInZHNiImSSJhR0YkNiMiIiImSSZhbHBoYUdGJEYnJkkiYkdGJEYn

map(indets,[seq(op(i,co),i=1..nops(co))])

NyU8I0kidkc2IkYjPCZGJCZJImFHRiU2IyIiIiZJJmFscGhhR0YlRikmSSJiR0YlRik=

collect(op(3,co),[a[1], b[1], alpha[1]],factor)

LCoqJiwsKiYiIiMiIiIpSSJ2RzYiIiIlRidGJyomIiM7RicpRikiIiRGJ0YnKiYiIzdGJylGKUYmRidGJyomRitGJ0YpRidGJ0YmRidGJyZJImFHRio2I0YnRidGJyomLCxGJSEiIkYsRjlGMEY5RjNGOUYmRjlGJyZJImJHRipGNkYnRicqJiwsKiZGL0YnRihGJ0YnKiYiI0NGJ0YuRidGJyomIiM9RidGMkYnRicqJiIiJ0YnRilGJ0YnRi9GJ0YnJkkmYWxwaGFHRipGNkYnRicqKEYmRidGKUYnLCgqJEYuRidGJ0YpRidGJ0YnRidGOQ==

collect(isolate(%,a[1]),[b[1], alpha[1]],factor)

LyZJImFHNiI2IyIiIiwoJkkiYkdGJUYmRicqJiMiIiQiIiNGJyZJJmFscGhhR0YlRiZGJyEiIiooSSJ2R0YlRicsKCokKUYzRi1GJ0YnRjNGJ0YnRidGJywsKiQpRjMiIiVGJ0YnKiYiIilGJ0Y2RidGJyomIiInRicpRjNGLkYnRicqJkYuRidGM0YnRidGJ0YnRjFGJw==

a1sol:=%: res5:=factor(subs(a1sol,res4/P)): nops(res5)

IiYmPTU=

co:=factor(coeff(res5,P,0)): nops(%);indets(%%);

IiIl

PChJInZHNiImSSJhR0YkNiMiIiMmSSZhbHBoYUdGJDYjIiIiJkkiYkdGJEYrJkYuRicmSSViZXRhR0YkRic=

map(indets,[seq(op(i,co),i=1..nops(co))])

NyY8IjwjSSJ2RzYiRiQ8KEYlJkkiYUdGJjYjIiIjJkkmYWxwaGFHRiY2IyIiIiZJImJHRiZGLiZGMUYqJkklYmV0YUdGJkYq

collect(op(4,co)/coeff(op(4,co),a[2]),[ a[2],b[2],b[1], a[1], alpha[1], beta[2]],factor)

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

a2sol:=isolate(%,a[2])

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

res6:=factor(subs(a2sol,res5/P)): nops(res6)

IiIl

co:=factor(coeff(res6,P,0)): nops(%);indets(%%);

IiIl

PChJInZHNiImSSJhR0YkNiMiIiQmSSZhbHBoYUdGJDYjIiIiJkkiYkdGJEYrJkYuNiMiIiMmSSViZXRhR0YkRjA=

map(indets,[seq(op(i,co),i=1..nops(co))])

NyY8IjwjSSJ2RzYiRiQ8KEYlJkkiYUdGJjYjIiIkJkkmYWxwaGFHRiY2IyIiIiZJImJHRiZGLiZGMTYjIiIjJkklYmV0YUdGJkYz

nops(op(4,co)); map(Z->degree(co,Z),[a[3], alpha[1], b[1], b[2], beta[2]])

IiReIg==

NyciIiIiIiRGI0YjRiM=

factor(coeff(op(4,co),a[3]));

LCQqKCIjOyIiIiwqKiYiIiVGJSlJInZHNiJGKEYlRiUqJkYoRiUpRioiIiRGJUYlKiZGKEYlRipGJSEiIkYlRjBGJSksLCokRilGJUYlKiYiIilGJUYtRiVGJSomIiInRiUpRioiIiNGJUYlKiZGOUYlRipGJUYlRiVGJUYuRiVGJQ==

a3sol:=collect(isolate(op(4,co),a[3]),[a[3], b[1], b[2], beta[2],alpha[1]],distributed,factor)

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

res7:=factor(subs(a3sol,res6/P)): nops(%); degree(%%,P)

IiIl

IiIn

map(indets,[seq(op(i,res7),i=1..nops(res7))])

NyY8IjwoSSJQRzYiSSJ2R0YmJkkmYWxwaGFHRiY2IyIiIiZJImJHRiZGKiZGLTYjIiIjJkklYmV0YUdGJkYvPCNGJ0Yz

res8:=op(2,res7): nops(%)

IiZFKj0=

co:=factor(coeff(res8,P,0)): nops(%);indets(%%);

IiIl

PCdJInZHNiImSSZhbHBoYUdGJDYjIiIiJkkiYkdGJEYnJkYqNiMiIiMmSSViZXRhR0YkRiw=

map(indets,[seq(op(i,co),i=1..nops(co))])

NyY8IjwjSSJ2RzYiRiQ8J0YlJkkmYWxwaGFHRiY2IyIiIiZJImJHRiZGKiZGLTYjIiIjJkklYmV0YUdGJkYv

nops(op(4,co)); map(Z->degree(co,Z),[alpha[1], b[1], b[2], beta[2]])

IiQuJA==

NyYiIiUiIiJGJCIiIw==

factor(coeff(op(4,co),b[1]));indets(%); factor(coeff(op(4,co),b[2]));indets(%);

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

PCVJInZHNiImSSZhbHBoYUdGJDYjIiIiJkklYmV0YUdGJDYjIiIj

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

PCVJInZHNiImSSZhbHBoYUdGJDYjIiIiJkklYmV0YUdGJDYjIiIj

Here we introduce a denominator. We take the smallest one, hence we solve for b2 b2sol:=factor(isolate(op(4,co),b[2])): den:=denom(op(2,b2sol)); indets(%)

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

PCVJInZHNiImSSZhbHBoYUdGJDYjIiIiJkklYmV0YUdGJDYjIiIj

res9:=numer(factor(subs(b2sol,res8/P))): nops(%)

IiY2QSU=

co:=factor(coeff(res9,P,0)): nops(%);indets(%%);

IiIm

PCZJInZHNiImSSZhbHBoYUdGJDYjIiIiJkkiYkdGJEYnJkklYmV0YUdGJDYjIiIj

Two types of solutions ? map(indets,[seq(op(i,co),i=1..nops(co))])

Nyc8IjwjSSJ2RzYiRiQ8JUYlJkkmYWxwaGFHRiY2IyIiIiZJJWJldGFHRiY2IyIiIzwmRiVGKCZJImJHRiZGKkYs

nops(op(5,co)); map(Z->degree(op(5,co),Z),[ b[1], alpha[1], beta[2]])

IiQmKik=

NyUiIiIiIigiIiQ=

nops(op(4,co)); map(Z->degree(op(4,co),Z),[alpha[1], beta[2]])

IiNN

NyQiIiMiIiI=

This looks simpler... but cancels the denominator of b2 factor(coeff(op(4,co),beta[2]))

LCQqKCIiJSIiIiwqKiZGJEYlKUkidkc2IkYkRiVGJSomRiRGJSlGKSIiJEYlRiUqJkYkRiVGKUYlISIiRiVGL0YlKSwsKiRGKEYlRiUqJiIiKUYlRixGJUYlKiYiIidGJSlGKSIiI0YlRiUqJkY4RiVGKUYlRiVGJUYlRjhGJUYv

factor(op(4,co)/den)

LCQqKCMiIiIiIztGJSwqKiYiIiVGJSlJInZHNiJGKUYlRiUqJkYpRiUpRisiIiRGJUYlKiZGKUYlRitGJSEiIkYlRjFGMSksLCokRipGJUYlKiYiIilGJUYuRiVGJSomIiInRiUpRisiIiNGJUYlKiZGOkYlRitGJUYlRiVGJUY6RjFGJQ==

Hence we solve the second factor b1sol:=factor(isolate(op(5,co),b[1])):nops(%)

IiIj

My laptop got stuck here... but it works on the bigger computer at uni On the laptop, one tries to simplify by forcing alpha1=0 alpha1sol:=alpha[1]=0: Below, the ambitious version (for bigger computers) alpha1sol:=alpha[1]=alpha[1]: res10:=numer(factor(subs(b1sol,alpha1sol,res9/P))): nops(%)

IiIk

map(indets,[seq(op(i,res10),i=1..nops(res10))]); map(nops,[seq(op(i,res10),i=1..nops(res10))])

NyU8JUkidkc2IiZJJmFscGhhR0YlNiMiIiImSSViZXRhR0YlNiMiIiNGIzwmSSJQR0YlRiRGJkYq

NyUiI0siIiMiJk1OJQ==

collect(op(1,res10),beta[2],factor)

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

beta2sola:=collect(isolate(%,beta[2]),alpha[1],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpiZXRhMnNvbGFHRigvJkklYmV0YUdGKDYjIiIjLCYqJiMiIioiIiUiIiIpJkkmYWxwaGFHRig2I0Y4RjJGOEY4KjApSSJ2R0YoRjJGOCwmRj9GOEY4ISIiRjgsJiomRjJGOEY/RjhGOEY4RjhGOCwmRj9GOEY4RjhGOCwqKiZGMkY4KUY/IiIkRjhGOComRkhGOEY+RjhGOComIiInRjhGP0Y4RjhGOEY4RjgsKiomRjdGOClGP0Y3RjhGOComRjdGOEZHRjhGOComRjdGOEY/RjhGQUY4RkFGQSksLCokRk5GOEY4KiYiIilGOEZHRjhGOComRktGOEY+RjhGOEZDRjhGOEY4RjJGQUZBNyNGLg==

The next term in res10 is a square collect(op(1,op(2,res10)),beta[2],factor)

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

beta2solb:=collect(isolate(%,beta[2]),alpha[1],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpiZXRhMnNvbGJHRigvJkklYmV0YUdGKDYjIiIjLCYqJiMiIioiIiUiIiIpJkkmYWxwaGFHRig2I0Y4RjJGOEY4KixJInZHRihGOCwmKiZGMkY4Rj5GOEY4RjhGOEY4LDAqJiIjPUY4KUY+IiInRjhGOComIiNGRjgpRj4iIiZGOEY4KiYiIzVGOClGPkY3RjhGOComIiNNRjgpRj4iIiRGOCEiIiomIiNhRjgpRj5GMkY4RlEqJiIjPkY4Rj5GOEZRRjJGUUY4LCoqJkY3RjhGTEY4RjgqJkY3RjhGT0Y4RjgqJkY3RjhGPkY4RlFGOEZRRlEpLCwqJEZMRjhGOComIiIpRjhGT0Y4RjgqJkZFRjhGVEY4RjhGQEY4RjhGOEYyRlFGUTcjRi4=

But this solution cancels the denominator of b2, so we will ignore it factor(subs(beta2solb,den))

IiIh

Let us consider the factor that still involves P (only done for alpha1=0, skip it otherwise) res11:=op(3,res10): degree(%,P)

IiIl

co:=factor(coeff(res11,P,3)): nops(co)

IiIl

map(indets,[seq(op(i,co),i=1..nops(co))]); map(nops,[seq(op(i,co),i=1..nops(co))]); map(degree,[seq(op(i,co),i=1..nops(co))],beta[2])

NyY8IjwjSSJ2RzYiRiQ8JUYlJkkmYWxwaGFHRiY2IyIiIiZJJWJldGFHRiY2IyIiIw==

NyYiIiIiIiYiIiUiJVUkKg==

NyYiIiFGI0YjIiIq

collect(op(7,co),beta[2],factor)

LCYqKCwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpLCwqJEYoRidGJyomIiIpRidGLEYnRicqJiIiJ0YnKUYpIiIjRidGJyomRjhGJ0YpRidGJ0YnRidGOEYnJkklYmV0YUdGKjYjRjhGJ0YnKixGN0YnLCZGKUYnRidGL0YnLCZGOUYnRidGJ0YnLCZGKUYnRidGJ0YnLCoqJkY4RidGLEYnRicqJkYtRidGN0YnRicqJkY2RidGKUYnRidGJ0YnRidGJw==

solve(%,beta[2])

LCQqMClJInZHNiIiIiMiIiIsJkYlRihGKCEiIkYoLCYqJkYnRihGJUYoRihGKEYoRigsJkYlRihGKEYoRigsKiomRidGKClGJSIiJEYoRigqJkYxRihGJEYoRigqJiIiJ0YoRiVGKEYoRihGKEYoLCoqJiIiJUYoKUYlRjdGKEYoKiZGN0YoRjBGKEYoKiZGN0YoRiVGKEYqRihGKkYqKSwsKiRGOEYoRigqJiIiKUYoRjBGKEYoKiZGNEYoRiRGKEYoRixGKEYoRihGJ0YqRio=

All ways lead to Rome: we have obtained the same value for beta2 beta2sola

LCQqMClJInZHNiIiIiMiIiIsJkYlRihGKCEiIkYoLCYqJkYnRihGJUYoRihGKEYoRigsJkYlRihGKEYoRigsKiomRidGKClGJSIiJEYoRigqJkYxRihGJEYoRigqJiIiJ0YoRiVGKEYoRihGKEYoLCoqJiIiJUYoKUYlRjdGKEYoKiZGN0YoRjBGKEYoKiZGN0YoRiVGKEYqRihGKkYqKSwsKiRGOEYoRigqJiIiKUYoRjBGKEYoKiZGNEYoRiRGKEYoRixGKEYoRihGJ0YqRio=

So let us reconstruct the expressions of zt and St ztalpha1:=factor(subs(alpha0sol,beta1sol, alpha1sol,alpha2sol,alpha1sol,a1sol,a2sol,a3sol,b2sol,alpha1sol, b1sol, beta2sola,alpha1sol, ztparam)): indets(%)

PCVJIlBHNiJJInZHRiQmSSZhbHBoYUdGJDYjIiIi

degree(numer(ztalpha1),P)

IiIk

It might be lighter to replace P by 1/P ztP0:=factor(subs(P=1/P0,ztalpha1))

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

StP0:=factor(subs(alpha0sol,beta1sol, alpha1sol,alpha2sol,alpha1sol,a1sol,a2sol,a3sol,b2sol,alpha1sol, b1sol, beta2sola,alpha1sol, P=1/P0,Stparam));

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

nops(denom(StP0))

IiIk

collect(op(2,denom(StP0)),alpha[1],factor): collect(op(2,denom(StP0)),[P0,alpha[1]],factor)

LCoqKiIiJSIiIiwqKiZGJEYlKUkidkc2IkYkRiVGJSomRiRGJSlGKSIiJEYlRiUqJkYkRiVGKUYlISIiRiVGL0YlKSwsKiRGKEYlRiUqJiIiKUYlRixGJUYlKiYiIidGJSlGKSIiI0YlRiUqJkY4RiVGKUYlRiVGJUYlRjhGJSlJI1AwR0YqRjhGJUYlKiwiIzdGJSZJJmFscGhhR0YqNiNGJUYlRiZGJUYwRiVGO0YlRi8qKiIiKkYlKUY+RjhGJUYmRiVGMEYlRiUqLkYkRiVGN0YlLCZGKUYlRiVGL0YlLCZGOUYlRiVGJUYlLCZGKUYlRiVGJUYlLCoqJkY4RiVGLEYlRiUqJkYtRiVGN0YlRiUqJkY2RiVGKUYlRiVGJUYlRiVGLw==

collect(op(3,denom(ztP0)),alpha[1],factor): collect(op(3,denom(ztP0)),[P0,alpha[1]],factor);

LCwqKiIiJSIiIiwqKiZGJEYlKUkidkc2IkYkRiVGJSomRiRGJSlGKSIiJEYlRiUqJkYkRiVGKUYlISIiRiVGL0YlKSwsKiRGKEYlRiUqJiIiKUYlRixGJUYlKiYiIidGJSlGKSIiI0YlRiUqJkY4RiVGKUYlRiVGJUYlRjhGJSlJI1AwR0YqRjhGJUYlKiYsJioqIiM3RiVGJkYlRjBGJSZJJmFscGhhR0YqNiNGJUYlRi8qLEYkRiVGKUYlLCZGOUYlRiVGJUYlRjFGJUYmRiVGJUYlRjtGJUYlKioiIipGJSlGQEY4RiVGJkYlRjBGJUYlKi5GNkYlRilGJUZERiVGMUYlRiZGJUZARiVGLyouRiRGJUY3RiUsJkYpRiVGJUYvRiUsJkYpRiVGJUYlRiUsKCokRjdGJUYlRilGJUYlRiVGJSlGREY4RiVGJQ==

coeff(%,P0)

LCYqKiIjNyIiIiwqKiYiIiVGJSlJInZHNiJGKEYlRiUqJkYoRiUpRioiIiRGJUYlKiZGKEYlRipGJSEiIkYlRjBGJSksLCokRilGJUYlKiYiIilGJUYtRiVGJSomIiInRiUpRioiIiNGJUYlKiZGOUYlRipGJUYlRiVGJUY5RiUmSSZhbHBoYUdGKzYjRiVGJUYwKixGKEYlRipGJSwmRjpGJUYlRiVGJUYyRiVGJkYlRiU=

factor(subs(isolate(%,alpha[1]),[ztP0,StP0]));

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

factor(subs(alpha[1]=0,[ztP0,StP0]));

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

StP00:=op(2,%)

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

collect(op(2,denom(%)),P0,factor)

LCYqKCwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpLCwqJEYoRidGJyomIiIpRidGLEYnRicqJiIiJ0YnKUYpIiIjRidGJyomRjhGJ0YpRidGJ0YnRidGOEYnKUkjUDBHRipGOEYnRicqLEY3RicsJkYpRidGJ0YvRicsJkY5RidGJ0YnRicsJkYpRidGJ0YnRicsKiomRjhGJ0YsRidGJyomRi1GJ0Y3RidGJyomRjZGJ0YpRidGJ0YnRidGJ0Yv

collect(numer(StP00),P0,factor)

LCYqKilJI1AwRzYiIiIjIiIiLCoqJiIiJUYoKUkidkdGJkYrRihGKComRitGKClGLSIiJEYoRigqJkYrRihGLUYoISIiRihGMkYoLCgqJkYnRihGL0YoRihGMUYyRihGMkYoKSwsKiRGLEYoRigqJiIiKUYoRi9GKEYoKiYiIidGKClGLUYnRihGKComRidGKEYtRihGKEYoRihGJ0YoRjIqLEY8RigsJkYtRihGKEYyRigsJkY9RihGKEYoRigsJkYtRihGKEYoRigsMComRitGKClGLUY7RihGKComRjtGKClGLSIiJkYoRigqJiIiKEYoRixGKEYoKiYiIzdGKEYvRihGKComIiNGRihGPEYoRigqJiIjOUYoRi1GKEYoRidGKEYoRig=

Much better pa1:=factor(subs(alpha[1]=0,P0=P0/(v^4 + 8*v^3 + 6*v^2 + 2*v + 1),[ztP0,StP0]));

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

collect(op(3,denom(pa1[2])),P0,factor)

LCYqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqLClGKUYyRicsJkYpRidGJ0YvRicsJiomRjJGJ0YpRidGJ0YnRidGJywmRilGJ0YnRidGJywqKiZGMkYnRixGJ0YnKiZGLUYnRjRGJ0YnKiYiIidGJ0YpRidGJ0YnRidGJ0Yv

collect(numer(pa1[2]),P0,factor)

LCYqKCwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicsKComIiIjRidGLEYnRidGLkYvRidGL0YnKUkjUDBHRipGMkYnRi8qLClGKUYyRicsJkYpRidGJ0YvRicsJiomRjJGJ0YpRidGJ0YnRidGJywmRilGJ0YnRidGJywwKiZGJkYnKUYpIiInRidGJyomRj5GJylGKSIiJkYnRicqJiIiKEYnRihGJ0YnKiYiIzdGJ0YsRidGJyomIiNGRidGNkYnRicqJiIjOUYnRilGJ0YnRjJGJ0YnRic=

The nicest expression is for 1/3+St factor(1/3+pa1[2])

KjApSSJ2RzYiIiIjIiIiLCZGJEYnRichIiJGJywmKiZGJkYnRiRGJ0YnRidGJ0YnLCZGJEYnRidGJ0YnKSwoKiRGI0YnRicqJiIiJUYnRiRGJ0YnRidGJ0YmRicsKComRiZGJylGJCIiJEYnRidGMEYpRidGKUYpLDYqJkYxRicpRiQiIilGJ0YpKiZGOUYnKUYkIiIoRidGKSooRjFGJylJI1AwR0YlRiZGJylGJEYxRidGJyomIiM2RicpRiQiIidGJ0YpKihGMUYnRj5GJ0Y0RidGJyomIiM5RidGQEYnRicqKEYxRidGPkYnRiRGJ0YpKiZGOUYnRjRGJ0YnKiRGPkYnRilGL0YnRik=

collect(op(2,denom(pa1[1])),P0,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqKkYpRicsJiomRjJGJ0YpRidGJ0YnRidGJ0YkRidGMUYnRicqLClGKUYyRicsJkYpRidGJ0YvRicsJkYpRidGJ0YnRicsKCokRjdGJ0YnRilGJ0YnRidGJylGNEYyRidGJw==

collect(numer(pa1[1]),P0,factor)

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

Not much better. Better for zt, not for St. We keep pa1 pa2:=factor(subs(alpha[1]=0,P0=(1+2*v)*P0/(v^4 + 8*v^3 + 6*v^2 + 2*v + 1),[ztP0,StP0]));

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

pa1

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv pazt:=pa1:

The expression of zt was the following paztbis :=subs(P1=P,(P1^3*v^8 + P1^3*v^7 + 4*P1^2*v^8 + 5*P1^3*v^6 + 4*P1^2*v^7 + 4*P1*v^8 + 7*P1^3*v^5 + 14*P1^2*v^6 + 4*P1*v^7 + 5*P1^3*v^4 + 19*P1^2*v^5 + 12*P1*v^6 - 5*P1^3*v^3 + 7*P1^2*v^4 + 16*P1*v^5 + 8*v^6 - 11*P1^3*v^2 - 22*P1^2*v^3 + 7*P1*v^4 + 12*v^5 - 3*P1^3*v - 32*P1^2*v^2 - 12*P1*v^3 + 4*v^4 - 11*P1^2*v - 11*P1*v^2 - 8*v^3 - P1^2 - 2*P1*v - 6*v^2 - v)/((v^4 + 8*v^3 + 6*v^2 + 2*v + 1)*P1*(P1^2*v^4 + P1^2*v^3 + 4*P1*v^4 + 4*P1*v^3 + 4*v^4 - P1^2*v + 4*v^3 - P1^2 - 4*P1*v - P1 - 4*v - 1)));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShwYXp0YmlzR0YoKipJIlBHRighIiIsam4qJilGLyIiJCIiIilJInZHRigiIilGNUY1KiZGM0Y1KUY3IiIoRjVGNSooIiIlRjUpRi8iIiNGNUY2RjVGNSooIiImRjVGM0Y1KUY3IiInRjVGNSooRj1GNUY+RjVGOkY1RjUqKEY9RjVGL0Y1RjZGNUY1KihGO0Y1RjNGNSlGN0ZBRjVGNSooIiM5RjVGPkY1RkJGNUY1KihGPUY1Ri9GNUY6RjVGNSooRkFGNUYzRjUpRjdGPUY1RjUqKCIjPkY1Rj5GNUZHRjVGNSooIiM3RjVGL0Y1RkJGNUY1KihGQUY1RjNGNSlGN0Y0RjVGMCooRjtGNUY+RjVGTEY1RjUqKCIjO0Y1Ri9GNUZHRjVGNSomRjhGNUZCRjVGNSooIiM2RjVGM0Y1KUY3Rj9GNUYwKigiI0FGNUY+RjVGUkY1RjAqKEY7RjVGL0Y1RkxGNUY1KiZGUEY1RkdGNUY1KihGNEY1RjNGNUY3RjVGMCooIiNLRjVGPkY1RllGNUYwKihGUEY1Ri9GNUZSRjVGMComRj1GNUZMRjVGNSooRlhGNUY+RjVGN0Y1RjAqKEZYRjVGL0Y1RllGNUYwKiZGOEY1RlJGNUYwKiRGPkY1RjAqKEY/RjVGL0Y1RjdGNUYwKiZGQ0Y1RllGNUYwRjdGMEY1LDoqJkY+RjVGTEY1RjUqJkY+RjVGUkY1RjUqKEY9RjVGL0Y1RkxGNUY1KihGPUY1Ri9GNUZSRjVGNUZcb0Y1KiZGPkY1RjdGNUYwKiZGPUY1RlJGNUY1RmBvRjAqKEY9RjVGL0Y1RjdGNUYwRi9GMComRj1GNUY3RjVGMEY1RjBGMCwsKiRGTEY1RjVGX29GNUZib0Y1KiZGP0Y1RjdGNUY1RjVGNUYwNyNGLg==

collect(solve(op(2,numer(factor(paztbis-pa1[1]))),P0),alpha[1],factor)

KigsJiomIiIjIiIiSSJ2RzYiRiZGJkYmRiZGJkYnRiZJIlBHRighIiI=

collect(numer(paztbis),P,factor)

LCoqLEkidkc2IiIiIiwmRiRGJkYmISIiRiYsJkYkRiZGJkYmRiYsLiokKUYkIiImRiZGJiokKUYkIiIlRiZGJiomIiInRiYpRiQiIiRGJkYmKiYiIilGJilGJCIiI0YmRiYqJiIjNkYmRiRGJkYmRjRGJkYmKUkiUEdGJUY0RiZGJiomLDQqJkYwRiYpRiRGNkYmRiYqJkYwRiYpRiQiIihGJkYmKiYiIzlGJilGJEYyRiZGJiomIiM+RiZGLEYmRiYqJkZDRiZGL0YmRiYqJiIjQUYmRjNGJkYoKiYiI0tGJkY3RiZGKEY5RihGJkYoRiYpRjxGOEYmRiYqKkYkRiYsKCokRjNGJkYmKiZGNEYmRiRGJkYmRjhGJkYmLCoqJkYwRiZGL0YmRiYqJkYwRiZGM0YmRiYqJkYwRiZGJEYmRihGJkYoRiZGPEYmRiYqKEYkRiYsJiomRjhGJkYkRiZGJkYmRiZGJkZTRiZGJg==

The correct series P0 zx

LCYqJkkidEc2IiIiIiwoSSJ4R0YlRiYqJEYoISIiRiZGJkYmRiZGJiomLCZGJEYmRiZGJkYmRidGKkYm

with(gfun): n:=6: eq:=convert(factor(series(subs(v=vser(n),numer(zx/(1-2*t)-pazt[1])),t,n)),polynom): P0serens:=map(allvalues,algeqtoseries(eq,t,P0,4));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlQMHNlcmVuc0dGKDclKy1JInRHRigqJiwoKiQpSSJ4R0YoIiIjIiIiRjdGNUY3RjdGNyEiIkY1RjciIiEsJComLChGM0Y3KiYiIiVGN0Y1RjdGOEY3RjdGN0YyRjhGOEY3LCQqKCwsKiQpRjVGPkY3RjcqJiIiJ0Y3KUY1IiIkRjdGNyomIiM8RjdGNEY3RjgqJkZFRjdGNUY3RjdGN0Y3RjdGNUY4RjJGOEY4RjYsJCooLDAqJClGNUZFRjdGNyomIiImRjcpRjVGUUY3RjcqJiIjSkY3RkNGN0Y3KiYiJCsiRjdGRkY3RjgqJkZURjdGNEY3RjcqJkZRRjdGNUY3RjdGN0Y3RjdGNEY4RjJGOEY4RkctSSJPR0YlNiNGN0Y+Ky1GMCokRjVGOEY3KiYsJkYzRjdGPkY3RjdGNUY4RjYqJiwqRkJGNyomRj5GN0ZGRjdGN0YzRjgqJiIjP0Y3RjVGN0Y3RjdGNEY4RkcqJiwsKiZGNkY3Rk9GN0Y3KiYiIihGN0ZSRjdGNyomIiNHRjdGQ0Y3RjcqJkZjb0Y3RkZGN0Y4KiYiJDkiRjdGNEY3RjdGN0ZGRjhGPkZZRlErLUYwRjVGNyomLCYqJkY+RjdGNEY3RjdGN0Y3RjdGNUY4RjYqJiwqKiZGXm9GN0ZGRjdGN0YzRjhGPUY3RjdGN0Y3RjRGOEZHKiYsLComRmhvRjdGQ0Y3RjdGZm9GOComRmVvRjdGNEY3RjcqJkZjb0Y3RjVGN0Y3RjZGN0Y3RkZGOEY+RllGUTcjRi4=

factor(series(subs(v=vser(n),P0=P0serens[1],pazt[2]),t,4)); factor(series(subs(v=vser(n),P0=P0serens[2],pazt[2]),t,4)); factor(series(subs(v=vser(n),P0=P0serens[3],pazt[2]),t,4))

KytJInRHNiIjISIiIiIkIiIhLCQqJiksKCokKUkieEdGJCIiIyIiIkYxRi9GMUYxRjFGMEYxRi5GJkYmRjAsJCoqRjBGMUYrRjEpRi9GJ0YmLCZGLUYxRjFGMUYxRiZGJy1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YxIiIl

KydJInRHNiIsJCoqIyIiIiIiJEYoLCYqJiIiI0YoKUkieEdGJEYsRihGKEYoRihGKCwmRi5GKEYoISIiRjAsJkYuRihGKEYoRjBGKCIiIS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRiw=

KydJInRHNiIsJCoqIyIiIiIiJEYoLCYqJClJInhHRiQiIiNGKEYoRi5GKEYoLCZGLUYoRighIiJGMCwmRi1GKEYoRihGMEYwIiIhLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRihGLg==

The true value is the second factor(series(subs(S(x)=Sex(n),R0=R0ex(n),StS),t,4))

KytJInRHNiIsJCoqIyIiIiIiJEYoLCYqJiIiI0YoKUkieEdGJEYsRihGKEYoRihGKCwmRi5GKEYoISIiRjAsJkYuRihGKEYoRjBGKCIiISoqRi1GKCwoKiRGLUYoRigqJkYsRihGLkYoRihGLEYoRihGL0YwRjFGMEYsLCQqKkYsRihGLUYoLChGNUYoRi5GKEYsRihGKEYvRjBGKEYpLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRigiIiU=

P0serens[2]

Ky1JInRHNiIqJEkieEdGJCEiIiIiIiomLCYqJClGJiIiI0YoRigiIiVGKEYoRiZGJ0YtKiYsKiokKUYmRi5GKEYoKiZGLkYoKUYmIiIkRihGKEYrRicqJiIjP0YoRiZGKEYoRihGLEYnRjUqJiwsKiZGLUYoKUYmIiInRihGKComIiIoRigpRiYiIiZGKEYoKiYiI0dGKEYyRihGKComRj5GKEY0RihGJyomIiQ5IkYoRixGKEYoRihGNEYnRi4tSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKEZA

with(gfun): n:=16: eq:=convert(factor(series(subs(v=vser(n),numer(zx/(1-2*t)-pazt[1])),t,n)),polynom): P0serens:=map(allvalues,algeqtoseries(eq,t,P0,12)): P0paramser:=%[2];

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

Here is what we obtained: The first expression below is zt, and the second is St pazt:=[(4*v^12+8*P0*v^10+8*v^11+4*P0^2*v^8+12*P0*v^9+25*v^10+4*P0^2*v^7+32*P0*v^8+49*v^9+12*P0^2*v^6+52*P0*v^7+53*v^8+4*P0^3*v^4+16*P0^2*v^5+33*P0*v^6+7*v^7+4*P0^3*v^3+7*P0^2*v^4-37*P0*v^5-59*v^6-12*P0^2*v^3-86*P0*v^4-61*v^5-4*P0^3*v-11*P0^2*v^2-54*P0*v^3-23*v^4-P0^3-2*P0^2*v-13*P0*v^2-3*v^3-P0*v)/((v^4+8*v^3+6*v^2+2*v+1)*(4*v^8+8*P0*v^6+8*v^7+4*P0^2*v^4+12*P0*v^5+5*v^6+4*P0^2*v^3+4*P0*v^4-3*v^5-8*P0*v^3-8*v^4-4*P0^2*v-6*P0*v^2-5*v^3-P0^2-P0*v-v^2)), -(-8*v^11-16*v^10+8*P0^2*v^7-12*v^9+8*P0^2*v^6-15*v^8-16*P0^2*v^5-46*v^7-28*P0^2*v^4-24*v^6-6*P0^2*v^3+48*v^5+16*P0^2*v^2+53*v^4+8*P0^2*v+18*v^3+P0^2+2*v^2)/((3*(2*v^3-4*v-1))*(-4*v^8-8*v^7+4*P0^2*v^4-11*v^6+4*P0^2*v^3+14*v^4-4*P0^2*v+8*v^3-P0^2+v^2))];

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

Let us check factor(subs(zt=pazt[1],St=pazt[2], algStvzt))

IiIh

A nice expression is for 1/3+St SdztP0:=factor(1/3+pazt[2])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdTZHp0UDBHRigqMClJInZHRigiIiMiIiIsJkYwRjJGMiEiIkYyLCYqJkYxRjJGMEYyRjJGMkYyRjIsJkYwRjJGMkYyRjIpLCgqJEYvRjJGMiomIiIlRjJGMEYyRjJGMkYyRjFGMiwoKiZGMUYyKUYwIiIkRjJGMkY7RjRGMkY0RjQsNiomRjxGMilGMCIiKUYyRjQqJkZERjIpRjAiIihGMkY0KihGPEYyKUkjUDBHRihGMUYyKUYwRjxGMkYyKiYiIzZGMilGMCIiJ0YyRjQqKEY8RjJGSUYyRj9GMkYyKiYiIzlGMkZLRjJGMiooRjxGMkZJRjJGMEYyRjQqJkZERjJGP0YyRjIqJEZJRjJGNEY6RjJGNDcjRi4=

The right choice for P0(x) P0paramser := t/x+(x^2+4)*t^2/x+(x^4+4*x^3-x^2+20*x)*t^3/x^2+(2*x^6+7*x^5+28*x^4-7*x^3+114*x^2)*t^4/x^3+(4*x^8+16*x^7+52*x^6+160*x^5-56*x^4+697*x^3)*t^5/x^4+(9*x^10+41*x^9+143*x^8+356*x^7+1058*x^6-397*x^5+4472*x^4)*t^6/x^5+(21*x^12+108*x^11+402*x^10+1066*x^9+2471*x^8+6823*x^7-2894*x^6+29644*x^5)*t^7/x^6+(51*x^14+294*x^13+1182*x^12+3371*x^11+8105*x^10+17108*x^9+46157*x^8-20773*x^7+201416*x^6)*t^8/x^7+(127*x^16+812*x^15+3513*x^14+10828*x^13+27447*x^12+59395*x^11+119536*x^10+314143*x^9-150623*x^8+1394371*x^7)*t^9/x^8+(323*x^18+2272*x^17+10552*x^16+35064*x^15+94814*x^14+215320*x^13+437370*x^12+840764*x^11+2183471*x^10-1093420*x^9+9798590*x^8)*t^10/x^9+(835*x^20+6412*x^19+31843*x^18+113556*x^17+327438*x^16+789555*x^15+1666134*x^14+3197244*x^13+5959785*x^12+15324589*x^11-7986035*x^10+69694888*x^9)*t^11/x^10+(2188*x^22+18223*x^21+96428*x^20+367415*x^19+1127541*x^18+2889558*x^17+6429524*x^16+12738556*x^15+23437113*x^14+42540465*x^13+108862718*x^12-58554217*x^11+500728130*x^10)*t^12/x^11+O(t^13): An alternative gives a slightly simpler expression for zt (at least at the denominator) factor(subs(P0=(1+2*v)*v/Q0, pazt[1]))

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

n:=10:factor(series(subs(v=vser(n), P0=P0paramser,S(x)=Sex(n),R0=R0ex(n), pazt[2]-StS),t,n));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

Let us check the values given in the paper for this parametrization. Sdpap:=-v^2*(v^2-1)*(2*v+1)*(v^2+4*v+1)^2/(2*v^3-4*v-1)/(w^2*P0^2+v^2*(v^2-1)*(2*v+1)*(2*v^3+3*v^2+6*v+1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZTZHBhcEdGKCwkKi4pSSJ2R0YoIiIjIiIiLCYqJEYwRjNGM0YzISIiRjMsJiomRjJGM0YxRjNGM0YzRjNGMyksKEY1RjMqJiIiJUYzRjFGM0YzRjNGM0YyRjMsKComRjJGMylGMSIiJEYzRjNGO0Y2RjNGNkY2LCYqJilJIndHRihGMkYzKUkjUDBHRihGMkYzRjMqKkYwRjNGNEYzRjdGMywqRj5GMyomRkBGM0YwRjNGMyomIiInRjNGMUYzRjNGM0YzRjNGM0Y2RjY3I0Yu

numer(factor(Sdpap-SdztP0)); rem(%,algwv,w)

LCQqMClJInZHNiIiIiMiIiIsJiomRidGKEYlRihGKEYoRihGKCksKCokRiRGKEYoKiYiIiVGKEYlRihGKEYoRihGJ0YoKUkjUDBHRiZGJ0YoLCZGJUYoRighIiJGKCwmRiVGKEYoRihGKCwsKiZGL0YoKUYlRi9GKEYoKiZGL0YoKUYlIiIkRihGKCokKUkid0dGJkYnRihGKEYuRjNGKEYzRihGMw==

IiIh

ztpa:=num/den/(v^4+8*v^3+6*v^2+2*v+1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV6dHBhR0YoKihJJG51bUdGKCIiIkkkZGVuR0YoISIiLCwqJClJInZHRigiIiVGMEYwKiYiIilGMClGNiIiJEYwRjAqJiIiJ0YwKUY2IiIjRjBGMComRj9GMEY2RjBGMEYwRjBGMjcjRi4=

num:=w^2*P0^3+v*w^2*P0^2*(v^3+3*v+2)-v*(2*v+1)*P0*(4*v^8+4*v^7+14*v^6+19*v^5+7*v^4-22*v^3-32*v^2-11*v-1)-v^3*(v^2-1)*(v^5+v^4+6*v^3+8*v^2+11*v+3)*(2*v+1)^2; den:=w^2*P0^2+v*w^2*(2*v+1)*P0-v^2*(v^2-1)*(1+v+v^2)*(2*v+1)^2

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRudW1HRigsKiomKUkid0dGKCIiIyIiIilJI1AwR0YoIiIkRjNGMyoqSSJ2R0YoRjNGMEYzKUY1RjJGMywoKiQpRjhGNkYzRjMqJkY2RjNGOEYzRjNGMkYzRjNGMyoqRjhGMywmKiZGMkYzRjhGM0YzRjNGM0YzRjVGMyw0KiYiIiVGMylGOCIiKUYzRjMqJkZDRjMpRjgiIihGM0YzKiYiIzlGMylGOCIiJ0YzRjMqJiIjPkYzKUY4IiImRjNGMyomRkhGMylGOEZDRjNGMyomIiNBRjNGPEYzISIiKiYiI0tGMylGOEYyRjNGVSomIiM2RjNGOEYzRlVGM0ZVRjNGVSoqRjxGMywmKiRGWEYzRjNGM0ZVRjMsLiokRk9GM0YzKiRGUkYzRjMqJkZMRjNGPEYzRjMqJkZFRjNGWEYzRjNGWUYzRjZGM0YzKUY/RjJGM0ZVNyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZW5HRigsKComKUkid0dGKCIiIyIiIilJI1AwR0YoRjJGM0YzKipJInZHRihGM0YwRjMsJiomRjJGM0Y3RjNGM0YzRjNGM0Y1RjNGMyoqKUY3RjJGMywmKiRGO0YzRjNGMyEiIkYzLChGPUYzRjdGM0YzRjNGMylGOEYyRjNGPjcjRi4=

numer(factor(ztpa-pazt[1])); rem(%,algwv,w)

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

IiIh

What is the equation of P0 over Q(t,x)? res:=numer(factor(pazt[1]-zx/(1-2*t))): res1:=factor(resultant(res,algv,v)): nops(%)

IiIk

map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyU8IjwjSSJ0RzYiPCVJI1AwR0YmRiVJInhHRiY=

res2:=op(3,res1): nops(%)

IiY5SCU=

algP0tx:=collect(res2,P0,factor): degree(%,P0)

IiNP

We observe that zt can be written in terms of yt and v, without using t yty:=y*t/(1-2*t)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR5dHlHRigqKEkieUdGKCIiIkkidEdGKEYwLCZGMEYwKiYiIiNGMEYxRjAhIiJGNTcjRi4=

The first term in zt is yt, and the second is... subs(isolate(yty-yt,y),(t+1)/y/(1-2*t))

KiosJkkidEc2IiIiIkYmRiZGJkkjeXRHRiUhIiJGJEYmKSwmRiZGJiomIiIjRiZGJEYmRihGLEYo

This can be rewritten in terms of v Rat:=factor(evala(Normal(subs(t=troot,%*yt))))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSYXRHRigqLEkidkdGKCIiIiwoKiQpRi8iIiNGMEYwRi9GMEYwRjBGMCksKCokKUYvIiIkRjBGMComRjlGMEYvRjAhIiJGMEY7RjlGMCwqKiYiIiVGMClGL0Y+RjBGMComRj5GMEY4RjBGMComRj5GMEYvRjBGO0YwRjtGOyksLCokRj9GMEYwKiYiIilGMEY4RjBGMComIiInRjBGM0YwRjAqJkY0RjBGL0YwRjBGMEYwRjRGOzcjRi4=

ztyt:=yt+Rat/yt

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV6dHl0R0YoLCZJI3l0R0YoIiIiKi5JInZHRihGMCwoKiQpRjIiIiNGMEYwRjJGMEYwRjBGMCksKCokKUYyIiIkRjBGMComRjtGMEYyRjAhIiJGMEY9RjtGMCwqKiYiIiVGMClGMkZARjBGMComRkBGMEY6RjBGMComRkBGMEYyRjBGPUYwRj1GPSksLCokRkFGMEYwKiYiIilGMEY6RjBGMComIiInRjBGNUYwRjAqJkY2RjBGMkYwRjBGMEYwRjZGPUYvRj1GMDcjRi4=

Now we would like to parametrize the equation in yt, which does not involve t algP0yt:=numer(factor(ztyt-pazt[1])): genus(algP0yt,yt,P0)

IiIh

The parametrization function of Maple works for a generic v res:=factor(parametrization(algP0yt,yt,P0,P1)): denom(op(2,res))

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

solve(%,P1);

LCQqJkkidkc2IiIiIixCKiYiIztGJilGJCIjOkYmRiYqJiIkZyJGJilGJCIjOUYmRiYqJiIkPyRGJilGJCIjOEYmRiYqJiIkdyJGJilGJCIjN0YmISIiKiYiJSVRIkYmKUYkIiM2RiZGOComIiUleSJGJilGJCIjNUYmRjgqJiIkJ0hGJilGJCIiKkYmRjgqJiIlazlGJilGJCIiKUYmRiYqJiIlcDpGJilGJCIiKEYmRiYqJiIkKVtGJilGJCIiJ0YmRiYqJiIkYCNGJilGJCIiJkYmRjgqJiIkTiRGJilGJCIiJUYmRjgqJiIkJD5GJilGJCIiJEYmRjgqJiIjb0YmKUYkIiIjRiZGOComRjNGJkYkRiZGOEYmRjhGJkY4

res1:=factor(subs(P1=%+P1,res)): collect(op(2,res1),P1,factor)

LCgqKCwsKiQpSSJ2RzYiIiIlIiIiRioqJiIiKUYqKUYnIiIkRipGKiomIiInRiopRiciIiNGKkYqKiZGMkYqRidGKkYqRipGKiEiIiksKiomRilGKkYmRipGKiomRilGKkYtRipGKiomRilGKkYnRipGNEYqRjRGMkY0SSNQMUdGKEYqRioqKEYxRiosJkYnRipGKkY0RiosJkYnRipGKkYqRipGNCoyRi1GKiwoKiRGMUYqRipGJ0YqRipGKkYqLCgqJEYtRipGKiomRi5GKkYnRipGNEYqRjRGKkYkRipGNkYqKUY8RjJGKilGPUYyRipGOkY0Rio=

A better choice payt:=factor(subs(P1=P1*(v^2-1)*(v^4 + 8*v^3 + 6*v^2 + 2*v + 1)*(4*v^4 + 4*v^3 - 4*v - 1),res1))

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

collect(payt[2]/(v^2-1),P1,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRi9JI1AxR0YqRidGJyokKUYpIiIjRidGLyoqRixGJywoRjFGJ0YpRidGJ0YnRicsKCokRixGJ0YnKiZGLUYnRilGJ0YvRidGL0YnRjBGL0Yn

replacing P1 by Rat1/P1 leaves the expression of P0 unchanged... Rat1:=v^3*(v^2 + v + 1)*(v^3 - 3*v - 1)*(4*v^4 + 4*v^3 - 4*v - 1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVSYXQxR0YoKiopSSJ2R0YoIiIkIiIiLCgqJClGMCIiI0YyRjJGMEYyRjJGMkYyLCgqJEYvRjJGMiomRjFGMkYwRjIhIiJGMkY6RjIsKiomIiIlRjIpRjBGPUYyRjIqJkY9RjJGL0YyRjIqJkY9RjJGMEYyRjpGMkY6RjI3I0Yu

... and replaces yt by Rat/yt factor(payt[1]*subs(P1=Rat1/P1,payt[1]));

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKiomIiIlRiUpRiNGM0YlRiUqJkYzRiVGLUYlRiUqJkYzRiVGI0YlRjBGJUYwRjApLCwqJEY0RiVGJSomIiIpRiVGLUYlRiUqJiIiJ0YlRihGJUYlKiZGKUYlRiNGJUYlRiVGJUYpRjA=

Rat

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKiomIiIlRiUpRiNGM0YlRiUqJkYzRiVGLUYlRiUqJkYzRiVGI0YlRjBGJUYwRjApLCwqJEY0RiVGJSomIiIpRiVGLUYlRiUqJiIiJ0YlRihGJUYlKiZGKUYlRiNGJUYlRiVGJUYpRjA=

The expression of St factor(subs(P0=payt[2],pazt[2]))

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

The expression of Sd=1/3 + St is as before much nicer SdP1:=factor(subs(P0=payt[2],1/3+pazt[2]))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVTZFAxR0YoKjIpSSJ2R0YoIiIjIiIiKUkjUDFHRihGMUYyLCYqJkYxRjJGMEYyRjJGMkYyRjIsKiomIiIlRjIpRjBGOUYyRjIqJkY5RjIpRjAiIiRGMkYyKiZGOUYyRjBGMiEiIkYyRj9GMiksKCokRi9GMkYyRj5GMkYyRjJGMUYyLEoqJkY5RjIpRjAiIzhGMkYyKiZGOUYyKUYwIiM3RjJGMiomRklGMilGMCIjNkYyRj8qJiIjQ0YyKUYwIiM1RjJGPyomIiIqRjIpRjBGUkYyRj8qKEY5RjJGNEYyKUYwIiIoRjJGPyomRk5GMilGMCIiKUYyRjIqKEY5RjJGNEYyKUYwIiInRjJGPyomIiNGRjJGVUYyRjIqKEY5RjJGNEYyKUYwIiImRjJGMiomRmZuRjJGZW5GMkYyKihGWUYyRjRGMkY6RjJGMiomRklGMkZqbkYyRj8qJkY0RjJGPEYyRjIqJkZWRjJGOkYyRj8qJkYzRjJGMEYyRjIqKEY5RjJGNEYyRi9GMkY/KiRGPEYyRj8qJEYzRjJGMiomRjRGMkYwRjJGP0Y/LEpGREYyKiZGSUYyRkhGMkYyKiZGOUYyRktGMkYyKiYiI0tGMkZPRjJGPyomIiNsRjJGU0YyRj9GVEY/KiYiI11GMkZYRjJGP0ZaRj8qJEZVRjJGMkZpbkYyKiYiI01GMkZlbkYyRjJGXW9GMiomIiNHRjJGam5GMkYyRl9vRjIqJkZSRjJGOkYyRjJGYW9GMkZib0Y/RmNvRjJGZG9GP0Zlb0Y/Rj8sKComRjFGMkY8RjJGMkY+Rj9GMkY/Rj83I0Yu

collect(op(1,denom(%)),P1,factor)

LCgqJiwmSSJ2RzYiIiIiRidGJ0YnKUkjUDFHRiYiIiNGJ0YnKixGJUYnLCZGJUYnRichIiJGJ0YkRicsKiomIiIlRicpRiVGMEYnRicqJkYwRicpRiUiIiRGJ0YnKiZGMEYnRiVGJ0YtRidGLUYnRilGJ0YtKixGM0YnRixGJywoKiQpRiVGKkYnRidGJUYnRidGJ0YnLCgqJEYzRidGJyomRjRGJ0YlRidGLUYnRi1GJ0YuRidGJw==

collect(op(2,denom(%%)),P1,factor)

LCgqJiwmSSJ2RzYiIiIiRichIiJGJylJI1AxR0YmIiIjRidGJyosRiVGJ0YkRicsJkYlRidGJ0YnRicsKiomIiIlRicpRiVGMEYnRicqJkYwRicpRiUiIiRGJ0YnKiZGMEYnRiVGJ0YoRidGKEYnRipGJ0YoKixGM0YnRi1GJywoKiQpRiVGK0YnRidGJUYnRidGJ0YnLCgqJEYzRidGJyomRjRGJ0YlRidGKEYnRihGJ0YuRidGJw==

Choice of P1 n:=10:series(subs(v=vser(n), numer(y*t/(1-2*t)-payt[1])),t,n+1): map(allvalues,algeqtoseries(convert(%,polynom),t,P1,6)): P1serens:=map(factor,map(simplify,subs(y=x+1/x+1,%),symbolic))

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

factor(series(subs(v=vser(n), P1=P1serens[1], SdP1),t)); factor(series(subs(v=vser(n), P1=P1serens[2], SdP1),t,9)); factor(series(subs(v=vser(n), P1=P1serens[3],SdP1),t,9))

Ky1JInRHNiIsJComKUkieEdGJCIiIyEiIiksKCokRiciIiJGLkYoRi5GLkYuRilGLkYqRiksJCoqRilGLiwmRi1GLkYuRi5GLkYrRi4pRigiIiRGKkYqRjMsJCooLCwqJiIiJ0YuKUYoIiIlRi5GLiomRjhGLkYyRi5GLiomIiM8Ri5GJ0YuRi4qJkY4Ri5GKEYuRi5GOEYuRi5GK0YuRjlGKkYqRjosJCoqRilGLiwwKiYiIilGLilGKEY4Ri5GLiomIiM3Ri4pRigiIiZGLkYuKiYiI0xGLkY5Ri5GLiomIiNGRi5GMkYuRi4qJkZKRi5GJ0YuRi4qJkZGRi5GKEYuRi5GQ0YuRi5GK0YuRkdGKkYqRkgtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGLkY4

KylJInRHNiIqKClJInhHRiQiIiMiIiIsJkYnRilGKSEiIkYrLCZGJ0YpRilGKUYrIiIhKiosKCokRiZGKUYpKiZGKEYpRidGKUYpRihGKUYpRiZGKUYqRitGLEYrRigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKSIiJA==

KylJInRHNiIsJComLCZJInhHRiQiIiJGKSEiIkYqLCZGKEYpRilGKUYqRioiIiEsJCoqKUYoIiIjRiosKComRjBGKUYvRilGKSomRjBGKUYoRilGKUYpRilGKUYnRipGK0YqRipGMC1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpIiIk

factor(series(subs(S(x)=Sex(n),R0=R0ex(n),StS+1/3),t,4))

KytJInRHNiIqKClJInhHRiQiIiMiIiIsJkYnRilGKSEiIkYrLCZGJ0YpRilGKUYrIiIhKiosKCokRiZGKUYpKiZGKEYpRidGKUYpRihGKUYpRiZGKUYqRitGLEYrRigsJCoqRihGKSwoRjBGKUYnRilGKEYpRilGJkYpRipGK0YpIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIiU=

So the second choice is the correct one P1serens[2]

KzFJInRHNiJJInhHRiQiIiMqJkYlIiIiLCZGJUYoIiIqRihGKCIiJComRiVGKCwoKiZGJkYoKUYlRiZGKEYoKiYiIzdGKEYlRihGKCIjbkYoRigiIiUqJkYlRigsKiomRjNGKClGJUYrRihGKComIiNFRihGL0YoRigqJiIkMiJGKEYlRihGKCIkeCVGKEYoIiImKiZGJUYoLCwqJkYqRigpRiVGM0YoRigqJiIjaEYoRjdGKEYoKiYiJGojRihGL0YoRigqJiIkbClGKEYlRihGKCIld0xGKEYoIiInKiZGJUYoLC4qJiIjQEYoKUYlRj1GKEYoKiYiJGAiRihGQUYoRigqJiIkKW9GKEY3RihGKComIiVEQkYoRi9GKEYoKiYiJSxuRihGJUYoRigiJk1SI0YoRigiIigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiKQ==

Here, the first expression is yt, and the second is P0 payt:=[v*(4*v^12 + 8*v^11 + 4*v^10 - 8*v^9 - 13*v^8 - 4*P1*v^6 - 5*v^7 - 4*P1*v^5 + 4*v^6 + 5*v^5 + 4*P1*v^3 + v^4 + P1*v^2 + P1^2)*(v^2 + v + 1)*(v^3 - 3*v - 1)^3/((v^4 + 8*v^3 + 6*v^2 + 2*v + 1)*(4*v^14 + 8*v^13 - 16*v^12 - 56*v^11 - 33*v^10 - 4*P1*v^8 + 75*v^9 - 4*P1*v^7 + 153*v^8 + 12*P1*v^6 + 96*v^7 + 20*P1*v^5 - 21*v^6 + 5*P1*v^4 - 73*v^5 + P1^2*v^2 - 12*P1*v^3 - 44*v^4 - 7*P1*v^2 - 11*v^3 - P1^2 - P1*v - v^2)*P1), (v - 1)*(v + 1)*(4*v^12 + 8*v^11 - 4*v^10 - 28*v^9 - 37*v^8 - 4*P1*v^6 - 13*v^7 - 4*P1*v^5 + 14*v^6 + 20*v^5 + 4*P1*v^3 + 8*v^4 + P1*v^2 + v^3 + P1^2)/(P1*(4*v^4 + 4*v^3 - 4*v - 1))]

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

Let us check that the equation between zt and P0 indeed holds ztyt := yt+v*(v^2+v+1)*(v^3-3*v-1)^3/((4*v^4+4*v^3-4*v-1)*(v^4+8*v^3+6*v^2+2*v+1)^2*yt)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV6dHl0R0YoLCZJI3l0R0YoIiIiKi5JInZHRihGMCwoKiQpRjIiIiNGMEYwRjJGMEYwRjBGMCksKCokKUYyIiIkRjBGMComRjtGMEYyRjAhIiJGMEY9RjtGMCwqKiYiIiVGMClGMkZARjBGMComRkBGMEY6RjBGMComRkBGMEYyRjBGPUYwRj1GPSksLCokRkFGMEYwKiYiIilGMEY6RjBGMComIiInRjBGNUYwRjAqJkY2RjBGMkYwRjBGMEYwRjZGPUYvRj1GMDcjRi4=

factor(subs(yt=payt[1],P0=payt[2],ztyt-pazt[1]))

IiIh

The correct choice for P1 P1paramser:=x*t^2+x*(x+9)*t^3+x*(2*x^2+12*x+67)*t^4+x*(4*x^3+26*x^2+107*x+477)*t^5+x*(9*x^4+61*x^3+263*x^2+865*x+3376)*t^6+x*(21*x^5+153*x^4+688*x^3+2325*x^2+6701*x+23934)*t^7+O(t^8)

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

The expression of P0 in terms of P1 Rat:=v*(v^2+v+1)*(v^3-3*v-1)^3/((4*v^4+4*v^3-4*v-1)*(v^4+8*v^3+6*v^2+2*v+1)^2); Rat1:=v^3*(v^2 + v + 1)*(v^3 - 3*v - 1)*(4*v^4 + 4*v^3 - 4*v - 1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSYXRHRigqLEkidkdGKCIiIiwoKiQpRi8iIiNGMEYwRi9GMEYwRjBGMCksKCokKUYvIiIkRjBGMComRjlGMEYvRjAhIiJGMEY7RjlGMCwqKiYiIiVGMClGL0Y+RjBGMComRj5GMEY4RjBGMComRj5GMEYvRjBGO0YwRjtGOyksLCokRj9GMEYwKiYiIilGMEY4RjBGMComIiInRjBGM0YwRjAqJkY0RjBGL0YwRjBGMEYwRjRGOzcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVSYXQxR0YoKiopSSJ2R0YoIiIkIiIiLCgqJClGMCIiI0YyRjJGMEYyRjJGMkYyLCgqJEYvRjJGMiomRjFGMkYwRjIhIiJGMkY6RjIsKiomIiIlRjIpRjBGPUYyRjIqJkY9RjJGL0YyRjIqJkY9RjJGMEYyRjpGMkY6RjI3I0Yu

collect(payt[2]/(v^2-1)*(4*v^4+4*v^3-4*v-1),P1,factor);

LChJI1AxRzYiIiIiKiYpSSJ2R0YkIiIjRiUsKiomIiIlRiUpRihGLEYlRiUqJkYsRiUpRigiIiRGJUYlKiZGLEYlRihGJSEiIkYlRjJGJUYyKixGL0YlLCgqJEYnRiVGJUYoRiVGJUYlRiUsKCokRi9GJUYlKiZGMEYlRihGJUYyRiVGMkYlRipGJUYjRjJGJQ==

Paper version P0P1pap:=-(v^2-1)/w^2*(P1+v^2*w^2+Rat1/P1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShQMFAxcGFwR0YoLCQqKCwmKiQpSSJ2R0YoIiIjIiIiRjVGNSEiIkY1KUkid0dGKEY0RjYsKEkjUDFHRihGNSomRjJGNUY3RjVGNSosKUYzIiIkRjUsKEYxRjVGM0Y1RjVGNUY1LCgqJEY9RjVGNSomRj5GNUYzRjVGNkY1RjZGNSwqKiYiIiVGNSlGM0ZFRjVGNSomRkVGNUY9RjVGNSomRkVGNUYzRjVGNkY1RjZGNUY6RjZGNUY1RjY3I0Yu

numer(factor(P0P1pap-payt[2])):rem(%,algwv,w)

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The expression of 1/3+St SdytP1:=factor(subs(P0=payt[2],pazt[2]+1/3))

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

Paper version den:=(v+1)*P+v*w^2*(v^2-1)+(v-1)*Rat1/P

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZW5HRigsKComLCZJInZHRigiIiJGMkYyRjJJIlBHRihGMkYyKihGMUYyKUkid0dGKCIiI0YyLCYqJClGMUY3RjJGMkYyISIiRjJGMiouLCZGMUYyRjJGO0YyKUYxIiIkRjIsKEY5RjJGMUYyRjJGMkYyLCgqJEY+RjJGMiomRj9GMkYxRjJGO0YyRjtGMiwqKiYiIiVGMilGMUZGRjJGMiomRkZGMkY+RjJGMiomRkZGMkYxRjJGO0YyRjtGMkYzRjtGMjcjRi4=

Sdpap:=-v^2*w^2*(1+2*v)*(1+4*v+v^2)^2/(2*v^3-4*v-1)/subs(P=P1,den)/subs(P=Rat1/P1,den)

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

numer(factor(Sdpap-SdytP1)): factor(rem(%,algwv,w))

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The expression of yt in terms of P1 num:=P+v^2*w^2-v^4*w^2*(v^2-1)*(1+v+v^2)/P

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRudW1HRigsKEkiUEdGKCIiIiomKUkidkdGKCIiI0YwKUkid0dGKEY0RjBGMCosKUYzIiIlRjBGNUYwLCYqJEYyRjBGMEYwISIiRjAsKEY7RjBGM0YwRjBGMEYwRi9GPEY8NyNGLg==

ytpap:=(v^3-3*v-1)^2*(v^2+v+1)*v^2/(v^4+8*v^3+6*v^2+2*v+1)*subs(P=P1,num)/subs(P=Rat1/P1,num)/P1;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ5dHBhcEdGKCowKSwoKiQpSSJ2R0YoIiIkIiIiRjUqJkY0RjVGM0Y1ISIiRjVGNyIiI0Y1LCgqJClGM0Y4RjVGNUYzRjVGNUY1RjVGO0Y1LCwqJClGMyIiJUY1RjUqJiIiKUY1RjJGNUY1KiYiIidGNUY7RjVGNSomRjhGNUYzRjVGNUY1RjVGNywoSSNQMUdGKEY1KiZGO0Y1KUkid0dGKEY4RjVGNSosRj5GNUZIRjUsJkY6RjVGNUY3RjVGOUY1RkZGN0Y3RjUsKCosRjJGNUY5RjVGMEY1LCoqJkY/RjVGPkY1RjUqJkY/RjVGMkY1RjUqJkY/RjVGM0Y1RjdGNUY3RjVGRkY3RjVGR0Y1Ki5GM0Y1RkhGNUZLRjVGMEY3Rk5GN0ZGRjVGN0Y3RkZGNzcjRi4=

numer(factor(ytpap-payt[1])): rem(%,algwv,w)

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Some properties a simple tranformation of P1 replaces yt par Rat/yt factor(subs(P1=Rat1/P1,payt[1])*payt[1]); factor(%/Rat)

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKiomIiIlRiUpRiNGM0YlRiUqJkYzRiVGLUYlRiUqJkYzRiVGI0YlRjBGJUYwRjApLCwqJEY0RiVGJSomIiIpRiVGLUYlRiUqJiIiJ0YlRihGJUYlKiZGKUYlRiNGJUYlRiVGJUYpRjA=

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and leaves P0 unchanged factor(subs(P1=Rat1/P1,payt[2])-payt[2])

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What is the equation of P1 over Q(t,x)? res:=numer(factor(payt[1]-t*(x+1/x+1)/(1-2*t))): res1:=factor(resultant(res,algv,v)): nops(%)

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map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyY8IjwjSSJ0RzYiRiQ8JUkjUDFHRiZGJUkieEdGJg==

res2:=op(4,res1): nops(%)

IiZzJEg=

algP1tx:=collect(res2,P1,factor): degree(%,P1)

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The equation for P1 algP1vtx:=factor(numer((x+1/x+1)*t/(1-2*t)-payt[1])):degree(%,t);degree(%%,x)

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genus(algP1vtx,x,P1)

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If we tell maple how v and t are related genus(subs(t=tv,algP1vtx),x,P1)

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We try to parametrize using Maple, at leats to get an idea of the form res:=parametrization(subs(t=tv,algP1vtx),x,P1,P2): indets(res)

PCVJI1AyRzYiSSJ2R0YkKiQpKigsMiomIiIpIiIiKUYlIiIoRixGLComIiM3RiwpRiUiIidGLEYsKiYiIiVGLClGJSIiJkYsISIiKiYiIz9GLClGJUY0RixGNyomIiM1RiwpRiUiIiRGLEY3KiZGLkYsKUYlIiIjRixGLComRjJGLEYlRixGLEYsRixGLCksLCokRjpGLEYsKiZGK0YsRj1GLEYsKiZGMkYsRkBGLEYsKiZGQUYsRiVGLEYsRixGLEZBRiwpLCoqJkZBRixGPUYsRiwqJkY+RixGQEYsRixGQkYsRixGLEY+RiwjRixGQUYs

We rewrite the square root that occurs in terns of t sdelta:=isolate(factor(tv)-t,sqrt((v - 1)*(2*v + 1)*(v + 1)*(4*v^4 + 4*v^3 - 4*v - 1)*(v^4 + 8*v^3 + 6*v^2 + 2*v + 1)^2*(2*v^3 + 3*v^2 + 6*v + 1)^3))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdzZGVsdGFHRigvKiQpKi4sJkkidkdGKCIiIkY0ISIiRjQsJiomIiIjRjRGM0Y0RjRGNEY0RjQsJkYzRjRGNEY0RjQsKiomIiIlRjQpRjNGPEY0RjQqJkY8RjQpRjMiIiRGNEY0KiZGPEY0RjNGNEY1RjRGNUY0KSwsKiRGPUY0RjQqJiIiKUY0Rj9GNEY0KiYiIidGNClGM0Y4RjRGNEY3RjRGNEY0RjhGNCksKiomRjhGNEY/RjRGNComRkBGNEZJRjRGNComRkhGNEYzRjRGNEY0RjRGQEY0I0Y0RjhGNCw+KipGOEY0SSJ0R0YoRjQsKCokRklGNEY0RkFGNEY0RjRGNCksKEY+RjRGTUY0RjRGNUZARjRGNSomRkZGNClGMyIjN0Y0RjUqJiIjc0Y0KUYzIiM2RjRGNSomIiRPJEY0KUYzIiM1RjRGNSomIiRfJ0Y0KUYzIiIqRjRGNSomIiR2J0Y0KUYzRkZGNEY1KiYiJClHRjQpRjMiIihGNEY1KiYiJG8iRjQpRjNGSEY0RjQqJiIkSyVGNClGMyIiJkY0RjQqJiIkXSVGNEY9RjRGNComIiRbI0Y0Rj9GNEY0KiZGZW5GNEZJRjRGNComRllGNEYzRjRGNEY0RjQ3I0Yu

res:=factor(subs(sdelta,factor(res))): degree(denom(res[2]),P2)

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collect(op(1,denom(res[2])),P2,factor)

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

nops(numer(res[2])); map(indets,[seq(op(i,numer(res[2])),i=1..nops(numer(res[2])))])

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Nyk8IjwjSSJ2RzYiRiQ8JUkjUDJHRiZJInRHRiZGJUYkRiQ8I0Yo

collect(op(4,numer(res[2])),P2,factor); degree(%,P2)

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collect(op(7,numer(res[2])),P2,factor);degree(%,P2)

SSNQMkc2Ig==

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This form suggests to consider P1t=1/P1 instead of P1 From now on, we choose the following ansatz xsol2:=factor(1/P2*(1+alpha*P2+beta*P2^2)/subs(P2=1/P2,(1+alpha*P2+beta*P2^2)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZ4c29sMkdGKCooLCgqJilJI1AyR0YoIiIjIiIiSSViZXRhR0YoRjRGNComRjJGNEkmYWxwaGFHRihGNEY0RjRGNEY0RjJGNCwoKiRGMUY0RjRGNkY0RjVGNCEiIjcjRi4=

Replacing P2 by 1/P2 will replace x by 1/y (and leave y invariant) factor(xsol2*subs(P2=1/P2,xsol2))

IiIi

P1solP2:=1/a/(P2+1/P2+c);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShQMXNvbFAyR0YoKiZJImFHRighIiIsKEkjUDJHRigiIiIqJEYyRjBGM0kiY0dGKEYzRjA3I0Yu

eq:=numer(factor(subs(x=xsol2, P1=P1solP2, algP1vtx)))/P2: nops(eq)

IiUubQ==

degree(eq,P2)

IiM1

factor(eq/subs(P2=1/P2,eq))

KiQpSSNQMkc2IiIjNSIiIg==

We write this in terms of SUM=P2+1/P2 temp:=eq/P2^5: eqsum:=0: for i from 0 to 5 do co:=coeff(temp,P2,5-i): temp:=expand(temp-co*(P2+1/P2)^(5-i)): eqsum:=eqsum+co*(SUM)^(5-i): od: indets(eqsum)

PClJJFNVTUc2IkkiYUdGJEkmYWxwaGFHRiRJJWJldGFHRiRJImNHRiRJInRHRiRJInZHRiQ=

factor(subs(SUM=P2+1/P2,eqsum)/eq)

KiQpSSNQMkc2IiIiJiEiIg==

res:=eqsum: factor(coeff(res,SUM,5)); nops(%)

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

IiIp

asol:=factor(solve(op(8,%%),a))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhc29sR0YoLCQqNEklYmV0YUdGKCIiIkkidEdGKEYxLCwqJClJInZHRigiIiVGMUYxKiYiIilGMSlGNiIiJEYxRjEqJiIiJ0YxKUY2IiIjRjFGMSomRj9GMUY2RjFGMUYxRjFGMSwmRjZGMUYxISIiRkIsJkY2RjFGMUYxRkIsKCokRj5GMUYxRjZGMUYxRjFGQiwoKiRGOkYxRjEqJkY7RjFGNkYxRkJGMUZCRkIsJkYxRkIqJkY/RjFGMkYxRjFGQkY6RkJGQjcjRi4=

res1:=numer(factor(subs(a=asol,res))): nops(res1)

IiIk

map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyU8I0kidkc2IjwoSSRTVU1HRiVJJmFscGhhR0YlSSViZXRhR0YlSSJjR0YlSSJ0R0YlRiQ8I0Yr

res2:=op(2,res1):degree(res2,SUM)

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factor(coeff(res2,SUM,4));nops(%)

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

IiIm

factor(solve(op(5,%%),c))

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

csol:=%: We still have alpha and beta to determine. But 4 conditions on them.We are going to combine all of them, not to solve them one by one res3:=numer(factor(subs(c=csol,res2))): nops(res3)

IiVVQA==

degree(res3,SUM)

IiIk

co:=factor(coeff(res3,SUM,3)): nops(%)

IiIm

map(indets,[seq(op(i,co),i=1..nops(co))])

Nyc8IjwjSSViZXRhRzYiPCNJInRHRiY8I0kidkdGJjwmSSZhbHBoYUdGJkYlRihGKg==

op(2,co)

KiQpSSViZXRhRzYiIiIjIiIi

co3:=op(5,co):degree(co3,alpha);degree(co3,beta)

IiIj

IiIk

Now the coefficient of SUM^2 co:=factor(coeff(res3,SUM,2)): nops(%)

IiIj

map(indets,[seq(op(i,co),i=1..nops(co))])

NyQ8I0klYmV0YUc2IjwmSSZhbHBoYUdGJUYkSSJ0R0YlSSJ2R0Yl

op(1,co)

SSViZXRhRzYi

co2:=op(2,co):degree(co2,alpha);degree(co2,beta)

IiIk

IiIl

The third equation: coefficient of SUM co:=factor(coeff(res3,SUM,1)): nops(%);indets(%%)

IiRqKA==

PCZJJmFscGhhRzYiSSViZXRhR0YkSSJ0R0YkSSJ2R0Yk

co1:=co:degree(co1,alpha);degree(co1,beta)

IiIl

IiIm

Finally, the constant coefficient co:=factor(coeff(res3,SUM,0)): nops(%);indets(%%)

IiRtKQ==

PCZJJmFscGhhRzYiSSViZXRhR0YkSSJ0R0YkSSJ2R0Yk

co0:=co:degree(co0,alpha);degree(co0,beta)

IiIm

IiIm

coeq:=[co0,co1,co2,co3]: map(degree,coeq,alpha)

NyYiIiYiIiUiIiQiIiM=

We can lower the degrees in alpha by taking remainders We form an equation of degree 1 in alpha res2:=factor(rem(co2,co3,alpha)): nops(%); degree(%%,alpha)

IiRxIg==

IiIi

collect(res2,[alpha,beta],factor)

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

co2bis:=res2: We do the same with co1 and co3 res1:=factor(rem(co1,co3,alpha)): nops(%); degree(%%,alpha)

IiIo

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map(indets,[seq(op(i,res1),i=1..nops(res1))])

Nyk8IjwmSSZhbHBoYUc2IkklYmV0YUdGJkkidEdGJkkidkdGJjwjRilGKjwjRidGKzwjRig=

res1:=op(2,res1): nops(%)

IiUtNQ==

degree(res1,alpha);

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co1bis:=res1: We now eliminate alpha res:=numer(factor(resultant(res2,res1,alpha))): nops(%)

IiIk

op(1,res); op(2,res)

SSJ0RzYi

LCwqJClJInZHNiIiIiUiIiJGKComIiIpRigpRiUiIiRGKEYoKiYiIidGKClGJSIiI0YoRigqJkYwRihGJUYoRihGKEYo

nops(op(3,res)); indets(op(3,res));degree(op(3,res),beta)

IiUjeiI=

PCVJJWJldGFHNiJJInRHRiRJInZHRiQ=

IiM3

We use the defining equation of v to obtain the degree of beta over Q(t) res4:=numer(factor(resultant(op(3,res),algv,v))): nops(%)

IiIm

map(indets,[seq(op(i,res4),i=1..nops(res4))]); map(nops,[seq(op(i,res4),i=1..nops(res4))]); map(degree,[seq(op(i,res4),i=1..nops(res4))],beta)

Nyc8IjwjSSJ0RzYiRiQ8JEklYmV0YUdGJkYlRic=

NyciIiIiIiNGJCIjXSIlMGA=

NyciIiFGI0YjIiM3IiRLIg==

We look now over Q(v) res5:=numer(factor(resultant(op(3,res),algv,t))): nops(%)

IiIm

map(indets,[seq(op(i,res5),i=1..nops(res5))]); map(nops,[seq(op(i,res5),i=1..nops(res5))]); map(degree,[seq(op(i,res5),i=1..nops(res5))],beta);

Nyc8I0kidkc2IkYjRiM8JEklYmV0YUdGJUYkRiY=

NyciIiNGI0YjIiM7IiUmUSI=

NyciIiFGI0YjIiIjIiNB

We consider the small factor collect(op(4,res5),beta,factor)

LCgqJiksKCokKUkidkc2IiIiJCIiIkYrKiZGKkYrRihGKyEiIkYrRi0iIiNGKylJJWJldGFHRilGLkYrRisqJiwsKiZGLkYrKUYoIiInRitGLSomRi5GKylGKCIiJkYrRi0qJiIiKEYrKUYoRi5GK0YtKiZGNUYrRihGK0YtRitGLUYrRjBGK0YrKiZGO0YrKSwoKiRGO0YrRitGKEYrRitGK0YuRitGKw==

Does it factor over Q(t,v) ? subs(troot=t,numer(factor(op(4,res5),RootOf(algv,t))))

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

betasolens:=factor([solve(%,beta)])

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

did we find a solution? or two ? Recall that we wanted to cancel 4 coefficients, co0, ..., co3, We hd also replaced co2 and co1 by co2bis and co1bis res:=numer(subs(troot=t,evala(Factor(subs(t=troot,numer(factor(subs(beta=betasola,co2bis)))))))): nops(res)

IiIl

map(indets, [seq(op(i,res),i=1..nops(res))])

NyY8I0kidkc2IjwkSSJ0R0YlRiRGIzwlSSZhbHBoYUdGJUYnRiQ=

alphasol:=factor(solve(op(4,res),alpha))

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

Let us check if we have a solution, by getting back to eqsum asol;collect(csol,[alpha,beta],factor)

LCQqNEklYmV0YUc2IiIiIkkidEdGJUYmLCwqJClJInZHRiUiIiVGJkYmKiYiIilGJilGKyIiJEYmRiYqJiIiJ0YmKUYrIiIjRiZGJiomRjRGJkYrRiZGJkYmRiZGJiwmRitGJkYmISIiRjcsJkYrRiZGJkYmRjcsKCokRjNGJkYmRitGJkYmRiZGNywoKiRGL0YmRiYqJkYwRiZGK0YmRjdGJkY3RjcsJkYmRjcqJkY0RiZGJ0YmRiZGN0YvRjdGNw==

LCYqJiwmIiIiISIiKiRJJWJldGFHNiJGJkYlRiVJJmFscGhhR0YpRiVGJSoqLDAqJkkidEdGKUYlKUkidkdGKSIiJUYlRiUqKCIiKUYlRi5GJSlGMCIiJEYlRiUqKCIjNUYlRi5GJSlGMCIiI0YlRiUqKEYxRiVGLkYlRjBGJUYlKiZGOUYlRjhGJUYmRi5GJUYwRiZGJUYuRiYsLCokRi9GJUYlKiZGM0YlRjRGJUYlKiYiIidGJUY4RiVGJSomRjlGJUYwRiVGJUYlRiVGJkYoRiZGJQ==

The first value of betasolens does not work, as shown by the following three lines res:=numer(factor(subs(a=asol,c=csol, alpha=alphasol,beta=betasolens[1], eqsum))): nops(%)

IiIk

indets(res)

PCVJJFNVTUc2IkkidEdGJEkidkdGJA==

factor(rem(res,algv,t));

IiIh

IiIi

The other value does not work res:=numer(factor(subs(a=asol,c=csol, alpha=alphasol,beta=betasolens[2], eqsum))): nops(%)

IiUnZSU=

factor(rem(res,algv,t)): nops(%)

IiM2

betasol:=betasolens[1];

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

alphasol;

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

We had already determined asol; csol

LCQqNEklYmV0YUc2IiIiIkkidEdGJUYmLCwqJClJInZHRiUiIiVGJkYmKiYiIilGJilGKyIiJEYmRiYqJiIiJ0YmKUYrIiIjRiZGJiomRjRGJkYrRiZGJkYmRiZGJiwmRitGJkYmISIiRjcsJkYrRiZGJkYmRjcsKCokRjNGJkYmRitGJkYmRiZGNywoKiRGL0YmRiYqJkYwRiZGK0YmRjdGJkY3RjcsJkYmRjcqJkY0RiZGJ0YmRiZGN0YvRjdGNw==

LCQqKixEKipJJmFscGhhRzYiIiIiSSViZXRhR0YnRihJInRHRidGKClJInZHRiciIiVGKEYoKiwiIilGKEYmRihGKUYoRipGKClGLCIiJEYoRigqKEYmRihGKkYoRitGKCEiIiosIiInRihGJkYoRilGKEYqRigpRiwiIiNGKEYoKipGL0YoRiZGKEYqRihGMEYoRjMqJkYqRihGK0YoRjMqLEY3RihGJkYoRilGKEYqRihGLEYoRigqKkY1RihGJkYoRipGKEY2RihGMyooRi9GKEYqRihGMEYoRjMqKEYmRihGKUYoRipGKEYoKipGN0YoRiZGKEYqRihGLEYoRjMqKCIjNUYoRipGKEY2RihGMyomRiZGKEYqRihGMyooRi1GKEYqRihGLEYoRjMqJkY3RihGNkYoRihGKkYzRixGKEYoRilGM0YqRjMsLCokRitGKEYoKiZGL0YoRjBGKEYoKiZGNUYoRjZGKEYoKiZGN0YoRixGKEYoRihGKEYzRjM=

We can now express csol csolnew:=evala(Normal(subs(t=troot,factor(subs(alpha=alphasol,beta=betasol,csol)))))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShjc29sbmV3R0YoKiYsKCokKUkidkdGKCIiIyIiIkY0KiYiIiVGNEYyRjRGNEY0RjRGNCwoRjBGNEYyRjRGNEY0ISIiNyNGLg==

A simple identity between alpha and beta, obtained by eliminating t collect(op(3,numer(factor(resultant(alpha-alphasol,beta-betasol,t)))),[alpha,beta],factor)

LCgqJiwoKiQpSSJ2RzYiIiIjIiIiRipGJ0YqRipGKkYqSSZhbHBoYUdGKEYqRioqJiwoKiQpRiciIiRGKkYqKiZGMEYqRidGKiEiIkYqRjJGKkklYmV0YUdGKEYqRioqJkYnRipGJEYqRjI=

alphanew:=collect(solve(%,alpha),beta,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlhbHBoYW5ld0dGKCwmKigsKCokKUkidkdGKCIiJCIiIkY1KiZGNEY1RjNGNSEiIkY1RjdGNSwoKiQpRjMiIiNGNUY1RjNGNUY1RjVGN0klYmV0YUdGKEY1RjdGM0Y1NyNGLg==

beta*t is simpler than beta subs(troot=t,factor(evala(Normal(subs(beta=betasol,t=troot,beta*t)))))

KiosKCokKUkidkc2IiIiIyIiIkYpRiZGKUYpRilGKSw0KihGKEYpSSJ0R0YnRikpRiYiIiZGKUYpKigiIzpGKUYsRikpRiYiIiVGKUYpKigiIz9GKUYsRikpRiYiIiRGKUYpKiRGMUYpRikqKCIjO0YpRixGKUYlRilGKSooIiInRilGLEYpRiZGKUYpKiZGNkYpRiVGKSEiIkYsRilGJkY9RiksLEY3RikqJiIiKUYpRjVGKUYpKiZGO0YpRiVGKUYpKiZGKEYpRiZGKUYpRilGKUY9LCoqJkYoRilGNUYpRilGPEYpKiZGO0YpRiZGKUYpRilGKUY9

The correct series P2 with(gfun): n:=20: ser:=normal(series(subs(v=vser(n),numer(factor(subs(alpha=alphasol, beta=betasol,numer(xsol2-x))))),t,n+1)): P2serens:=factor(algeqtoseries(convert(ser,polynom),t,P2,6))

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

factor(series(subs(v=vser(n+1),factor(subs(P1=P1solP2,a=asol,beta=betasol,c=csolnew, P2=P2serens[1],SdytP1))),t,n)); factor(series(subs(v=vser(n+1),factor(subs(P1=P1solP2,a=asol,beta=betasol,c=csolnew,P2=P2serens[2],SdytP1))),t,5)); factor(series(subs(v=vser(n+1),factor(subs(P1=P1solP2,a=asol,beta=betasol,c=csolnew,P2=P2serens[3],SdytP1))),t,n))

KytJInRHNiIsJComLCZJInhHRiQiIiJGKSEiIkYqLCZGKEYpRilGKUYqRioiIiEsJCoqKUYoIiIjRiosKComRjBGKUYvRilGKSomRjBGKUYoRilGKUYpRilGKUYnRipGK0YqRipGMCwkKipGMEYpKUYoIiIkRiosKEYyRilGKEYpRilGKUYpRidGKkYqRjctSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKSIiJQ==

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiM=

Ky1JInRHNiIqKClJInhHRiQiIiMiIiIsJkYnRilGKSEiIkYrLCZGJ0YpRilGKUYrIiIhKiosKCokRiZGKUYpKiZGKEYpRidGKUYpRihGKUYpRiZGKUYqRitGLEYrRigsJCoqRihGKSwoRjBGKUYnRilGKEYpRilGJkYpRipGK0YpIiIkKiosLComIiInRikpRiciIiVGKUYpKiYiIz1GKSlGJ0Y1RilGKSomIiNURilGJkYpRikqJiIjX0YpRidGKUYpIiNTRilGKUYmRilGKkYrRixGK0Y7LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIiY=

The correct expansion of Sd factor(series(subs(S(x)=Sex(n),R0=R0ex(n),StS+1/3),t,4))

KytJInRHNiIqKClJInhHRiQiIiMiIiIsJkYnRilGKSEiIkYrLCZGJ0YpRilGKUYrIiIhKiosKCokRiZGKUYpKiZGKEYpRidGKUYpRihGKUYpRiZGKUYqRitGLEYrRigsJCoqRihGKSwoRjBGKUYnRilGKEYpRilGJkYpRipGK0YpIiIkLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRikiIiU=

P2paramser:=P2serens[2]

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

Back to Sd: its denominator, written in terms of P1, factors over Q(t,v) op(1,denom(SdytP1))

LEoqJiIiJSIiIilJInZHNiIiIzhGJUYlKiZGJEYlKUYnIiM3RiVGJSomRixGJSlGJyIjNkYlISIiKiYiI0NGJSlGJyIjNUYlRjAqJiIiKkYlKUYnRjZGJUYwKihGJEYlSSNQMUdGKEYlKUYnIiIoRiVGMComRjJGJSlGJyIiKUYlRiUqKEYkRiVGOUYlKUYnIiInRiVGMComIiNGRiVGOkYlRiUqKEYkRiVGOUYlKUYnIiImRiVGJSomRkFGJUZARiVGJSooRj5GJUY5RiUpRidGJEYlRiUqJkYsRiVGRUYlRjAqJkY5RiUpRiciIiRGJUYlKiZGO0YlRklGJUYwKiYpRjkiIiNGJUYnRiVGJSooRiRGJUY5RiUpRidGUUYlRjAqJEZMRiVGMCokRlBGJUYlKiZGOUYlRidGJUYw

numer(subs(troot=t,factor(subs(w^2=-(4*v^4+4*v^3-4*v-1),den),RootOf(algv,t))))

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

rootdenSdP1:=collect([solve(%,P1)],t,factor)

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

map(Z->collect(subs(troot=t,evala(Normal(subs(beta=betatimest/t,t=troot,Z*asol)))),t,factor),rootdenSdP1)

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

collect(subs(troot=t,map(Z->factor(evala(Normal(subs(t=troot,1/(1-betasol)*Z)))),rootdenSdP1)),t,factor)

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

Here is the form that we have obtained xsolP2:=(P2^2*beta+P2*alpha+1)*P2/(P2^2+P2*alpha+beta); P1solP2:=1/(a*(P2+1/P2+c))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSd4c29sUDJHRigqKCwoKiYpSSNQMkdGKCIiIyIiIkklYmV0YUdGKEY0RjQqJkYyRjRJJmFscGhhR0YoRjRGNEY0RjRGNEYyRjQsKCokRjFGNEY0RjZGNEY1RjQhIiI3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShQMXNvbFAyR0YoKiZJImFHRighIiIsKEkjUDJHRigiIiIqJEYyRjBGM0kiY0dGKEYzRjA3I0Yu

Here are the coefficients involved in P1solP2 asol:=-beta*t*(v^4+8*v^3+6*v^2+2*v+1)/((v-1)*(v+1)*(v^2+v+1)*(v^3-3*v-1)*(-1+2*t)*v^3); csolnew:=(v^2+4*v+1)/(v^2+v+1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhc29sR0YoLCQqNEklYmV0YUdGKCIiIkkidEdGKEYxLCwqJClJInZHRigiIiVGMUYxKiYiIilGMSlGNiIiJEYxRjEqJiIiJ0YxKUY2IiIjRjFGMSomRj9GMUY2RjFGMUYxRjFGMSwmRjZGMUYxISIiRkIsJkY2RjFGMUYxRkIsKCokRj5GMUYxRjZGMUYxRjFGQiwoKiRGOkYxRjEqJkY7RjFGNkYxRkJGMUZCRkIsJkYxRkIqJkY/RjFGMkYxRjFGQkY6RkJGQjcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShjc29sbmV3R0YoKiYsKCokKUkidkdGKCIiIyIiIkY0KiYiIiVGNEYyRjRGNEY0RjRGNCwoRjBGNEYyRjRGNEY0ISIiNyNGLg==

Here are the coefficients involved in xsolP2 betatimest:=(v^2+v+1)*(2*t*v^5+15*t*v^4+20*t*v^3+v^4+16*t*v^2+6*t*v-3*v^2+t-v)/((v^4+8*v^3+6*v^2+2*v+1)*(2*v^3+3*v^2+6*v+1)); alphanew:=-(v^3-3*v-1)*beta/(v^2+v+1)+v

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStiZXRhdGltZXN0R0YoKiosKCokKUkidkdGKCIiIyIiIkY0RjJGNEY0RjRGNCw0KihGM0Y0SSJ0R0YoRjQpRjIiIiZGNEY0KigiIzpGNEY3RjQpRjIiIiVGNEY0KigiIz9GNEY3RjQpRjIiIiRGNEY0KiRGPEY0RjQqKCIjO0Y0RjdGNEYxRjRGNCooIiInRjRGN0Y0RjJGNEY0KiZGQUY0RjFGNCEiIkY3RjRGMkZIRjQsLEZCRjQqJiIiKUY0RkBGNEY0KiZGRkY0RjFGNEY0KiZGM0Y0RjJGNEY0RjRGNEZILCoqJkYzRjRGQEY0RjRGR0Y0KiZGRkY0RjJGNEY0RjRGNEZINyNGLg==

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSlhbHBoYW5ld0dGKCwmKigsKCokKUkidkdGKCIiJCIiIkY1KiZGNEY1RjNGNSEiIkY1RjdGNSwoKiQpRjMiIiNGNUY1RjNGNUY1RjVGN0klYmV0YUdGKEY1RjdGM0Y1NyNGLg==

Let us check that the defining equation of P1 holds res:=numer(factor(subs(P1=P1solP2,x=xsolP2, a=asol,c=csolnew,alpha=alphanew,beta=betatimest/t,payt[1]-t*(x+1/x+1)/(1-2*t)))): nops(res);

IiIm

map(indets,[seq(op(i,res),i=1..nops(res))])

Nyc8IjwjSSJ2RzYiPCRJI1AyR0YmRiU8JEkidEdGJkYlPCVGKEYqRiU=

rem(op(4,res),algv,t)

IiIh

collect(op(2,betatimest),t,factor)

LCYqJiwuKiYiIiMiIiIpSSJ2RzYiIiImRidGJyomIiM6RicpRikiIiVGJ0YnKiYiIz9GJylGKSIiJEYnRicqJiIjO0YnKUYpRiZGJ0YnKiYiIidGJ0YpRidGJ0YnRidGJ0kidEdGKkYnRicqJiwoKiRGMkYnRicqJkYzRidGKUYnISIiRidGPkYnRilGJ0Yn

Algebraic equation of P2 over Q(t,x) numer(factor(subs(alpha=alphasol,beta=betatimest/t,x-xsolP2)))

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

res:=factor(resultant(%,algv,v)): nops(res)

IiIn

map(indets,[seq(op(i,res),i=1..nops(res))])

Nyg8IjwjSSJ0RzYiRiRGJEYkPCVJI1AyR0YmRiVJInhHRiY=

nops(op(6,res))

IiUzPg==

algP2tx:=collect(op(6,res),P2,factor): degree(%,P2)

IiNP

Correct value of P2 P2paramser := 1/x-(x-1)*(x+1)*t/x^2-(x-1)*(x+1)*(x^2+4*x+2)*t^2/x^3-(x-1)*(x+1)*(x^4+2*x^3+20*x^2+10*x+4)*t^3/x^4-(x-1)*(x+1)*(2*x^6+6*x^5+26*x^4+118*x^3+80*x^2+30*x+9)*t^4/x^5-(x-1)*(x+1)*(4*x^8+14*x^7+54*x^6+132*x^5+727*x^4+502*x^3+260*x^2+84*x+21)*t^5/x^6+O(t^6)

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

zx:=t*(x+1/x+1)+(t+1)/(x+1/x+1); StS:=((x+1/x+1)*S(x)-R0/t+2*x*(1/3)+1/(3*x))/(x-1/x)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN6eEdGKCwmKiZJInRHRigiIiIsKEkieEdGKEYxKiRGMyEiIkYxRjFGMUYxRjEqJiwmRjBGMUYxRjFGMUYyRjVGMTcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRTdFNHRigqJiwmSSJ4R0YoIiIiKiRGMCEiIkYzRjMsKiomLChGMEYxRjJGMUYxRjFGMS1JIlNHRig2I0YwRjFGMSomSSNSMEdGKEYxSSJ0R0YoRjNGMyomIyIiIyIiJEYxRjBGMUYxKiYjRjFGQEYxRjBGM0YxRjE3I0Yu

Here is what we obtained: The first expression below is zt, and the second is St pazt:=[(4*v^12+8*P0*v^10+8*v^11+4*P0^2*v^8+12*P0*v^9+25*v^10+4*P0^2*v^7+32*P0*v^8+49*v^9+12*P0^2*v^6+52*P0*v^7+53*v^8+4*P0^3*v^4+16*P0^2*v^5+33*P0*v^6+7*v^7+4*P0^3*v^3+7*P0^2*v^4-37*P0*v^5-59*v^6-12*P0^2*v^3-86*P0*v^4-61*v^5-4*P0^3*v-11*P0^2*v^2-54*P0*v^3-23*v^4-P0^3-2*P0^2*v-13*P0*v^2-3*v^3-P0*v)/((v^4+8*v^3+6*v^2+2*v+1)*(4*v^8+8*P0*v^6+8*v^7+4*P0^2*v^4+12*P0*v^5+5*v^6+4*P0^2*v^3+4*P0*v^4-3*v^5-8*P0*v^3-8*v^4-4*P0^2*v-6*P0*v^2-5*v^3-P0^2-P0*v-v^2)), -(-8*v^11-16*v^10+8*P0^2*v^7-12*v^9+8*P0^2*v^6-15*v^8-16*P0^2*v^5-46*v^7-28*P0^2*v^4-24*v^6-6*P0^2*v^3+48*v^5+16*P0^2*v^2+53*v^4+8*P0^2*v+18*v^3+P0^2+2*v^2)/((3*(2*v^3-4*v-1))*(-4*v^8-8*v^7+4*P0^2*v^4-11*v^6+4*P0^2*v^3+14*v^4-4*P0^2*v+8*v^3-P0^2+v^2))];

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

SdztP0:=v^2*(v - 1)*(2*v + 1)*(v + 1)*(v^2 + 4*v + 1)^2/((2*v^3 - 4*v - 1)*(-4*v^8 - 8*v^7 + 4*P0^2*v^4 - 11*v^6 + 4*P0^2*v^3 + 14*v^4 - 4*P0^2*v + 8*v^3 - P0^2 + v^2))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdTZHp0UDBHRigqMClJInZHRigiIiMiIiIsJkYwRjJGMiEiIkYyLCYqJkYxRjJGMEYyRjJGMkYyRjIsJkYwRjJGMkYyRjIpLCgqJEYvRjJGMiomIiIlRjJGMEYyRjJGMkYyRjFGMiwoKiZGMUYyKUYwIiIkRjJGMkY7RjRGMkY0RjQsNiomRjxGMilGMCIiKUYyRjQqJkZERjIpRjAiIihGMkY0KihGPEYyKUkjUDBHRihGMUYyKUYwRjxGMkYyKiYiIzZGMilGMCIiJ0YyRjQqKEY8RjJGSUYyRj9GMkYyKiYiIzlGMkZLRjJGMiooRjxGMkZJRjJGMEYyRjQqJkZERjJGP0YyRjIqJEZJRjJGNEY6RjJGNDcjRi4=

The series Sh and Rh eqRS := (S(x)-2*S(1/x)+x*R0/(t*(x^2+x+1))-1/(x^2+x+1))*sqrt(De)-(3*(x^2+x+1))*R(x)/x-3*R1+(t*x^4+2*t*x^3+2*t*x^2+2*t*x-x^2+t)*R0/(x*t*(x^2+x+1))-(t*x^2+t-x)/(x*(x^2+x+1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcVJTR0YoLCwqJiwqLUkiU0dGKDYjSSJ4R0YoIiIiKiYiIiNGNS1GMjYjKiRGNCEiIkY1RjsqKkY0RjVJI1IwR0YoRjVJInRHRihGOywoKiQpRjRGN0Y1RjVGNEY1RjVGNUY7RjUqJEY/RjtGO0Y1KUkjRGVHRigjRjVGN0Y1RjUqKiIiJEY1Rj9GNS1JIlJHRihGM0Y1RjRGO0Y7KiZGR0Y1SSNSMUdGKEY1RjsqLCwuKiZGPkY1KUY0IiIlRjVGNSooRjdGNUY+RjUpRjRGR0Y1RjUqKEY3RjVGPkY1RkFGNUY1KihGN0Y1Rj5GNUY0RjVGNUZARjtGPkY1RjVGPUY1RjRGO0Y+RjtGP0Y7RjUqKCwoKiZGPkY1RkFGNUY1Rj5GNUY0RjtGNUY0RjtGP0Y7Rjs3I0Yu

In terms of St collect(subs(isolate(St(x)-StS,S(x)),isolate(St(1/x)-subs(x=1/x,StS),S(1/x)), eqRS),[De,R,R1,R0],factor);

LCwqLCwmSSJ4RzYiIiIiRichIiJGJywmRiVGJ0YnRidGJywmLUkjU3RHRiY2I0YlRicqJiIiI0YnLUYsNiMqJEYlRihGJ0YnRicsKCokKUYlRi9GJ0YnRiVGJ0YnRidGKClJI0RlR0YmI0YnRi9GJ0YnKioiIiRGJ0YzRictSSJSR0YmRi1GJ0YlRihGKComRjpGJ0kjUjFHRiZGJ0YoKiwsLiomSSJ0R0YmRicpRiUiIiVGJ0YnKihGL0YnRkJGJylGJUY6RidGJyooRi9GJ0ZCRidGNUYnRicqKEYvRidGQkYnRiVGJ0YnRjRGKEZCRidGJ0kjUjBHRiZGJ0YlRihGQkYoRjNGKEYnKigsKComRkJGJ0Y1RidGJ0ZCRidGJUYoRidGJUYoRjNGKEYo

RhR:=-subs(De=0,eqRS);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSaFJHRigsKioqIiIkIiIiLCgqJClJInhHRigiIiNGMUYxRjVGMUYxRjFGMS1JIlJHRig2I0Y1RjFGNSEiIkYxKiZGMEYxSSNSMUdGKEYxRjEqLCwuKiZJInRHRihGMSlGNSIiJUYxRjEqKEY2RjFGQEYxKUY1RjBGMUYxKihGNkYxRkBGMUY0RjFGMSooRjZGMUZARjFGNUYxRjFGM0Y6RkBGMUYxSSNSMEdGKEYxRjVGOkZARjpGMkY6RjoqKCwoKiZGQEYxRjRGMUYxRkBGMUY1RjpGMUY1RjpGMkY6RjE3I0Yu

The monic equation satisfied by St with coefficients in Q(zt,v) POL:=collect(algStvzt/lcoeff(algStvzt,St),St,factor): coeff(%,St,2); indets(POL)

IiIh

PCVJI1N0RzYiSSJ2R0YkSSN6dEdGJA==

A property of the roots of a cubic depressed equation eq:=s^3+p*s+q; factor(discrim(eq,s))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNlcUdGKCwoKiQpSSJzR0YoIiIkIiIiRjMqJkkicEdGKEYzRjFGM0YzSSJxR0YoRjM3I0Yu

LCYqJiIiJSIiIilJInBHNiIiIiRGJSEiIiomIiNGRiUpSSJxR0YoIiIjRiVGKg==

el1:=s1+s2+s3; el2:=s1*s2+s1*s3+s2*s3; el3:=s1*s2*s3; sqd:=(s1-s2)*(s1-s3)*(s2-s3)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlbDFHRigsKEkjczFHRigiIiJJI3MyR0YoRjBJI3MzR0YoRjA3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlbDJHRigsKComSSNzMUdGKCIiIkkjczJHRihGMUYxKiZGMEYxSSNzM0dGKEYxRjEqJkYyRjFGNEYxRjE3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlbDNHRigqKEkjczFHRigiIiJJI3MyR0YoRjBJI3MzR0YoRjA3I0Yu

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzcWRHRigqKCwmSSNzMUdGKCIiIkkjczJHRighIiJGMSwmRjBGMUkjczNHRihGM0YxLCZGMkYxRjVGM0YxNyNGLg==

A symmetric function in s2 and s3 collect((s2-s3)*sqd,s3,factor)

LCoqJiwmSSNzMUc2IiEiIkkjczJHRiYiIiJGKSlJI3MzR0YmIiIkRilGKSooLCZGJUYpRihGJ0YpLCYqJiIiI0YpRihGKUYpRiVGKUYpKUYrRjFGKUYpKipGKEYpRi5GKSwmRihGKSomRjFGKUYlRilGKUYpRitGKUYnKigpRihGMUYpRi5GKUYlRilGKQ==

We want to write this in terms of s1 and the elementary symmtric functions of the s_i expand((s2-s3)*sqd- ( el3/s1*el1^2-s1*el1^3-4*el3^2/s1^2 +2*el3*el1+4*s1^2*el1^2-7*s1*el3-5*s1^3*el1+2*s1^4));

IiIh

collect(eq-(s-s1)*(s-s2)*(s-s3),s,factor)

LCoqJiwoSSNzMUc2IiIiIkkjczJHRiZGJ0kjczNHRiZGJ0YnKUkic0dGJiIiI0YnRicqJiwqKiZGJUYnRihGJyEiIiomRiVGJ0YpRidGMComRihGJ0YpRidGMEkicEdGJkYnRidGK0YnRicqKEYlRidGKEYnRilGJ0YnSSJxR0YmRic=

( -4*(-q)^2/s1^2-7*s1*(-q)+2*s1^4)

LCgqKCIiJSIiIilJInFHNiIiIiNGJSlJI3MxR0YoRikhIiJGLCooIiIoRiVGK0YlRidGJUYlKiZGKUYlKUYrRiRGJUYl

expand(subs(s1=s,%)+4*q/s^2*eq)

LCgqKCIjNiIiIkkic0c2IkYlSSJxR0YnRiVGJSomIiIjRiUpRiYiIiVGJUYlKipGLEYlRihGJUYmISIiSSJwR0YnRiVGJQ==

expand(%-4*p/s*eq)

LCoqJiIiIyIiIilJInNHNiIiIiVGJUYlKihGKUYlSSJwR0YoRiUpRidGJEYlISIiKiZGKUYlKUYrRiRGJUYtKigiIzZGJUkicUdGKEYlRidGJUYl

Here is an expression for sqrt(delta)*(s2-s3), where s=s1 exprsddiff:=rem(%,eq,s)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStleHByc2RkaWZmR0YoLCgqKCIiJyIiIkkicEdGKEYxKUkic0dGKCIiI0YxISIiKiYiIiVGMSlGMkY1RjFGNiooIiIqRjFJInFHRihGMUY0RjFGMTcjRi4=

let us check sqd*(s2-s3)-subs(s=s1,exprsddiff); factor(resultant(%,subs(s=s2,eq),s2)) ; factor(resultant(%,subs(s=s3,eq),s3)); factor(resultant(%,subs(s=s1,eq),s1))

LCoqKCksJkkjczJHNiIiIiJJI3MzR0YnISIiIiIjRigsJkkjczFHRidGKEYmRipGKCwmRi1GKEYpRipGKEYoKigiIidGKEkicEdGJ0YoKUYtRitGKEYoKiYiIiVGKClGMUYrRihGKCooIiIqRihGLUYoSSJxR0YnRihGKg==

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

KigpLCgqKCIiJyIiIkkicEc2IkYnKUkjczFHRikiIiNGJ0YnKiYiIiVGJylGKEYsRidGJyooIiIqRidJInFHRilGJ0YrRichIiIiIiRGJyksKCokKUYrRjRGJ0YnKiZGKEYnRitGJ0YnRjJGJ0YsRicpLDAqKCIjXUYnKUYoRjRGJ0Y4RidGJyooIiNLRicpRihGLkYnRitGJ0YnKioiJFYjRidGL0YnRjJGJ0YqRidGMyooIiNGRicpRjJGLEYnRjhGJ0YzKigiJDciRidGPkYnRjJGJ0YzKioiJDsjRidGKEYnRkZGJ0YrRidGJyomRkVGJylGMkY0RidGM0YsRic=

IiIh

Now we compute the discriminant of POL disc:=factor(discrim(POL,St))

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

We want to form the part of disc that is not a square -- and the part that IS a square.We recognize below the first term: up to a sign, this is w^2 numdisc:=numer(disc); nops(%)

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

IiIo

op(6,numdisc)

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

Let us factor this over Q(t,v) factor(subs(zt=ztyt,op(6,numdisc)))

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

disc1:=factor(disc/op(6,numdisc)*%)

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

In the denominator there is one term that is not a square denomdisc:=denom(disc1);

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

sfdisc:=op(1,op(2,denomdisc))

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

Let us factor this as well sfdiscyt:=factor(subs(zt=ztyt,%))

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

Now consider the other discriminant, since we want to form the ratio Delta/disc Delta

LCYqJCksJiIiIkYmKiZJInRHNiJGJiwmSSJ4R0YpRiYqJEYrISIiRiZGJkYtIiIjRiZGJiooIiIlRiYpRihGLkYmKSwoRitGJkYsRiZGJkYmRi5GJkYt

In terms of y and then yt Deltay:=(1-t*(y-1))^2-4*t^2*y^2; Deltayt:=collect(subs(y=(1-2*t)*yt/t,Deltay),yt,factor); factor(%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdEZWx0YXlHRigsJiokKSwmIiIiRjIqJkkidEdGKEYyLCZJInlHRihGMkYyISIiRjJGNyIiI0YyRjIqKCIiJUYyKUY0RjhGMilGNkY4RjJGNzcjRi4=

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShEZWx0YXl0R0YoLCgqKCIiJCIiIiksJkYxISIiKiYiIiNGMUkidEdGKEYxRjFGNkYxKUkjeXRHRihGNkYxRjQqKkY2RjEsJkY3RjFGMUYxRjFGM0YxRjlGMUYxKiQpRjtGNkYxRjE3I0Yu

LCQqJiwqKigiIiciIiJJInRHNiJGJ0kjeXRHRilGJ0YnRihGJyomIiIkRidGKkYnISIiRidGJ0YnLCoqKCIiI0YnRihGJ0YqRidGJ0YoRi1GKkYtRidGLUYnRi0=

ytrootDelta:=[solve(Deltayt,yt)]

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSx5dHJvb3REZWx0YUdGKDckLCQqKCMiIiIiIiRGMiwmSSJ0R0YoRjJGMkYyRjIsJkYyISIiKiYiIiNGMkY1RjJGMkY3RjcqJkY0RjJGNkY3NyNGLg==

We expect to find these roots also in the bigger discriminant, and indeed factor(rem(numer(factor(subs(yt=-(t+1)/(3*(2*t-1)),sfdiscyt))),algv,t))

IiIh

factor(rem(numer(factor(subs(yt=(t+1)/(2*t-1),sfdiscyt))),algv,t))

IiIh

We thus want to factor sfdiscyt further, using t and v. We see indeed 4 linear factors (subs(troot=t,evala(Factor(numer(sfdiscyt),RootOf(algv,t)))))

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

factor(op(2,%))

KiYpLCoqJiIiJSIiIilJInZHNiJGJkYnRicqJkYmRicpRikiIiRGJ0YnKiZGJkYnRilGJyEiIkYnRi8iIiNGJyksLCokRihGJ0YnKiYiIilGJ0YsRidGJyomIiInRicpRilGMEYnRicqJkYwRidGKUYnRidGJ0YnRiZGJw==

rootsden:=solve(%%,yt)

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

What are really these roots? We expect to see functions of t only factor(resultant(numer(r1-rootsden[1]),algv,v))

LCQqKCI+bjUiW3cvWHRRPDQnUUlUIiIiIiksJkYlISIiKiYiIiNGJUkidEc2IkYlRiUiIzdGJSksKCooRipGJUkjcjFHRixGJUYrRiVGJUYxRigqJiIiJEYlRitGJUYlRi1GJUYo

r1sol:=op(1,[solve(%,r1)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyMXNvbEdGKCwkKigiIiQiIiJJInRHRihGMSwmRjEhIiIqJiIiI0YxRjJGMUYxRjRGNDcjRi4=

factor(resultant(numer(r2-rootsden[2]),algv,v))

LCQqKCJDWnZEZWZyWVIhW3N6XF5tJTR2IiIiKSwmRiUhIiIqJiIiI0YlSSJ0RzYiRiVGJSIjN0YlKSwoKihGKkYlSSNyMkdGLEYlRitGJUYlRjFGKEYrRihGLUYlRig=

r2sol:=op(1,[solve(%,r2)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyMnNvbEdGKComSSJ0R0YoIiIiLCZGMCEiIiomIiIjRjBGL0YwRjBGMjcjRi4=

factor(resultant(numer(r3-rootsden[3]),algv,v))

LCQqKCI+bjUiW3cvWHRRPDQnUUlUIiIiIiksJkYlISIiKiYiIiNGJUkidEc2IkYlRiUiIzdGJSksKiooIiInRiVJI3IzR0YsRiVGK0YlRiUqJiIiJEYlRjJGJUYoRitGJUYlRiVGLUYlRig=

r3sol:=op(1,[solve(%,r3)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyM3NvbEdGKCwkKigjIiIiIiIkRjEsJkkidEdGKEYxRjFGMUYxLCZGMSEiIiomIiIjRjFGNEYxRjFGNkY2NyNGLg==

factor(resultant(numer(r4-rootsden[4]),algv,v))

LCQqKCI+bjUiW3cvWHRRPDQnUUlUIiIiIiksJkYlISIiKiYiIiNGJUkidEc2IkYlRiUiIzdGJSksKiooRipGJUkjcjRHRixGJUYrRiVGJUYxRihGK0YoRiVGKEYtRiVGKA==

r4sol:=op(1,[solve(%,r4)])

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZyNHNvbEdGKComLCZJInRHRigiIiJGMUYxRjEsJkYxISIiKiYiIiNGMUYwRjFGMUYzNyNGLg==

factor(lcoeff(sfdiscyt,yt))

LCQqKCIiJCIiIiwqKiYiIiVGJSlJInZHNiJGKEYlRiUqJkYoRiUpRipGJEYlRiUqJkYoRiVGKkYlISIiRiVGL0YlKSwsKiRGKUYlRiUqJiIiKUYlRi1GJUYlKiYiIidGJSlGKiIiI0YlRiUqJkY4RiVGKkYlRiVGJUYlRjhGJUYl

We can thus rewrite the square free part of the discriminant as follows factor(lcoeff(sfdiscyt,yt))

LCQqKCIiJCIiIiwqKiYiIiVGJSlJInZHNiJGKEYlRiUqJkYoRiUpRipGJEYlRiUqJkYoRiVGKkYlISIiRiVGL0YlKSwsKiRGKUYlRiUqJiIiKUYlRi1GJUYlKiYiIidGJSlGKiIiI0YlRiUqJkY4RiVGKkYlRiVGJUYlRjhGJUYl

sfdisc1yt:=%*(yt-r1sol)*(yt-r2sol)*(yt-r3sol)*(yt-r4sol)/yt^2

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpzZmRpc2MxeXRHRigsJCoyIiIkIiIiLCoqJiIiJUYxKUkidkdGKEY0RjFGMSomRjRGMSlGNkYwRjFGMSomRjRGMUY2RjEhIiJGMUY6RjEpLCwqJEY1RjFGMSomIiIpRjFGOEYxRjEqJiIiJ0YxKUY2IiIjRjFGMSomRkNGMUY2RjFGMUYxRjFGQ0YxLCZJI3l0R0YoRjEqKEYwRjFJInRHRihGMSwmRjFGOiomRkNGMUZIRjFGMUY6RjFGMSwmRkZGMSomRkhGMUZJRjpGOkYxLCZGRkYxKigjRjFGMEYxLCZGSEYxRjFGMUYxRklGOkYxRjEsJkZGRjEqJkZQRjFGSUY6RjpGMSlGRkZDRjpGMTcjRi4=

Let us combine the two roots that do not come from Delta pro:=factor(subs(yt=t*y/(1-2*t),y=1+x+1/x,(yt-r1sol)*(yt-r2sol)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRwcm9HRigqLClJInRHRigiIiMiIiIpLCZJInhHRihGMkYyISIiRjFGMiksJkY1RjJGMkYyRjFGMilGNUYxRjYpLCZGMkY2KiZGMUYyRjBGMkYyRjFGNjcjRi4=

sfdisc2yt:=factor(sfdisc1yt/Deltayt/(yt-r1sol)/(yt-r2sol)*pro*DELTA)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpzZmRpc2MyeXRHRigsJCo0SSZERUxUQUdGKCIiIiksJkkieEdGKEYxRjFGMSIiI0YxKSwmRjRGMUYxISIiRjVGMSlJInRHRihGNUYxLCoqJiIiJUYxKUkidkdGKEY9RjFGMSomRj1GMSlGPyIiJEYxRjEqJkY9RjFGP0YxRjhGMUY4RjEpLCwqJEY+RjFGMSomIiIpRjFGQUYxRjEqJiIiJ0YxKUY/RjVGMUYxKiZGNUYxRj9GMUYxRjFGMUY1RjEpRjRGNUY4KUkjeXRHRihGNUY4KSwmRjFGOComRjVGMUY6RjFGMUY9RjhGODcjRi4=

Recall that sfdisc was cubed disc1;sfdisc;

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

discfinal:=factor(disc1*sfdisc^3/sfdisc2yt^3)

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

Let us check this n:=10: normal(series(subs(DELTA=Delta, zt=zx/(1-2*t),yt= (x+1/x+1)*t/(1-2*t), v=vser(n),discfinal-disc),t,n))

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIik=

The following ratio of discriminants is now a square in Q(t,x,w) (there is w because of the factor (1+4v-4v^3-4v^4) discratio:=factor(DELTA/discfinal/(-4*v^4-4*v^3+4*v+1)^3*w^6): sqdiscratio:=factor(simplify(sqrt(%),symbolic))

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

Can we still simplify some pieces? denom(sqdiscratio)

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

collect(op(6,denom(sqdiscratio)),yt,factor);

LCYqKCwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpLCwqJEYoRidGJyomIiIpRidGLEYnRicqJiIiJ0YnKUYpIiIjRidGJyomRjhGJ0YpRidGJ0YnRidGOEYnKUkjeXRHRipGOEYnRicqKEYpRicsKCokRjdGJ0YnRilGJ0YnRidGJyksKCokRixGJ0YnKiZGLUYnRilGJ0YvRidGL0YtRidGLw==

We recognize the factor Rat, which was in fact a fraction in t Rat; factor(evala(Normal(subs(t=troot,t*(1+t)/(1-2*t)^2))))

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKiomIiIlRiUpRiNGM0YlRiUqJkYzRiVGLUYlRiUqJkYzRiVGI0YlRjBGJUYwRjApLCwqJEY0RiVGJSomIiIpRiVGLUYlRiUqJiIiJ0YlRihGJUYlKiZGKUYlRiNGJUYlRiVGJUYpRjA=

KixJInZHNiIiIiIsKCokKUYjIiIjRiVGJUYjRiVGJUYlRiUpLCgqJClGIyIiJEYlRiUqJkYuRiVGI0YlISIiRiVGMEYuRiUsKiomIiIlRiUpRiNGM0YlRiUqJkYzRiVGLUYlRiUqJkYzRiVGI0YlRjBGJUYwRjApLCwqJEY0RiVGJSomIiIpRiVGLUYlRiUqJiIiJ0YlRihGJUYlKiZGKUYlRiNGJUYlRiVGJUYpRjA=

sqdiscratio1:=factor(rem(factor(simplify(factor(subs(yt=t*y/(1-2*t),sqdiscratio*op(6,denom(sqdiscratio))/coeff(op(6,denom(sqdiscratio)),yt,2)/(yt^2-t*(1+t)/(1-2*t)^2))))),algwv,w));

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

n:=10: factor(series(subs(zt=ztyt,yt=t*y/(1-2*t),y=1+x+1/x,w=wser(n), v=vser(n),sqdiscratio-sqdiscratio1),t,n+1));

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

We still need to adjust the sign n:=2: factor(series(subs(s3=-s1-s2,s1=StS,s2=subs(x=1/x,StS),S(x)=Sex(n),S(1/x)=subs(x=1/x,Sex(n)),R0=R0ex(n),sqrt(Delta)/(s1-s2)/(s1-s3)/(s2-s3)),t,n))

KylJInRHNiIsJCoqKSwmSSJ4R0YkIiIiRiohIiIiIiRGKiksJkYpRipGKkYqRixGKilGKSIiI0YrLCYqJEYvRipGKkYqRipGK0YrIiIhKigpRilGLEYrRidGKkYtRipGKi1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YqRjA=

n:=2: factor(series(subs(DELTA=Delta,zt=ztyt,yt=t*y/(1-2*t),y=1+x+1/x,w=wser(n), v=vser(n),sqdiscratio),t,n+1));

KylJInRHNiIqKiksJkkieEdGJCIiIkYpISIiIiIkRikpLCZGKEYpRilGKUYrRikpRigiIiNGKiwmKiRGLkYpRilGKUYpRioiIiEsJCooKUYoRitGKkYmRilGLEYpRipGKS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YpRi8=

sqdiscratio2:=-sqdiscratio1: Paper version drpap:=DELTA^2*(v^4+8*v^3+6*v^2+2*v+1)^2*(2*v^3-4*v-1)^3*(x-1/x)^3*w/y^2/(t*y^2-t-1)/(v^2+4*v+1)^2/(v^2-1)/(2*v+1)/(1-2*t)^2/P

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZkcnBhcEdGKCo6KUkmREVMVEFHRigiIiMiIiIpLCwqJClJInZHRigiIiVGMkYyKiYiIilGMilGNyIiJEYyRjIqJiIiJ0YyKUY3RjFGMkYyKiZGMUYyRjdGMkYyRjJGMkYxRjIpLCgqJkYxRjJGO0YyRjIqJkY4RjJGN0YyISIiRjJGRUY8RjIpLCZJInhHRihGMiokRkhGRUZFRjxGMkkid0dGKEYyKUkieUdGKEYxRkUsKComSSJ0R0YoRjJGS0YyRjJGT0ZFRjJGRUZFKSwoKiRGP0YyRjJGREYyRjJGMkYxRkUsJkZSRjJGMkZFRkUsJkZARjJGMkYyRkUpLCZGMkYyKiZGMUYyRk9GMkZFRjFGRUkiUEdGKEZFNyNGLg==

collect(solve(factor(1/drpap-1/sqdiscratio2),P),zt,factor)

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

Now we can reconstruct an expression for R-hat exprsddiff := -6*p*s^2-4*p^2+9*q*s

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SStleHByc2RkaWZmR0YoLCgqKCIiJyIiIkkicEdGKEYxKUkic0dGKCIiI0YxISIiKiYiIiVGMSlGMkY1RjFGNiooIiIqRjFJInFHRihGMUY0RjFGMTcjRi4=

Let us check the expression of Rhat n:=4: factor(series(subs(R(x)=Rex(n), R1=R1ex(n), R0=R0ex(n),RhR),t,n))

Ky1JInRHNiIsJCokLCgqJClJInhHRiQiIiMiIiJGLEYqRixGLEYsISIiRi0iIiEqKCwmRihGLEYsRixGLEYqRi1GJ0YtRiwqJiwsKiQpRioiIiVGLEYsKiZGK0YsKUYqIiIkRixGLComRjVGLEYpRixGLComRjVGLEYqRixGLEYrRixGLEYnRi1GKyooLDAqJClGKiIiJ0YsRiwqJkYrRiwpRioiIiZGLEYsKiZGQkYsRjRGLEYsKiZGP0YsRjdGLEYsKiYiIzVGLEYpRixGLEY6RixGK0YsRixGKkYtRidGLUY4LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRixGNQ==

res:=factor((x-1/x)/y*sqdiscratio2*subs(s=St,p=coeff(POL, St,1), q=coeff(POL, St,0),exprsddiff)): indets(%);

PCpJJkRFTFRBRzYiSSNTdEdGJEkidEdGJEkidkdGJEkid0dGJEkieEdGJEkieUdGJEkjenRHRiQ=

n:=5: factor(series(subs(St=StS, S(x)=Sex(n), R0=R0ex(n),DELTA=Delta, w=wser(n),zt=z/(1-2*t), z=zx, yt=y*t/(1-2*t),y=x+1/x+1,v=vser(n),res),t,4))

Ky1JInRHNiIsJCokLCgqJClJInhHRiQiIiMiIiJGLEYqRixGLEYsISIiRi0iIiEqKCwmRihGLEYsRixGLEYqRi1GJ0YtRiwqJiwsKiQpRioiIiVGLEYsKiZGK0YsKUYqIiIkRixGLComRjVGLEYpRixGLComRjVGLEYqRixGLEYrRixGLEYnRi1GKyooLDAqJClGKiIiJ0YsRiwqJkYrRiwpRioiIiZGLEYsKiZGQkYsRjRGLEYsKiZGP0YsRjdGLEYsKiYiIzVGLEYpRixGLEY6RixGK0YsRixGKkYtRidGLUY4LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRixGNQ==

exprRh:=res: denom(exprRh);

LCQqOiIiKiIiIiwoKiYiIiNGJSlJInZHNiIiIiRGJUYlKiYiIiVGJUYqRiUhIiJGJUYvRiUpLGpvKigiIzdGJSlGKkYzRiUpSSN6dEdGK0YoRiVGJSooIiIpRiVGNEYlRjZGJUYlKigiJC8jRiUpRioiIzZGJUY1RiVGJSomIiM/RiVGNEYlRi8qKCIkTyJGJUY7RiVGNkYlRiUqKCIlLzZGJSlGKiIjNUYlRjVGJUYlKiYiIyUpRiVGO0YlRi8qKCIkTyhGJUZDRiVGNkYlRiUqKCIlK0BGJSlGKkYkRiVGNUYlRiUqJiIkUyNGJUZDRiVGLyooIiUrOUYlRktGJUY2RiVGJSooIiVYPUYlKUYqRjhGJUY1RiVGJSomIiQzJkYlRktGJUYvKigiJUk3RiVGUkYlRjZGJUYlKigiJGckRiUpRioiIihGJUY1RiVGJSomIiRiKUYlRlJGJUYvKihGTUYlRllGJUY2RiVGJSooIiRjKEYlKUYqIiInRiVGNUYlRi8qJiIkI3pGJUZZRiVGLyooIiQvJkYlRmpuRiVGNkYlRi8qKCIkKypGJSlGKiIiJkYlRjVGJUYvKiZGRkYlRmpuRiVGLyooIiQrJ0YlRmJvRiVGNkYlRi8qKCIkSSdGJSlGKkYuRiVGNUYlRi8qJiIkRylGJUZib0YlRiUqKCIkPyVGJUZpb0YlRjZGJUYvKigiJCskRiVGKUYlRjVGJUYvKiYiJXE2RiVGaW9GJUYlKigiJCsjRiVGKUYlRjZGJUYvKigiIycqRiUpRipGKEYlRjVGJUYvKiYiJCNwRiVGKUYlRiUqKCIja0YlRmZwRiVGNkYlRi8qKCIjQ0YlRipGJUY1RiVGLyomIiQjPkYlRmZwRiVGJSooIiM7RiVGKkYlRjZGJUYvKiZGLEYlRjVGJUYvKiZGXHFGJUYqRiVGJSomRihGJUY2RiVGL0YlRiVGKEYlKSwmRiVGLyomRihGJUkidEdGK0YlRiVGKEYlLCZGKkYlRiVGL0YlLCYqJkYoRiVGKkYlRiVGJUYlRiUsJkYqRiVGJUYlRiUpLCgqJEZmcEYlRiVGLUYlRiVGJUYoRiUsaG8qKEYuRiVGNEYlRjVGJUYlRjdGLyooIiNvRiVGO0YlRjVGJUYlKiZGLkYlRjRGJUYlKigiI3NGJUY7RiVGNkYlRi8qKCIkbyRGJUZDRiVGNUYlRiUqJkYuRiVGO0YlRiUqKEZARiVGQ0YlRjZGJUYvKigiJCsoRiVGS0YlRjVGJUYlKiZGXHFGJUZDRiVGJSooIiQpR0YlRktGJUY2RiVGLyooIiQ6J0YlRlJGJUY1RiVGJSomIiNPRiVGS0YlRiUqKCIkUCVGJUZSRiVGNkYlRi8qKCIkPyJGJUZZRiVGNUYlRiUqJiIjWUYlRlJGJUYlKigiJD8kRiVGWUYlRjZGJUYvKigiJF8jRiVGam5GJUY1RiVGLyomIiNXRiVGWUYlRiUqKCIkSSJGJUZqbkYlRjZGJUYlKihGX3BGJUZib0YlRjVGJUYvKiZGREYlRmpuRiVGJSooIiRtJUYlRmJvRiVGNkYlRiUqKCIkNSNGJUZpb0YlRjVGJUYvKiYiI2VGJUZib0YlRi8qKCIkKVFGJUZpb0YlRjZGJUYlKigiJCsiRiVGKUYlRjVGJUYvKiYiJDkiRiVGaW9GJUYvKihGXnFGJUYpRiVGNkYlRiUqKCIjS0YlRmZwRiVGNUYlRi8qJiIjISlGJUYpRiVGLyooIiNxRiVGZnBGJUY2RiVGJSooRjhGJUYqRiVGNUYlRi8qJiIjQUYlRmZwRiVGLyooIiM5RiVGKkYlRjZGJUYlKiRGNUYlRi9GanFGL0Y2RiVGJSwoKiZGZ3FGJSlJInlHRitGKEYlRiVGZ3FGL0YlRi9GJSlJInhHRitGLkYlKUZfdkYsRiVGJQ==

sfdisc; sfdisc2yt

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

LCQqNEkmREVMVEFHNiIiIiIpLCZJInhHRiVGJkYmRiYiIiNGJiksJkYpRiZGJiEiIkYqRiYpSSJ0R0YlRipGJiwqKiYiIiVGJilJInZHRiVGMkYmRiYqJkYyRiYpRjQiIiRGJkYmKiZGMkYmRjRGJkYtRiZGLUYmKSwsKiRGM0YmRiYqJiIiKUYmRjZGJkYmKiYiIidGJilGNEYqRiZGJiomRipGJkY0RiZGJkYmRiZGKkYmKUYpRipGLSlJI3l0R0YlRipGLSksJkYmRi0qJkYqRiZGL0YmRiZGMkYtRi0=

exprRh1:=factor(exprRh*sfdisc^2/sfdisc2yt^2): In terms of P0 RhP0a:=factor(subs(zt=pazt[1],St=pazt[2],exprRh1))

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

RhP0b:=factor(subs(yt=y*t/(1-2*t),factor(RhP0a*op(2,isolate(algwv,w^2))/w^2)))

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

n:=4: factor(series(subs(R(x)=Rex(n), R1=R1ex(n), R0=R0ex(n),RhR),t,n))

Ky1JInRHNiIsJCokLCgqJClJInhHRiQiIiMiIiJGLEYqRixGLEYsISIiRi0iIiEqKCwmRihGLEYsRixGLEYqRi1GJ0YtRiwqJiwsKiQpRioiIiVGLEYsKiZGK0YsKUYqIiIkRixGLComRjVGLEYpRixGLComRjVGLEYqRixGLEYrRixGLEYnRi1GKyooLDAqJClGKiIiJ0YsRiwqJkYrRiwpRioiIiZGLEYsKiZGQkYsRjRGLEYsKiZGP0YsRjdGLEYsKiYiIzVGLEYpRixGLEY6RixGK0YsRixGKkYtRidGLUY4LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRixGNQ==

n:=4: factor(series(subs( y=x+1/x+1,v=vser(n),w=wser(n),P0=P0paramser,RhP0b),t,8))

Ky1JInRHNiIsJCokLCgqJClJInhHRiQiIiMiIiJGLEYqRixGLEYsISIiRi0iIiEqKCwmRihGLEYsRixGLEYqRi1GJ0YtRiwqJiwsKiQpRioiIiVGLEYsKiZGK0YsKUYqIiIkRixGLComRjVGLEYpRixGLComRjVGLEYqRixGLEYrRixGLEYnRi1GKyooLDAqJClGKiIiJ0YsRiwqJkYrRiwpRioiIiZGLEYsKiZGQkYsRjRGLEYsKiZGP0YsRjdGLEYsKiYiIzVGLEYpRixGLEY6RixGK0YsRixGKkYtRidGLUY4LUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRixGNQ==

Could we identify more factors in Rh? collect(op(3,numer(RhP0b)),P0,factor); collect(op(1,numer(RhP0b)),P0,factor); collect(op(2,numer(RhP0b)),P0,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqLkYyRicpRilGMkYnLCZGKUYnRidGL0YnLCZGKUYnRidGJ0YnRiRGJ0YxRidGJyoqRixGJywqKiYiIilGJ0YsRidGJyomIiM3RidGNEYnRicqJiIjOkYnRilGJ0YnRiZGJ0YnKUY1RjJGJylGNkYyRidGJw==

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqLEYyRidGKUYnLCYqJkYyRidGKUYnRidGJ0YnRidGJEYnRjFGJ0YnKihGKUYnLCwqJkYtRicpRikiIiZGJ0YnKiZGLUYnRihGJ0YnKiZGMkYnRixGJ0YnKiZGLUYnRilGJ0YnRidGJ0YnKUY0RjJGJ0Yn

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqJiksKCokKUYpRjJGJ0YnRi5GJ0YnRidGMkYnRjFGJ0YnKixGN0YnLCZGKUYnRidGL0YnLCYqJkYyRidGKUYnRidGJ0YnRicsJkYpRidGJ0YnRicsKiomRjJGJ0YsRidGJyomRi1GJ0Y3RidGJyomIiInRidGKUYnRidGJ0YnRidGLw==

collect(op(1,op(4,denom(RhP0b))),P0,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqKkYpRicsJiomRjJGJ0YpRidGJ0YnRidGJ0YkRidGMUYnRicqLClGKUYyRicsJkYpRidGJ0YvRicsJkYpRidGJ0YnRicsKCokRjdGJ0YnRilGJ0YnRidGJylGNEYyRidGJw==

collect(op(2,denom(pazt[1])),P0,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqKkYpRicsJiomRjJGJ0YpRidGJ0YnRidGJ0YkRidGMUYnRicqLClGKUYyRicsJkYpRidGJ0YvRicsJkYpRidGJ0YnRicsKCokRjdGJ0YnRilGJ0YnRidGJylGNEYyRidGJw==

factor(numer(pazt[1]))

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

We can have a factor (1-8t) rather than (1-2t)^2 using our favourite identity factor(evala(Normal(subs(t=troot,(1-8*t)/(1-2*t)^2))))

KiosKCokKUkidkc2IiIiIyIiIkYpKiYiIiVGKUYmRilGKUYpRilGKSksKComRitGKSlGJiIiJEYpRikqJkYwRilGJUYpRilGKSEiIkYwRiksKiomRitGKSlGJkYrRilGKUYuRilGKkYyRilGMkYyKSwsKiRGNUYpRikqJiIiKUYpRi9GKUYpKiYiIidGKUYlRilGKSomRihGKUYmRilGKUYpRilGKEYy

But it does not look much nicer RhP0c:=factor(simplify(factor(RhP0b*(1-8*t)/(1-2*t)^2/%)))/(4*v^4+4*v^3-4*v-1)*(-w^2)

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

RhP0b

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

collect(op(1,op(4,denom(RhP0b))),P0,factor)

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJ0YnKiZGJkYnKUYpIiIkRidGJyomRiZGJ0YpRichIiJGJ0YvRicpSSNQMEdGKiIiI0YnRicqKkYpRicsJiomRjJGJ0YpRidGJ0YnRidGJ0YkRidGMUYnRicqLClGKUYyRicsJkYpRidGJ0YvRicsJkYpRidGJ0YnRicsKCokRjdGJ0YnRilGJ0YnRidGJylGNEYyRidGJw==

factor(%/denom(pazt[1]))

KiQsLCokKUkidkc2IiIiJSIiIkYpKiYiIilGKSlGJiIiJEYpRikqJiIiJ0YpKUYmIiIjRilGKSomRjFGKUYmRilGKUYpRikhIiI=

paper version den:=subs(isolate(algwv,w^2),w^2*P0^2+v*w^2*(2*v+1)*P0-v^2*(v^2-1)*(v^2+v+1)*(2*v+1)^2)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZW5HRigsKComLCoqJiIiJSIiIilJInZHRihGMkYzISIiKiZGMkYzKUY1IiIkRjNGNiomRjJGM0Y1RjNGM0YzRjNGMylJI1AwR0YoIiIjRjNGMyoqRjVGM0YwRjMsJiomRj1GM0Y1RjNGM0YzRjNGM0Y8RjNGMyoqKUY1Rj1GMywmKiRGQkYzRjNGM0Y2RjMsKEZERjNGNUYzRjNGM0YzKUY/Rj1GM0Y2NyNGLg==

factor(denom(pazt[1])/den)

LCwqJClJInZHNiIiIiUiIiIhIiIqJiIiKUYoKUYlIiIkRihGKSomIiInRigpRiUiIiNGKEYpKiZGMUYoRiVGKEYpRihGKQ==

Rhpap:=y*(1-2*t)^2*(1+2*v)*N1*N2*N3/w/(t*y^2-t-1)/(2*v^3-4*v-1)/(v^4+8*v^3+6*v^2+2*v+1)^2/den^2

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

res:=factor(Rhpap/RhP0b)

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

collect(-op(1,denom(res)),P0,factor); collect(-op(2,denom(res)),P0,factor); collect(-op(3,denom(res)),P0,factor);

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJyEiIiomRiZGJylGKSIiJEYnRisqJkYmRidGKUYnRidGJ0YnRicpSSNQMEdGKiIiI0YnRicqLkYyRicpRilGMkYnLCZGKUYnRidGK0YnLCZGKUYnRidGJ0YnLCpGJUYnRixGJ0YvRitGJ0YrRidGMUYnRisqKkYtRicsKiomIiIpRidGLUYnRicqJiIjN0YnRjRGJ0YnKiYiIzpGJ0YpRidGJ0YmRidGJylGNUYyRicpRjZGMkYnRis=

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJyEiIiomRiZGJylGKSIiJEYnRisqJkYmRidGKUYnRidGJ0YnRicpSSNQMEdGKiIiI0YnRicqJiksKCokKUYpRjJGJ0YnRi9GJ0YnRidGMkYnRjFGJ0YrKixGN0YnLCZGKUYnRidGK0YnLCYqJkYyRidGKUYnRidGJ0YnRicsJkYpRidGJ0YnRicsKiomRjJGJ0YtRidGJyomRi5GJ0Y3RidGJyomIiInRidGKUYnRidGJ0YnRidGJw==

LCgqJiwqKiYiIiUiIiIpSSJ2RzYiRiZGJyEiIiomRiZGJylGKSIiJEYnRisqJkYmRidGKUYnRidGJ0YnRicpSSNQMEdGKiIiI0YnRicqLEYyRidGKUYnLCYqJkYyRidGKUYnRidGJ0YnRicsKkYlRidGLEYnRi9GK0YnRitGJ0YxRidGKyooRilGJywsKiZGLkYnKUYpIiImRidGJyomRi5GJ0YoRidGJyomRjJGJ0YtRidGJyomRi5GJ0YpRidGJ0YnRidGJylGNEYyRidGKw==

Let us try with P1. No fun factor(subs(P0=payt[2],RhP0b))

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

RhP0b:=(12*v^8 + 16*P0*v^6 + 24*v^7 + 4*P0^2*v^4 + 24*P0*v^5 + 23*v^6 + 4*P0^2*v^3 + 8*P0*v^4 + 11*v^5 - 16*P0*v^3 + 14*v^4 - 4*P0^2*v - 12*P0*v^2 + 16*v^3 - P0^2 - 2*P0*v + 7*v^2 + v)*(-4*v^8 - 8*v^7 + 4*P0^2*v^4 - 11*v^6 + 4*P0^2*v^3 + P0*v^4 + 8*P0*v^3 + 14*v^4 - 4*P0^2*v + 18*P0*v^2 + 8*v^3 - P0^2 + 8*P0*v + v^2 + P0)*(8*v^10 + 8*P0*v^8 + 12*v^9 + 8*P0*v^7 - v^8 - 8*P0*v^6 - 20*v^7 + 4*P0^2*v^4 - 16*P0*v^5 - 22*v^6 + 4*P0^2*v^3 - 2*P0*v^4 + 4*v^5 + 8*P0*v^3 + 15*v^4 - 4*P0^2*v + 2*P0*v^2 + 4*v^3 - P0^2)*(2*v + 1)*(-1 + 2*t)^2*y/(w*(t*y^2 - t - 1)*(v^4 + 8*v^3 + 6*v^2 + 2*v + 1)^2*(4*v^8 + 8*P0*v^6 + 8*v^7 + 4*P0^2*v^4 + 12*P0*v^5 + 5*v^6 + 4*P0^2*v^3 + 4*P0*v^4 - 3*v^5 - 8*P0*v^3 - 8*v^4 - 4*P0^2*v - 6*P0*v^2 - 5*v^3 - P0^2 - P0*v - v^2)^2*(2*v^3 - 4*v - 1));

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

pazt:=[(4*v^12+8*P0*v^10+8*v^11+4*P0^2*v^8+12*P0*v^9+25*v^10+4*P0^2*v^7+32*P0*v^8+49*v^9+12*P0^2*v^6+52*P0*v^7+53*v^8+4*P0^3*v^4+16*P0^2*v^5+33*P0*v^6+7*v^7+4*P0^3*v^3+7*P0^2*v^4-37*P0*v^5-59*v^6-12*P0^2*v^3-86*P0*v^4-61*v^5-4*P0^3*v-11*P0^2*v^2-54*P0*v^3-23*v^4-P0^3-2*P0^2*v-13*P0*v^2-3*v^3-P0*v)/((v^4+8*v^3+6*v^2+2*v+1)*(4*v^8+8*P0*v^6+8*v^7+4*P0^2*v^4+12*P0*v^5+5*v^6+4*P0^2*v^3+4*P0*v^4-3*v^5-8*P0*v^3-8*v^4-4*P0^2*v-6*P0*v^2-5*v^3-P0^2-P0*v-v^2)), -(-8*v^11-16*v^10+8*P0^2*v^7-12*v^9+8*P0^2*v^6-15*v^8-16*P0^2*v^5-46*v^7-28*P0^2*v^4-24*v^6-6*P0^2*v^3+48*v^5+16*P0^2*v^2+53*v^4+8*P0^2*v+18*v^3+P0^2+2*v^2)/((3*(2*v^3-4*v-1))*(-4*v^8-8*v^7+4*P0^2*v^4-11*v^6+4*P0^2*v^3+14*v^4-4*P0^2*v+8*v^3-P0^2+v^2))];

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

RhR;R0w;R1w; RhP0b

LCoqKiIiJCIiIiwoKiQpSSJ4RzYiIiIjRiVGJUYpRiVGJUYlRiUtSSJSR0YqNiNGKUYlRikhIiJGJSomRiRGJUkjUjFHRipGJUYlKiwsLiomSSJ0R0YqRiUpRikiIiVGJUYlKihGK0YlRjVGJSlGKUYkRiVGJSooRitGJUY1RiVGKEYlRiUqKEYrRiVGNUYlRilGJUYlRidGL0Y1RiVGJUkjUjBHRipGJUYpRi9GNUYvRiZGL0YvKigsKComRjVGJUYoRiVGJUY1RiVGKUYvRiVGKUYvRiZGL0Yl

LCQqKCMiIiIiIiNGJUkidEc2IkYlLCYqKEkid0dGKEYlLCYqJkYmRiVJInZHRihGJUYlRiVGJUYlLCgqJkYmRiUpRi4iIiRGJSEiIiomIiIlRiVGLkYlRiVGJUYlRjNGJUYlRjNGJUYl

LCgjIiIiIiInRiQqJiNGJCIiJEYkSSJ0RzYiRiRGJCowRiNGJCwmKiYiIiNGJEkidkdGKkYkRiRGJEYkRiQsJkYkRiQqJkYuRiRGKUYkISIiRiQsMComIiM7RiQpRi9GJUYkRiQqJiIjQ0YkKUYvIiImRiRGJComIiIoRiQpRi8iIiVGJEYkKiZGOEYkKUYvRihGJEYyKiYiI0lGJClGL0YuRiRGMiomIiM1RiRGL0YkRjJGJEYyRiRJIndHRipGMiwoKiZGLkYkRkBGJEYyKiZGPkYkRi9GJEYkRiRGJEYyLCwqJEY9RiRGJComIiIpRiRGQEYkRiQqJkYlRiRGQ0YkRiRGLUYkRiRGJEYyRiQ=

SSZSaFAwYkc2Ig==

We use the expression of Rh that we have just obtained res:=factor(resultant(subs(y=x+1+1/x,Rhx=RhR,R(x)=R,R0=R0w,R1=R1w,x=2,numer(RhP0b-Rhx)), numer(subs(x=2,zx/(1-2*t)-pazt[1])),P0)): nops(res)

IiM1

map(indets,[seq(op(i,res),i=1..nops(res))])

Nyw8IjwjSSJ2RzYiPCNJInRHRiZGJEYkRiRGJEYkRiQ8JkkiUkdGJkYoRiVJIndHRiY=

res1:=op(10,res): nops(%)

IiUtUA==

degree(res1,t);degree(res1,w);

IiIn

IiIn

res2:=factor(resultant(res1,algwv,w)):nops(%)

IiUnMyc=

indets(res2);degree(res,t)

PCVJIlJHNiJJInRHRiRJInZHRiQ=

IiM3

Before we go further let us reduce the degree in t res3:=factor(rem(res2,algv,t)):nops(%)

IiIn

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyg8IjwjSSJ2RzYiRiQ8JUkiUkdGJkkidEdGJkYlRiRGJA==

res4:=op(4,res3): nops(%);degree(res4,R)

IiVFQA==

IiIn

algRof2vt:=res4: res5:=factor(resultant(res4,algv,v)):nops(%)

IiIm

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Nyc8IjwjSSJ0RzYiRiRGJDwkSSJSR0YmRiU=

res6:=op(5,res5): nops(%)

IiVEYA==

degree(res6,R)

IiNz

n:=10:series(subs(R=Rex(n),x=2,v=vser(n),res6),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

algRof2:=res6:

We use the expression of Rh that we have just obtained res:=factor(resultant(subs(y=x+1+1/x,Rhx=RhR,R(x)=R,R0=R0w,R1=R1w,x=3,numer(RhP0b-Rhx)), numer(subs(x=3,zx/(1-2*t)-pazt[1])),P0)): nops(res)

IiM1

map(indets,[seq(op(i,res),i=1..nops(res))])

Nyw8IjwjSSJ2RzYiPCNJInRHRiZGJEYkRiRGJEYkRiQ8JkkiUkdGJkYoRiVJIndHRiY=

res1:=op(10,res): nops(%)

IiUtUA==

degree(res1,t);degree(res1,w);

IiIn

IiIn

res2:=factor(resultant(res1,algwv,w)):nops(%)

IiUnMyc=

indets(res2);degree(res,t)

PCVJIlJHNiJJInRHRiRJInZHRiQ=

IiM3

Before we go further let us reduce the degree in t res3:=factor(rem(res2,algv,t)):nops(%)

IiIn

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyg8IjwjSSJ2RzYiRiQ8JUkiUkdGJkkidEdGJkYlRiRGJA==

res4:=op(4,res3): nops(%);degree(res4,R)

IiVFQA==

IiIn

algRof3vt:=res4: res5:=factor(resultant(res4,algv,v)):nops(%)

IiIm

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Nyc8IjwjSSJ0RzYiRiRGJDwkSSJSR0YmRiU=

res6:=op(5,res5): nops(%)

IiVEYA==

degree(res6,R)

IiNz

n:=10:series(subs(R=Rex(n),x=3,v=vser(n),res6),t,n+1);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

algRof3:=res6:

RhR := 3*(x^2 + x + 1)*R(x)/x + 3*R1 - (t*x^4 + 2*t*x^3 + 2*t*x^2 + 2*t*x - x^2 + t)*R0/(x*t*(x^2 + x + 1)) + (t*x^2 + t - x)/(x*(x^2 + x + 1))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRSaFJHRigsKioqIiIkIiIiLCgqJClJInhHRigiIiNGMUYxRjVGMUYxRjFGMS1JIlJHRig2I0Y1RjFGNSEiIkYxKiZGMEYxSSNSMUdGKEYxRjEqLCwuKiZJInRHRihGMSlGNSIiJUYxRjEqKEY2RjFGQEYxKUY1RjBGMUYxKihGNkYxRkBGMUY0RjFGMSooRjZGMUZARjFGNUYxRjFGM0Y6RkBGMUYxSSNSMEdGKEYxRjVGOkZARjpGMkY6RjoqKCwoKiZGQEYxRjRGMUYxRkBGMUY1RjpGMUY1RjpGMkY6RjE3I0Yu

RhP0b := (12*v^8 + 16*P0*v^6 + 24*v^7 + 4*P0^2*v^4 + 24*P0*v^5 + 23*v^6 + 4*P0^2*v^3 + 8*P0*v^4 + 11*v^5 - 16*P0*v^3 + 14*v^4 - 4*P0^2*v - 12*P0*v^2 + 16*v^3 - P0^2 - 2*P0*v + 7*v^2 + v)*(-4*v^8 - 8*v^7 + 4*P0^2*v^4 - 11*v^6 + 4*P0^2*v^3 + P0*v^4 + 8*P0*v^3 + 14*v^4 - 4*P0^2*v + 18*P0*v^2 + 8*v^3 - P0^2 + 8*P0*v + v^2 + P0)*(8*v^10 + 8*P0*v^8 + 12*v^9 + 8*P0*v^7 - v^8 - 8*P0*v^6 - 20*v^7 + 4*P0^2*v^4 - 16*P0*v^5 - 22*v^6 + 4*P0^2*v^3 - 2*P0*v^4 + 4*v^5 + 8*P0*v^3 + 15*v^4 - 4*P0^2*v + 2*P0*v^2 + 4*v^3 - P0^2)*(2*v + 1)*(-1 + 2*t)^2*y/(w*(t*y^2 - t - 1)*(v^4 + 8*v^3 + 6*v^2 + 2*v + 1)^2*(4*v^8 + 8*P0*v^6 + 8*v^7 + 4*P0^2*v^4 + 12*P0*v^5 + 5*v^6 + 4*P0^2*v^3 + 4*P0*v^4 - 3*v^5 - 8*P0*v^3 - 8*v^4 - 4*P0^2*v - 6*P0*v^2 - 5*v^3 - P0^2 - P0*v - v^2)^2*(2*v^3 - 4*v - 1))

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

We begin with M(x,y) eqM:=-t*(x*y^2+x-2*y)*M(0, 0)/(2*x*y^2)-(t*x*y^2+2*t*y^2+t*x+2*t*y-x*y+2*t)*M(0, y)/(2*x*y)-t*(x^2+x+1)*M(x, 0)/(x*y)+(t*x^2*y^2+t*x^2*y+t*x*y^2+t*x^2+t*y^2+t*x+t*y-x*y+t)*M(x, y)/(x*y)+t*(y^2+y+1)*M(y, 0)/(2*y^2)-t*(D[1](M))(0, 0)/(2*y)+(1/3)*x;

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

This equation at x=3, y=2 (and even t=1/100, which guarantees convergence?) eqM1:=subs(M(x,y)=M, M(x,0)=R(x)/t^2, M(y,0)=R(y)/t^2, M(0,y)=S(y)/t/y,M(0,0)=R0/t^2,(D[1](M))(0, 0)=R1/t^2,x=3,y=2, #t=1/100, eqM)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcU0xR0YoLDAqKCMiIzYiI0MiIiJJI1IwR0YoRjNJInRHRighIiJGNioqI0YzRjJGMywmKiYiI0hGM0Y1RjNGMyIiJ0Y2RjMtSSJTR0YoNiMiIiNGM0Y1RjZGNiooIyIjOEY8RjNGNUY2LUkiUkdGKDYjIiIkRjNGNiooI0YzRjxGMywmKiYiIyYpRjNGNUYzRjNGPEY2RjNJIk1HRihGM0YzKigjIiIoIiIpRjNGNUY2LUZFRj9GM0YzKigjRjMiIiVGM0Y1RjZJI1IxR0YoRjNGNkYzRjM3I0Yu

Trying to work with series of smaller degree, we work with S-tilde and R-hat instead of S and R subs1:={isolate(subs(x=2,StS-Stof2),S(2)), isolate(subs(x=2,RhR-Rhof2),R(2)), isolate(subs(x=3,RhR-Rhof3),R(3))};

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

Observe that R1 has disappeared in the new equation eqM2:=collect(subs(subs1, #t=1/100, eqM1),[R0,R1,M,Stof2,Rhof2,Rhof3],factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcU0yR0YoLC4qKiMiI1oiJXdLIiIiLCYqJiIjJilGM0kidEdGKEYzRjMiIichIiJGMylGNyIiI0Y5SSNSMEdGKEYzRjkqJiwmKiYjRjZGOEYzRjdGM0YzRjNGOUYzSSJNR0YoRjNGMyoqI0YzIiNjRjMsJiomIiNIRjNGN0YzRjNGOEY5RjNGN0Y5SSZTdG9mMkdGKEYzRjkqKCNGMyIjN0YzRjdGOUkmUmhvZjJHRihGM0YzKigjRjNGOEYzRjdGOUkmUmhvZjNHRihGM0Y5KigjIiNmRjJGM0Y0RjNGN0Y5RjM3I0Yu

Parametrisation by P0 indets(RhP0b);

PCdJI1AwRzYiSSJ0R0YkSSJ2R0YkSSJ3R0YkSSJ5R0Yk

subs2:=subs(z=zx,y=x+1+1/x,x=2,P0=P0of2, #t=1/100, {Rhof2=RhP0b,Stof2=SdztP0-1/3}): eqM3:=numer(factor(subs(subs2,R0=R0w,#t=1/100, eqM2))): indets(%);

PChJIk1HNiJJJlAwb2YyR0YkSSZSaG9mM0dGJEkidEdGJEkidkdGJEkid0dGJA==

degree(eqM3,w);degree(eqM3,v); nops(eqM3)

IiIj

IiNO

IiV3RQ==

More or less terms if we decrease the degree in t of v? res:=numer(factor(rem(eqM3,subs(t=t,algv),t))): nops(%)

IiIj

op(1,res)

KiQpLCwqJClJInZHNiIiIiUiIiJGKiomIiIpRiopRiciIiRGKkYqKiYiIidGKilGJyIiI0YqRioqJkYyRipGJ0YqRipGKkYqRjJGKg==

nops(op(2,res))

IiU2SQ==

pazt[1];

KigsXG8qJiIiJSIiIilJInZHNiIiIzdGJkYmKigiIilGJkkjUDBHRilGJilGKCIjNUYmRiYqJkYsRiYpRigiIzZGJkYmKihGJUYmKUYtIiIjRiYpRihGLEYmRiYqKEYqRiZGLUYmKUYoIiIqRiZGJiomIiNERiZGLkYmRiYqKEYlRiZGNEYmKUYoIiIoRiZGJiooIiNLRiZGLUYmRjZGJkYmKiYiI1xGJkY4RiZGJiooRipGJkY0RiYpRigiIidGJkYmKigiI19GJkYtRiZGPUYmRiYqJiIjYEYmRjZGJkYmKihGJUYmKUYtIiIkRiYpRihGJUYmRiYqKCIjO0YmRjRGJilGKCIiJkYmRiYqKCIjTEYmRi1GJkZERiZGJiomRj5GJkY9RiZGJiooRiVGJkZLRiYpRihGTEYmRiYqKEY+RiZGNEYmRk1GJkYmKigiI1BGJkYtRiZGUEYmISIiKiYiI2ZGJkZERiZGWiooRipGJkY0RiZGVkYmRloqKCIjJylGJkYtRiZGTUYmRloqJiIjaEYmRlBGJkZaKihGJUYmRktGJkYoRiZGWiooRjJGJkY0RiYpRihGNUYmRloqKCIjYUYmRi1GJkZWRiZGWiomIiNCRiZGTUYmRloqJEZLRiZGWiooRjVGJkY0RiZGKEYmRloqKCIjOEYmRi1GJkZeb0YmRloqJkZMRiZGVkYmRloqJkYtRiZGKEYmRlpGJiwsKiRGTUYmRiYqJkYsRiZGVkYmRiYqJkZFRiZGXm9GJkYmKiZGNUYmRihGJkYmRiZGJkZaLEQqJkYlRiZGNkYmRiYqKEYsRiZGLUYmRkRGJkYmKiZGLEYmRj1GJkYmKihGJUYmRjRGJkZNRiZGJiooRipGJkYtRiZGUEYmRiYqJkZRRiZGREYmRiYqKEYlRiZGNEYmRlZGJkYmKihGJUYmRi1GJkZNRiZGJiomRkxGJkZQRiZGWiooRixGJkYtRiZGVkYmRloqJkYsRiZGTUYmRloqKEYlRiZGNEYmRihGJkZaKihGRUYmRi1GJkZeb0YmRloqJkZRRiZGVkYmRloqJEY0RiZGWkZob0ZaKiRGXm9GJkZaRlo=

ztx:=zx/(1-2*t)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSR6dHhHRigqJiwmKiZJInRHRigiIiIsKEkieEdGKEYyKiRGNCEiIkYyRjJGMkYyRjIqJiwmRjFGMkYyRjJGMkYzRjZGMkYyLCZGMkYyKiYiIiNGMkYxRjJGNkY2NyNGLg==

algP0of2:=subs(P0=P0of2,pazt[1])-subs(x=2,ztx);

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

res1:=factor(resultant(numer(eqM3),numer(algP0of2),P0of2)): nops(%);

IiM1

map(indets,[seq(op(i,res1),i=1..nops(res1))])

Nyw8IjwjSSJ2RzYiPCNJInRHRiZGJEYkRiRGJEYkRiQ8J0kiTUdGJkkmUmhvZjNHRiZGKEYlSSJ3R0Ym

res2:=op(10,res1): nops(%);

IiZvLiI=

degree(res2,w)

IiIn

res3:=factor(rem(res2,algwv,w)): nops(%)

IiU/cg==

subs3:=subs(z=zx,y=x+1+1/x,x=3,P0=P0of3,{Rhof3=RhP0b}): algP0of3:=subs(P0=P0of3,pazt[1])-subs(x=3,ztx);

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

res4:=subs(subs3,res3): indets(res3);

PCdJIk1HNiJJJlJob2YzR0YkSSJ0R0YkSSJ2R0YkSSJ3R0Yk

degree(res4,w)

IiIi

res5:=factor(resultant(numer(res4),numer(algP0of3),P0of3)): nops(%); save(res5,resultant5):

IiM3

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Ny48IjwjSSJ2RzYiRiRGJDwjSSJ0R0YmRiRGJEYkRiRGJEYkPCZJIk1HRiZGKEYlSSJ3R0Ym

res6:=op(12,res5): nops(res6);

Iicreko=

res7:=factor(rem(res6,algwv,w)): nops(%);

IiIk

IiM3

map(indets,[seq(op(i,res7),i=1..nops(res7))])

NyU8IjwjSSJ2RzYiPCZJIk1HRiZJInRHRiZGJUkid0dGJg==

res8:=op(3,res7): nops(%)

IidTIjQi

indets(res8);

PCZJIk1HNiJJInRHRiRJInZHRiRJIndHRiQ=

degree(res8,M)

IiIq

res9:=factor(resultant(res8,algwv,w)): nops(%);

IidZOlY=

degree(res9,M);indets(res9)

IiM9

PCVJIk1HNiJJInRHRiRJInZHRiQ=

Let us check n:=10: series(subs(M=subs(x=3,y=2,Mex(n)),v=vser(n),res9),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

res10:=factor(rem(res9,algv,t)): nops(%)

IiIn

map(indets,[seq(op(i,res10),i=1..nops(res10))])

Nyg8IjwjSSJ2RzYiRiQ8JUkiTUdGJkkidEdGJkYlRiRGJA==

res11:=op(4,res10): nops(%);

IiZIKFI=

Dernier effort res12:=factor(resultant(subs(t=1/100,res11),subs(t=1/100,algv),v)): nops(res12)

IiQ8Iw==

degree(res12,M)

IiQ7Iw==

We proceed with P(x,y) eqP:=-P(x,y)+ M(x, y)/x - M(0, y)/x + M(y, x)/y - M(0, x)/y

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcVBHRigsLC1JIlBHRig2JEkieEdGKEkieUdGKCEiIiomLUkiTUdGKEYxIiIiRjJGNEY4KiYtRjc2JCIiIUYzRjhGMkY0RjQqJi1GNzYkRjNGMkY4RjNGNEY4KiYtRjc2JEY8RjJGOEYzRjRGNDcjRi4=

eqP1:=subs(isolate(eqM,M(x,y)), isolate(subs({x=y,y=x},eqM),M(y,x)), eqP)

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

eqP2:=collect(numer(subs(P(x,y)=P, M(x,0)=R(x)/t^2, M(y,0)=R(y)/t^2, M(0,y)=S(y)/t/y,M(0,x)=S(x)/t/x,M(0,0)=R0/t^2,(D[1](M))(0, 0)=R1/t^2,x=3,y=2,eqP1)),[P,R,S],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcVAyR0YoLDIqKiIjNyIiIkkiUEdGKEYxSSJ0R0YoRjEsJiomIiMmKUYxRjNGMUYxIiInISIiRjFGOComIiNARjEtSSJSR0YoNiMiIiNGMUYxKiYiI0VGMS1GPDYjIiIkRjFGMSomLCYqJiIkVCJGMUYzRjFGOEY3RjFGMS1JIlNHRihGPUYxRjEqJiwmKiYiJEMiRjFGM0YxRjhGN0YxRjEtRklGQkYxRjEqJiIjREYxSSNSMEdGKEYxRjEqJkYwRjFJI1IxR0YoRjFGMSomIiNbRjFGM0YxRjg3I0Yu

Trying to work with series of smaller degree, we work with S-tilde and R-hat instead of S and R subs1:={isolate(subs(x=2,StS-Stof2),S(2)), isolate(subs(x=3,StS-Stof3),S(3)), isolate(subs(x=2,RhR-Rhof2),R(2)), isolate(subs(x=3,RhR-Rhof3),R(3))};

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

Observe again that R1 has disappeared in the new equation eqP3:=collect(subs(subs1,eqP2),[R0,R1,P,Stof2,Stof3,Rhof2,Rhof3],factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcVAzR0YoLDIqKiMiIyUqIiR0IyIiIiwmKiYiIyYpRjNJInRHRihGM0YzIiInISIiRjNGN0Y5SSNSMEdGKEYzRjkqKiIjN0YzSSJQR0YoRjNGN0YzRjRGM0Y5KiYsJiomIyIkQiUiIihGM0Y3RjNGOSMiIz1GQ0YzRjNJJlN0b2YyR0YoRjNGMyomLCYqJiMiJCMqKiIjOEYzRjdGM0Y5IyIjW0ZMRjNGM0kmU3RvZjNHRihGM0YzKiYjIiZdJj5GMkYzRjdGM0YzIyIkZyUiIyIqRjkqJiIiI0YzSSZSaG9mMkdGKEYzRjMqJkZXRjNJJlJob2YzR0YoRjNGMzcjRi4=

Parametrisation with P0 subs2:=subs(z=zx,y=x+1+1/x,x=2,P0=P0of2,{Rhof2=RhP0b,Stof2=SdztP0-1/3}): eqP4:=subs(subs2,R0=R0w,eqP3): indets(%);

PClJIlBHNiJJJlAwb2YyR0YkSSZSaG9mM0dGJEkmU3RvZjNHRiRJInRHRiRJInZHRiRJIndHRiQ=

subs3:=subs(z=zx,y=x+1+1/x,x=3,P0=P0of3,{Rhof3=RhP0b,Stof3=SdztP0-1/3}): eqP5:=numer(subs(subs3,R0=R0w,eqP4)): indets(%); nops(eqP5)

PChJIlBHNiJJJlAwb2YyR0YkSSZQMG9mM0dGJEkidEdGJEkidkdGJEkid0dGJA==

IiZTZSQ=

degree(eqP5,w)

IiIj

eqP6:=factor(rem(eqP5,algwv,w)): nops(eqP6)

IiZnJkc=

Let us specialize t as well eqP7:=numer(factor(subs(t=1/100,eqP6))): nops(%)

IiVTcg==

indets(algP0of2)

PCVJJlAwb2YyRzYiSSJ0R0YkSSJ2R0Yk

res1:=factor(resultant(numer(eqP7),numer(subs(t=1/100,algP0of2)),P0of2)): nops(%);

IiIq

map(indets,[seq(op(i,res1),i=1..nops(res1))])

Nys8IjwjSSJ2RzYiRiRGJEYkRiRGJEYkPCZJIlBHRiZJJlAwb2YzR0YmRiVJIndHRiY=

res2:=op(9,res1): nops(%);

IiY0KyM=

degree(res2,w)

IiIk

res3:=factor(rem(res2,algwv,w)): nops(%)

IiY9WiI=

subs3:=subs(z=zx,y=x+1+1/x,x=3,P0=P0of3,t=1/100,{Rhof3=RhP0b}): res4:=numer(factor(subs(subs3,res3))): indets(res3);

PCZJIlBHNiJJJlAwb2YzR0YkSSJ2R0YkSSJ3R0Yk

nops(res4);degree(res4,w)

IiY9WiI=

IiIi

degree(res4,v)

IiRGIg==

res:=factor(rem(res4,subs(t=1/100,algv),v)): nops(%)

IiU3PQ==

res6:=factor(resultant(res,numer(subs(t=1/100,algP0of3)),P0of3)): nops(%);

IiZPLSI=

indets(res6)

PCVJIlBHNiJJInZHRiRJIndHRiQ=

res7:=factor(rem(res6,algwv,w)): nops(%);

IiVlZA==

indets(res7);

PCVJIlBHNiJJInZHRiRJIndHRiQ=

degree(res7,w);degree(res7,P)

IiIi

IiIq

res8:=factor(resultant(res7,algwv,w)): nops(%);

IiZoOiI=

degree(res8,P); indets(res8)

IiM9

PCRJIlBHNiJJInZHRiQ=

res9:=numer(factor(rem(res8,subs(t=1/100,algv),v))): nops(%)

IiRHIw==

Dernier effort res10:=factor(resultant(res9,subs(t=1/100,algv),v)): nops(res10)

IiQ8Iw==

indets(res10);

PCNJIlBHNiI=

degree(res10,P)

IiQ7Iw==

We proceed with A(x,y). We use its functional equation. Its degree is the same as the degree of (x^2+x+1) Am(1/x) + (t^2+y+1)*Am(1/y)+A00 eqA1:=-sum+subs(Am(1/x)=1/x*M(1/x,0),Am(1/y)=1/y*M(1/y,0), A00=2*M10,M10=R1/t^2,x=1/x,y=1/y,(x^2+x+1) * Am(1/x) + (y^2+y+1)*Am(1/y)+A00)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcUExR0YoLCpJJHN1bUdGJSEiIiooLCgqJClJInhHRigiIiNGMCIiIiokRjVGMEY3RjdGN0Y3RjVGNy1JIk1HRig2JEY1IiIhRjdGNyooLCgqJClJInlHRihGNkYwRjcqJEZBRjBGN0Y3RjdGN0ZBRjctRjo2JEZBRjxGN0Y3KihGNkY3SSNSMUdGKEY3KUkidEdGKEY2RjBGNzcjRi4=

eqA2:=collect(numer(subs(M(x,0)=R(x)/t^2, M(y,0)=R(y)/t^2,x=3,y=2,eqA1)),[sum,R],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcUEyR0YoLCoqKCIiJyIiIkkkc3VtR0YlRjEpSSJ0R0YoIiIjRjEhIiIqJiIjRUYxLUkiUkdGKDYjIiIkRjFGMSomIiNARjEtRjo2I0Y1RjFGMSomIiM3RjFJI1IxR0YoRjFGMTcjRi4=

Trying to work with series of smaller degree, we work with R-hat instead of R subs1:={ isolate(subs(x=2,RhR-Rhof2),R(2)), isolate(subs(x=3,RhR-Rhof3),R(3))};

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZzdWJzMUdGKDwkLy1JIlJHRig2IyIiIywsKiYjRjMiIigiIiJJI1IxR0YoRjghIiIqKiNGOCIkWiJGOCwmKiYiI1hGOEkidEdGKEY4RjgiIiVGOkY4SSNSMEdGKEY4RkFGOkY4KiYjIiImRj1GOEZBRjhGOiNGM0Y9RjgqJiNGMyIjQEY4SSZSaG9mMkdGKEY4RjgvLUYxNiMiIiQsLComI0ZPIiM4RjhGOUY4RjoqKiNGOCIkMiZGOCwmKiYiJGciRjhGQUY4RjgiIipGOkY4RkNGOEZBRjpGOComIyIjNUZWRjhGQUY4RjojRjgiJHAiRjgqJiNGOEZTRjhJJlJob2YzR0YoRjhGODcjRi4=

Observe again that R1 has disappeared in the new equation eqA3:=collect(subs(subs1,eqA2),[R0,R1,P,Rhof2,Rhof3],factor);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVlcUEzR0YoLC4qKiMiI1oiJHQjIiIiLCYqJiIjJilGM0kidEdGKEYzRjMiIichIiJGM0Y3RjlJI1IwR0YoRjNGMyooRjhGM0kkc3VtR0YlRjMpRjciIiNGM0Y5KiYjIiROJEYyRjNGN0YzRjkjIiNTIiMiKkYzKiZGPkYzSSZSaG9mM0dGKEYzRjMqJkY+RjNJJlJob2YyR0YoRjNGMzcjRi4=

Parametrisation with P0 subs2:=subs(z=zx,y=x+1+1/x,x=2,P0=P0of2,{Rhof2=RhP0b}): eqA4:=subs(subs2,R0=R0w,eqA3): indets(%);

PChJJlAwb2YyRzYiSSZSaG9mM0dGJEkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkSSJ0R0YkSSJ2R0YkSSJ3R0Yk

subs3:=subs(z=zx,y=x+1+1/x,x=3,P0=P0of3,{Rhof3=RhP0b}): eqA5:=numer(subs(subs3,R0=R0w,eqA4)): indets(%); nops(eqP5)

PChJJlAwb2YyRzYiSSZQMG9mM0dGJEkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkSSJ0R0YkSSJ2R0YkSSJ3R0Yk

IiZTZSQ=

degree(eqA5,w)

IiIj

eqA6:=factor(rem(eqA5,algwv,w)): nops(eqA6)

IiYhMzY=

Let us specialize t as well eqA7:=numer(factor(subs(t=1/100,eqA6))): nops(%)

IiVxSA==

indets(algP0of2)

PCVJJlAwb2YyRzYiSSJ0R0YkSSJ2R0Yk

res1:=factor(resultant(numer(eqA7),numer(subs(t=1/100,algP0of2)),P0of2)): nops(%);

IiIq

map(indets,[seq(op(i,res1),i=1..nops(res1))])

Nys8IjwjSSJ2RzYiRiRGJEYkRiRGJEYkPCZJJlAwb2YzR0YmSSRzdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiZGJUkid0dGJg==

res2:=op(9,res1): nops(%);

IiY/LSI=

degree(res2,w)

IiIk

res3:=factor(rem(res2,algwv,w)): nops(%)

IiVddw==

subs3:=subs(z=zx,y=x+1+1/x,x=3,P0=P0of3,t=1/100,{Rhof3=RhP0b}): res4:=numer(factor(subs(subs3,res3))): indets(res3);

PCZJJlAwb2YzRzYiSSRzdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRJInZHRiRJIndHRiQ=

nops(res4);degree(res4,w)

IiVddw==

IiIi

degree(res4,v)

IiMiKg==

res:=factor(rem(res4,subs(t=1/100,algv),v)): nops(%)

IiUzOA==

res6:=factor(resultant(res,numer(subs(t=1/100,algP0of3)),P0of3)): nops(%);

IiUpeSg=

indets(res6)

PCVJJHN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkkidkdGJ0kid0dGJw==

res7:=factor(rem(res6,algwv,w)): nops(%);

IiUhUiU=

indets(res7);

PCVJJHN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkkidkdGJ0kid0dGJw==

degree(res7,w);degree(res7,P)

IiIi

IiIh

res8:=factor(resultant(res7,algwv,w)): nops(%);

IiVEKSk=

degree(res8,sum); indets(res8)

IiM9

PCRJJHN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkkidkdGJw==

res9:=numer(factor(rem(res8,subs(t=1/100,algv),v))): nops(%)

IiRHIw==

Dernier effort res10:=factor(resultant(res9,subs(t=1/100,algv),v)): nops(res10)

IiQ8Iw==

indets(res10);

PCNJJHN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2Ig==

degree(res10,sum)

IiQ7Iw==

The catalytic equation for S(x) factors at x=1 res:=numer(factor(subs(x=1,eqScat)));indets(%)

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

PCdJI0IxRzYiSSNCMkdGJEkjUjBHRiRJI1IxR0YkSSJ0R0Yk

We check which factor is zero n:=4: normal(series(subs(R0=R0ex(n), R1=R1ex(n), B1=B1ex(n), B2=B2ex(n), S(1)=subs(x=1,Sex(n)),op(2,res)),t,n+1)); normal(series(subs(R0=R0ex(n), R1=R1ex(n), B1=B1ex(n), B2=B2ex(n), S(1)=subs(x=1,Sex(n)),op(3,res)),t,n+1))

KytJInRHNiIiIiJGJSIiJiIiJCIjOyIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YlRiY=

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiY=

algSof1R0R1B1B2:=collect(op(3,res),S(1),factor)

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

factor(discrim(subs(S(1)=Sof1,%),Sof1))

LCQqKiIiJSIiIixEKigiI0dGJSlJI1IwRzYiIiIjRiUpSSJ0R0YrRixGJUYlKioiJEUiRiVGKkYlSSNSMUdGK0YlRi1GJUYlKigiIzlGJUYqRiUpRi4iIiRGJSEiIiooIiMiKUYlKUYxRixGJUYtRiVGJSooIiIqRiVGMUYlRjRGJUYlKiYiIiZGJSlGLkYkRiVGNiooRjtGJUkjQjFHRitGJUYtRiVGJSoqIiM9RiVJI0IyR0YrRiVGKkYlRi5GJUY2KihGO0YlRkNGJUYtRiVGNiooRixGJUYpRiVGLkYlRiUqKkZCRiVGKkYlRjFGJUYuRiVGJSooIiNERiVGKkYlRi1GJUY2KihGQkYlRjFGJUYtRiVGNiomRiRGJUY0RiVGNiokRilGJUYlKihGLEYlRipGJUYuRiVGNiokRi1GJUYlRiUsJiomRiRGJUYuRiVGJUYlRiVGJSwmKiYiIilGJUYuRiVGJUYlRjZGJUY2

disc:=op(2,%)

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

collect(factor(subs(isolate(subs(x=1,ShS)-Sh(1),S(1)),algSof1R0R1B1B2)),Sh,factor)

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

StS

KiYsJkkieEc2IiIiIiokRiQhIiJGKEYoLCoqJiwoRiRGJkYnRiZGJkYmRiYtSSJTR0YlNiNGJEYmRiYqJkkjUjBHRiVGJkkidEdGJUYoRigqJiMiIiMiIiRGJkYkRiZGJiomI0YmRjVGJkYkRihGJkYm

factor(rem(numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,disc))),algwv,w))

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

factor(rem(op(2,%),algv,t))

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

We now replace R0 et al. by their expressions res1:=numer(factor(subs(R0=R0w,R1=R1w,B1=B1v,B2=B2w,S(1)=Sof1,op(3,res)))): Reduction of the degree in w res2:=numer(factor(rem(res1,algwv,w))): nops(res2)

IiIk

op(1,res2); op(2,res2)

ISIj

SSJ0RzYi

res3:=op(3,res2): indets(res3); nops(res3)

PCZJJVNvZjFHNiJJInRHRiRJInZHRiRJIndHRiQ=

IiQzJQ==

Reduction of the degree in t res4:=factor(rem(res3,algv,t)):nops(%)

IiIm

map(indets,[seq(op(i,res4),i=1..nops(res4))])

Nyc8IjwjSSJ2RzYiRiQ8JkklU29mMUdGJkkidEdGJkYlSSJ3R0YmRiQ=

res5:=op(4,res4): nops(%)

IiRBIw==

algSof1tvw:=collect(res5,[Sof1,w],factor); degree(%,Sof1)

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

IiIj

The coefficient of w factor(coeff(%%,w))

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

Introduce a new series T collect(numer(factor(subs(Sof1=T-1/2,algSof1tvw))),[T,w],factor)

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

Much nicer! This suggests to write rather S(1)+1/2 = w * T. This new series T (denoted w-tilde in the paper) is quadratic over Q(t,v) algTvt:=subs(w=sqrt(1+4*v-4*v^3-4*v^4), collect(numer(factor(subs(Sof1=T*w-1/2,algSof1tvw))),[T,w],factor)); indets(%)

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

PCVJIlRHNiJJInRHRiRJInZHRiQ=

nops(factor(algTvt))

IiRdIg==

T has degree 4 over Q(v) algTv:=collect(op(9,factor(resultant(algTvt,algv,t))),T,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdUdkdGKCwsKi4iJEslIiIiLCgqJiIiJUYxKUkidkdGKCIiJEYxRjEqJkY3RjEpRjYiIiNGMUYxRjEhIiJGMSwqKiZGOkYxRjVGMUYxRjhGMSomIiInRjFGNkYxRjFGMUYxRjEpLCoqJkY0RjEpRjZGNEYxRjFGM0YxKiZGNEYxRjZGMUY7RjFGO0Y6RjEpLChGPUYxRkRGO0YxRjtGNEYxKUkiVEdGKEY0RjFGMSowIiQpR0YxLCYqJkY6RjFGNkYxRjFGMUYxRjFGMkYxRjxGMUZARjEpRkZGN0YxKUZIRjdGMUYxKjAiI0NGMUZLRjFGQUYxLDQqJiIkRyJGMSlGNiIiKUYxRjEqJiIkJVFGMSlGNiIiKEYxRjEqJiIkXyRGMSlGNkY/RjFGMSomIiN3RjEpRjYiIiZGMUY7KiYiJDMlRjFGQ0YxRjsqJiIkeSNGMUY1RjFGOyomIiM2RjFGOUYxRjEqJiIjVUYxRjZGMUYxRllGMUYxRjxGMSlGRkY6RjEpRkhGOkYxRjEqMEZVRjFGRkYxRjxGMUZBRjEsNComIiNrRjFGVEYxRjEqJiIkUyNGMUZYRjFGMSomIiRbI0YxRmZuRjFGMSomIiM/RjFGaW5GMUY7KiZGSkYxRkNGMUY7KiYiJEUjRjFGNUYxRjsqJEY5RjFGMSomIiNJRjFGNkYxRjFGam5GMUYxKUZLRjpGMUZIRjFGMSomRktGMSxGKiYiJUM1RjEpRjYiIzxGMUYxKiYiJU96RjEpRjYiIztGMUYxKiYiJiNSRkYxKUY2IiM6RjFGMSomIiYzZSZGMSlGNiIjOUYxRjEqJiImK1MnRjEpRjYiIzhGMUYxKiYiJit3IkYxKUY2IiM3RjFGMSomIiZfJG9GMSlGNkZgb0YxRjsqJiInITM/IkYxKUY2IiM1RjFGOyomIiY7KypGMSlGNiIiKkYxRjsqJiImKz8jRjFGVEYxRjsqJiImdzYjRjFGWEYxRjEqJiImJXlPRjFGZm5GMUYxKiYiJlN5JEYxRmluRjFGMSomIiYkb0NGMUZDRjFGMSomIiUvJypGMUY1RjFGMSomIiVnQEYxRjlGMUYxKiYiJGcjRjFGNkYxRjFGW3JGMUYxRjE3I0Yu

and degree 24 over Q(t) res:=factor(resultant(algTv,algv,v)): nops(res)

IiIk

map(indets,[seq(op(i,res),i=1..nops(res))])

NyU8IjwkSSJURzYiSSJ0R0YmRiQ=

n:=4:series( subs(T=(1/2+subs(x=1,Sex(n)))/wser(n), op(2,res)),t,n); series( subs(T=(1/2+subs(x=1,Sex(n)))/wser(n), op(3,res)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiU=

Ky1JInRHNiIiOTM1ND03eUJValAuOiIiISE7RyQ+Xy8wVXN5Vj9BeSYiIiIiPUc4KCp6T21YeU8nZjpfJmUiIiMiQDNZIW8yLj1OQmZBW0N6OjgiIiQtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGKCIiJQ==

n:=10:series( subs(T=(1/2+subs(x=1,Sex(n)))/wser(n), op(2,res)),t,n);

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

nops(op(2,res))

IiRwJw==

algT:=collect(op(2,res),T,factor): degree(%,T)

IiND

Intermediate extensions between Q(v) and Q(v,T) ? Only one, which must be Q(t,v) for v0 from 2 to 6 do : evala(Subfields(subs(v=v0,algTv), 2));od

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIlWGYhIiI=

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIlbWUhIiI=

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiInMEpVISIi

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIoJUhXPiEiIg==

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIrMCRbN2UiISIi

A simpler version of the equation of T over Q(t,v) algTvtalt:=collect(op(2,subs(troot=t,numer(factor(subs(t=troot, algTvt),RootOf(algv,t))))),T,factor)

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

algTv2:=collect(algTvtalt/lcoeff(algTvtalt,T),T,factor)

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

The correct value of T n:=10:series(subs(v=vser(n),algTvtalt),t,n): Tserens:=map(allvalues,algeqtoseries(convert(%,polynom),t,T,5));

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShUc2VyZW5zR0YoNyQrL0kidEdGKCMiIiIiIiMiIiEhIiJGMkYzRjMhIiUiIiQiI0oiIiUtSSJPR0YlNiNGMiIiJistRjAjRjUiIidGNCNGMkY3RjIjRjZGN0YzIyEjKCpGN0Y5RjpGPTcjRi4=

series(wser(n)*Tserens[1]-1/2,t); series(wser(n)*Tserens[2]-1/2,t); series(subs(x=1,Sex(n)),t)

KytJInRHNiIiIiNGJSIiJyIiJCIjZSIiJS1JIk9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyIiIiIiJg==

Ky1JInRHNiIjISIjIiIkIiIhIyEiJUYnIiIjIyEjOUYnRicjISRTIkYnIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjIiIiIiIm

Ky1JInRHNiIiIiNGJSIiJyIiJCIjZSIiJSIkSSQiIiYtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiJGJg==

Can we simplify a bit the equation of T? factor(op(3,algTv2))

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

subs(troot=t,factor(evala(Normal(subs(t=troot,t*op(3,algTv2))))))

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

conew:=1/(1-2*t)*subs(troot=t,factor(evala(Normal(subs(t=troot,(1-2*t)*op(3,algTv2))))))

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

denom(conew)

LCQqLiIjNyIiIiwmRiUhIiIqJiIiI0YlSSJ0RzYiRiVGJUYlKSwqKiZGKUYlKUkidkdGKyIiJEYlRiUqJkYxRiUpRjBGKUYlRiUqJiIiJ0YlRjBGJUYlRiVGJUYpRiUpLChGLkYlKiYiIiVGJUYwRiVGJ0YlRidGKUYlLCoqJkY5RiUpRjBGOUYlRiUqJkY5RiVGL0YlRiVGOEYnRiVGJ0YlLChGPUYlRjJGJUYlRidGJUYl

collect(numer(conew),t,factor)

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

algTv3:=subsop(3=conew,algTv2)

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

Let us check n:=9:normal(series(subs(T=1/w*(1/2+subs(x=1,Sex(n))),v=vser(n),w=wser(n),algTv3),t,n))

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIio=

the equation for T=w-tilde given in the paper is written in terms of co-new. Below are various attempts to describe this extension of Q(t,v) in simpler terms algTv;

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algT1v:= collect(subs(T=T1-(1+2*v)/6/(2*v^3-4*v-1), algTv),T1,factor)

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subs(T1=sqrt(T2),%)

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factor(discrim(%,T2))

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algTu:=collect(factor(resultant(algTv,algvu,v)),T,factor):degree(%,T);nops(factor(%%))

IiM3

IiReJA==

Sub extensions of degree 2 over Q(u): one only finds Q(t,u) for u0 from 3 to 6 do : map(allvalues,evala(Subfields(subs(u=u0,algTu), 2)));ifactor(op(1,%)^2/discrim(subs(u=u0,algu),t));od

PCQqJCkiJVhEIyIiIiIiI0YnLCRGIyEiIg==

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PCQqJCkiJnAoRyMiIiIiIiNGJywkRiMhIiI=

KiYpLUkhRzYiNiMiIiQiIiMhIiIpLUYlNiMiIzhGKUYq

PCQqJCkiJTZUIyIiIiIiI0YnLCRGIyEiIg==

KiQpLUkhRzYiNiMiIiMiIzshIiI=

PCQqJCkiKGxbRSQjIiIiIiIjRicsJEYjISIi

KiQpLUkhRzYiNiMiIz4iIiMhIiI=

Sub extensions of degree 3 over Q(u): only one, which must thus be Q(v) for u0 from 3 to 6 do : evala(Subfields(subs(u=u0,algTu), 3));od

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIiQiSCIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIhIiIiJTE1ISIi

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIiRjIiIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIhIiIiJDQoISIi

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIiVGWyIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIhIiIiJnEneiEiIg==

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiQpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJCIiIiIiIiomIiY3RSIiIiJJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiISIiIidmYj4hIiI=

Subextensions of degree 4: there is one, which has a subextension of degree 2. Thus is must be a quadratic extension of Q(t,u) for u0 from 3 to 6 do : evala(Subfields(subs(u=u0,algTu), 4));#solve(subs(_Z=sqrt(z),op(op(%))),z); od

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiYiI1MiIiIpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiJSIiIiIiIiomIiZERiIiIiIpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIocyozSiEiIg==

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiYiJ1NJPSIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIlIiIiIiIiKiYiKyRScmpSIyIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIjIiIiIiIiIiwrOztWOCQhIiI=

PCMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiYiJkI5JCIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIlIiIiIiIiKiYiLEMnKTRRbCUiIiIpSSNfWkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIyIiIiIiIiIuJSlbWmY2dCMhIiI=

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This Z must be in Q(t,u) subs(_Z=sqrt(Z),op(op(%))); solve(%);

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discrim(%%,Z)

Ij4mZW9GR0tteSU0VmxVMlIk

subs(u=6,factor(discrim(algu,t)))

IitsaWh5Ng==

ifactor(%%/%)

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So we seek a cublic factor in the factorization of algTu over Q(u,T) u0:=2: res:=subs(RootOf(subs(u=u0,algTu),T)=T,factor(subs(u=u0,T=F,algTu),RootOf(subs(u=u0,algTu),T))): map(degree,[seq(op(i,res),i=1..nops(res))],F);

NykiIiEiIiUiIiNGJUYlIiIiRiY=

In what follows, we extract the factor of degree 2, say P2(F), such that the coefficients of (F-T)P2(F) have degree 4 over Q(u0) for u0 from 2 to 4 do res:=subs(RootOf(subs(u=u0,algTu),T)=T,factor(subs(u=u0,T=F,algTu),RootOf(subs(u=u0,algTu),T))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-T) : M:=factor(resultant(numer(coeff(P3, F,2)-p2),subs(u=u0,algTu),T)): #map(nops,[seq(op(i,M),i=1..nops(M))]): print(%): #map(degree,[seq(op(i,M),i=1..nops(M))],p2): print(%): if nops(M)=2 then M:=simplify((M/op(1,M))^(1/3),symbolic): M:=collect(M/lcoeff(M,p2),P2): Mlist[u0]:=M; print(M): fi: fi:od:od:

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With p1 instead : not better for u0 from 2 to 4 do res:=subs(RootOf(subs(u=u0,algTu),T)=T,factor(subs(u=u0,T=F,algTu),RootOf(subs(u=u0,algTu),T))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-T) : M:=factor(resultant(numer(coeff(P3, F,1)-p2),subs(u=u0,algTu),T)): #map(nops,[seq(op(i,M),i=1..nops(M))]): print(%): #map(degree,[seq(op(i,M),i=1..nops(M))],p2): print(%): if nops(M)=2 then M:=simplify((M/op(1,M))^(1/3),symbolic): M:=collect(M/lcoeff(M,p2),P2): Mlist[u0]:=M; print(M): fi: fi:od:od:

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LCwqJClJI3AyRzYiIiIlIiIiRigqJiMiJCJHIiMqKkYoKUYlIiIkRighIiIqJiMiLEZ1Li8sJCIrXyg+ZEQjRigpRiUiIiNGKEYoKiYjIi1SJkcmeVduIixPYiZIZ1NGKEYlRihGLyMiM2hSXkBNKVEhR14iMydcJ1EwY0syI28iRig=

umax:=20: for u0 from 2 to umax do res:=subs(RootOf(subs(u=u0,algTu),T)=T,factor(subs(u=u0,T=F,algTu),RootOf(subs(u=u0,algTu),T))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-T) : M:=factor(resultant(numer(coeff(P3, F,2)-p2),subs(u=u0,algTu),T)): #map(nops,[seq(op(i,M),i=1..nops(M))]): print(%): #map(degree,[seq(op(i,M),i=1..nops(M))],p2): print(%): if nops(M)=2 then M:=simplify((M/op(1,M))^(1/3),symbolic): M:=collect(M/lcoeff(M,p2),P2): Mlist[u0]:=M; #print(M): fi: fi:od:od: umax:=50: for u0 from 22 to umax do res:=subs(RootOf(subs(u=u0,algTu),T)=T,factor(subs(u=u0,T=F,algTu),RootOf(subs(u=u0,algTu),T))): for i from 1 to nops(res) do if degree(op(i,res),F)=2 then P3:=op(i,res)/coeff(op(i,res),F,2)*(F-T) : M:=factor(resultant(numer(coeff(P3, F,2)-p2),subs(u=u0,algTu),T)): #map(nops,[seq(op(i,M),i=1..nops(M))]): print(%): #map(degree,[seq(op(i,M),i=1..nops(M))],p2): print(%): if nops(M)=2 then M:=simplify((M/op(1,M))^(1/3),symbolic): M:=collect(M/lcoeff(M,p2),P2): Mlist[u0]:=M; #print(M): fi: fi:od:od: with(CurveFitting): c3:=factor(RationalInterpolation([seq([u0, coeff(Mlist[u0],p2,3)],u0=2..20),seq([u0, coeff(Mlist[u0],p2,3)],u0=22..umax)],u));

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c2:=factor(RationalInterpolation([seq([u0, coeff(Mlist[u0],p2,2)],u0=2..20),seq([u0, coeff(Mlist[u0],p2,2)],u0=22..umax)],u));

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c1:=factor(RationalInterpolation([seq([u0, coeff(Mlist[u0],p2,1)],u0=2..20),seq([u0, coeff(Mlist[u0],p2,1)],u0=22..umax)],u));

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

c0:=factor(RationalInterpolation([seq([u0, coeff(Mlist[u0],p2,0)],u0=2..20),seq([u0, coeff(Mlist[u0],p2,0)],u0=22..umax)],u));

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

We have thus a conjectured minimal polynomial of p2 over Q(u) M2conj:=collect(numer(factor(c0+c1*p+c2*p^2+c3*p^3+p^4)),p,factor);

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

algz:=subs(p=z/(u^3-5*u^2+3*u+7),M2conj)

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

genus(algz,u,z)

IiIm

lcoeff(algz,z)

LCQqKiIlJ0giIiIiKSwqKiYiI0ZGJSlJInVHNiIiIiVGJUYlKiYiIz1GJSlGKyIiI0YlISIiKiZGLUYlRitGJUYlRiVGMkYxRiUsJiomIiIkRiVGK0YlRiVGJUYyRiUsJkY1RiVGJUYlRiVGJQ==

factor(discrim(algu,t))

KigsJkkidUc2IiIiIkYmISIiRiYsKiomIiNGRiYpRiQiIiVGJkYmKiYiIz1GJilGJCIiI0YmRicqJkYsRiZGJEYmRiZGJkYnRiYpLCYqJiIiJEYmRiRGJkYmRiZGJkY1RiY=

factor(discrim(algz,z))

LCQqMiIzRyhwIjNCL2gmNCIiIiIsJiomIiIkRiVJInVHNiJGJUYlRiUhIiJGJSksJkYpRiVGJUYrRihGJSksLComIiIqRiUpRikiIiVGJUYlKiYiI2dGJSlGKUYoRiVGKyomIiMkKkYlKUYpIiIjRiVGJSomIiNRRiVGKUYlRisiIilGJUYzRiUpLDQqJiIjRkYlKUYpRj1GJUYlKiYiJE0jRiUpRikiIihGJUYrKiYiJW81RiUpRikiIidGJUYlKiYiJSl5I0YlKUYpIiImRiVGKyomIiUyR0YlRjJGJUYlKiYiJUk5RiVGNkYlRiUqJiIlPUFGJUY5RiVGKyomIiRHIkYlRilGJUYlIiN3RitGM0YlKSwqKiZGQUYlRjJGJUYlKiYiIz1GJUY5RiVGKyomRjNGJUYpRiVGJUYlRitGPUYlKSwmRiVGJUYpRiVGMUYlKSwmRidGJUYlRiVGKEYlRis=

algumonic

LCoqJClJI3VwRzYiIiIlIiIiRigqKiIkJ1tGKClGJSIiI0YoKUkidEdGJkYsRigpLCZGLkYoRihGKEYsRighIiIqLCIkSChGKEYtRigsJiomIiIpRihGLUYoRihGKEYoRihGL0YoRiVGKEYxKigiJiRvPkYoKUYuRidGKClGMEYnRihGMQ==

res:=factor(numer(subs(RootOf(algwv,w)=w,RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t), factor(algB2v,{RootOf(algvp,tp),RootOf(algwv,w)})))): nops(res) algvp

LCgqJClJI3RwRzYiIiIjIiIiRigqJiw8KiYiIilGKClJInZHRiYiIzdGKCEiIiomIiNzRigpRi4iIzZGKEYwKiYiJE8kRigpRi4iIzVGKEYwKiYiJF8nRigpRi4iIipGKEYwKiYiJHYnRigpRi5GLEYoRjAqJiIkKUdGKClGLiIiKEYoRjAqJiIkbyJGKClGLiIiJ0YoRigqJiIkSyVGKClGLiIiJkYoRigqJiIkXSVGKClGLiIiJUYoRigqJiIkWyNGKClGLiIiJEYoRigqJkYyRigpRi5GJ0YoRigqJkYvRihGLkYoRihGKEYoRihGJUYoRigqLEYuRigsKCokRlVGKEYoRi5GKEYoRihGKCwoRllGKComRk9GKEYuRihGKEYoRihGKCksKComRk9GKEZSRihGKComRlNGKEZVRihGKEYoRjBGU0YoKSwoKiRGUkYoRigqJkZTRihGLkYoRjBGKEYwRlNGKEYw

algup:=collect(subs(t=tp/lcoeff(algu,t),-algu*(3*u-1)^3*(1+u)),tp,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGd1cEdGKCwoKiQpSSN0cEdGKCIiIyIiIkYzKiYsKComIiNGRjMpSSJ1R0YoIiIlRjMhIiIqJiIjPUYzKUY5RjJGM0YzRjNGM0YzRjFGM0YzKihGOUYzKSwmKiYiIiRGM0Y5RjNGM0YzRjtGQ0YzLCZGM0YzRjlGM0YzRjM3I0Yu

res:=factor(subs(RootOf(algup,tp)=tp,tp=t*lcoeff(algu,t),numer(factor(algz,RootOf(algup,tp)))))

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

collect(op(3,res),z,factor); collect(op(4,res),z,factor)

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

factor(discrim(%,z))

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

degree(%,t)

IiIi

is_hyperelliptic(algz,z,u)

SSZmYWxzZUclKnByb3RlY3RlZEc=

read(`Calculs/Hoeij/NormalBasis`); n := degree(algz,z);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJuR0YoIiIlNyNGLg==

alpha := RootOf(algz,z): V := Candidates(algz,u,z): select(has,V,z): nops(%);

IiIi

V

SSVGQUlMRyUqcHJvdGVjdGVkRw==

beta := select(has,V,z)[1];

Error, invalid subscript selector

beta := select(has,V,z)[1]: beta := subs(z=alpha, beta): m_beta := collect(evala(Norm(P - beta)),P,factor);

Error, invalid subscript selector

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdtX2JldGFHRigsJkkiUEdGKCIiIkklYmV0YUdGKCEiIjcjRi4=

algTvtalt

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

algTtvt:=subs(T=Tt/(2*v^3-4*v-1)/(2*v^3+3*v^2+6*v+1),algTvtalt)

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

IiIo

algTv3

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

JSFH

Now R(1) factor(subs(x=1,Delta));

LCQqJiwmKiYiIiUiIiJJInRHNiJGJ0YnRidGJ0YnLCYqJiIiKUYnRihGJ0YnRichIiJGJ0Yt

We start from the equation that relates R(x), S(x) and S(1/x) subs(x=1,S(1)=w*T-1/2,De=factor(subs(x=1,Delta)),R0=R0w,R1=R1w,R(1)=Rof1,op(1,eqRS)^2-subs(De=0,eqRS)^2)

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

res0:=numer(factor(%)): nops(%)

IiRNJA==

degree(res0,w)

IiIl

res1:=factor(rem(res0,algwv,w)):nops(res1);

IiQkSA==

factor(coeff(res1,w))

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

This suggests to write R(1)=U+t/3 collect(numer(factor(subs(Rof1=U-t/3,res1))),U,factor): coeff(%,w)

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

Even better: Rof1=U/w-t/3, numer(factor(subs(Rof1=U/w-t/3,res1))): res2:=op(2,factor(rem(%,algwv,w))): indets(res2); nops(res2)

PCZJIlRHNiJJIlVHRiRJInRHRiRJInZHRiQ=

IiRPIw==

res3:=numer(factor(resultant(res2,algTv3,T))):nops(res3);

IiIj

op(1,res3)

IiM7

res4:=factor(rem(res3,algv,t)): nops(%)

IiIo

map(indets,[seq(op(i,res4),i=1..nops(res4))])

Nyk8IjwjSSJ2RzYiRiRGJDwlSSJVR0YmSSJ0R0YmRiVGJEYk

res5:=op(5,res4): nops(%)

IiRiJw==

degree(res5,U)

IiIl

This is a square res4:=factor(resultant(res5,algv,t));nops(%);

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

IiIn

res5:=collect(op(1,op(5,res4)),U,factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVyZXM1R0YoLCgqLCIiKiIiIiksKComIiIlRjEpSSJ2R0YoIiIkRjFGMSomRjhGMSlGNyIiI0YxRjFGMSEiIkY4RjEpLCgqJkY7RjFGNkYxRjEqJkY1RjFGN0YxRjxGMUY8RjtGMSwoKiRGOkYxRjFGQEYxRjFGMUYxKUkiVUdGKEY7RjFGMSouRjhGMSwmKiZGO0YxRjdGMUYxRjFGMUYxLCoqJkY1RjEpRjdGNUYxRjFGNEYxRkBGPEYxRjxGMSw4KiYiIztGMSlGNyIjNUYxRjEqJiIkLyJGMSlGN0YwRjFGPComIiRSJEYxKUY3IiIpRjFGPComIiQ/JEYxKUY3IiIoRjFGPComIiRPIkYxKUY3IiInRjFGMSomIiQpW0YxKUY3IiImRjFGMSomIiRFJUYxRkpGMUYxKiYiJFMjRjFGNkYxRjEqJiIjKSlGMUY6RjFGMSomRk1GMUY3RjFGMUYxRjFGMUY+RjFGREYxRjEqKkY3RjFGRkYxRkhGMSw+KiYiI2tGMSlGNyIjOEYxRjEqJiIkMyNGMSlGNyIjN0YxRjEqJiIkMyJGMSlGNyIjNkYxRjEqJiIkKFJGMUZORjFGPComIiQqXEYxRlJGMUY8KiYiJDklRjFGVUYxRjEqJiIlcjZGMUZZRjFGMSomIiQ5JkYxRmduRjFGMSomIiRwJ0YxRltvRjFGPComIiRqKkYxRkpGMUY8KiYiJD4mRjFGNkYxRjwqJiIkVCJGMUY6RjFGPComIiM+RjFGN0YxRjxGMUY8RjFGPDcjRi4=

factor(discrim(res5,U))

LCQqMiIiKiIiIiwmSSJ2RzYiRiVGJSEiIkYlLCYqJiIiI0YlRidGJUYlRiVGJUYlLCZGJ0YlRiVGJUYlLCoqJkYsRiUpRiciIiRGJUYlKiZGMUYlKUYnRixGJUYlKiYiIidGJUYnRiVGJUYlRiVGJSwqKiYiIiVGJSlGJ0Y4RiVGJSomRjhGJUYwRiVGJSomRjhGJUYnRiVGKUYlRilGJSksKEYvRiVGO0YpRiVGKUYsRiUpLDgqJiIjJypGJSlGJyIjNUYlRiUqJiIkcyNGJSlGJ0YkRiVGJSomIiRZJUYlKUYnIiIpRiVGJSomIiQlUUYlKUYnIiIoRiVGJSomRjFGJSlGJ0Y1RiVGJSomIiRrJUYlKUYnIiImRiVGKSomIiRgJkYlRjlGJUYpKiYiJClIRiVGMEYlRikqJiIjKClGJUYzRiVGKSomIiM5RiVGJ0YlRilGJUYpRixGJUYl

algvp:=tp^2+(-8*v^12-72*v^11-336*v^10-652*v^9-675*v^8-288*v^7+168*v^6+432*v^5+450*v^4+248*v^3+72*v^2+12*v+1)*tp-v*(v^2+v+1)*(v^2+4*v+1)*(4*v^3+3*v^2-1)^3*(v^3-3*v-1)^3

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

res:=numer(subs(RootOf(algvp,tp)=tp,tp=t*lcoeff(algv,t),factor(res5,{RootOf(algvp,tp)}))); nops(res)

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

IiIj

Usolens:=factor([solve(%%,U)])

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

The correct value of U n:=4: map(Z->series(subs(v=vser(n),Z),t,n),Usolens)

NyQrK0kidEc2IiMiIiIiIiRGJ0YnIiIjIyIjNUYoRigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNGJyIiJSstRiRGJiIiISMiIzhGKEYnIiNQRikiJDEkRihGLEYy

series(wser(n)*(subs(x=1,Rex(n))+t/3),t,n)

KytJInRHNiIjIiIiIiIkRiZGJiIiIyMiIzVGJ0YnLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiYiIiU=

Usoltv:=Usolens[1]

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

collect(numer(Usoltv),t,factor);

LCYqJiw4KiYiIycqIiIiKUkidkc2IiIjNUYnISIiKiYiJHMjRicpRikiIipGJ0YsKiYiJFklRicpRikiIilGJ0YsKiYiJCVRRicpRikiIihGJ0YsKiYiIiRGJylGKSIiJ0YnRiwqJiIkayVGJylGKSIiJkYnRicqJiIkYCZGJylGKSIiJUYnRicqJiIkKUhGJylGKUY6RidGJyomIiMoKUYnKUYpIiIjRidGJyomIiM5RidGKUYnRidGJ0YnRidJInRHRipGJ0YnKipGKUYnLCZGKUYnRidGJ0YnLCoqJkZLRidGR0YnRicqJkZERidGSkYnRicqJkZARidGKUYnRidGJ0YnRicsMComRkRGJ0Y7RidGJyomRjpGJ0Y/RidGJyomRjRGJ0ZDRidGLComRjxGJ0ZHRidGLComIiM3RidGSkYnRicqJiIjNkYnRilGJ0YnRktGJ0YnRiw=

denom(Usoltv)

LCQqKiIiJCIiIiwoKiYiIiNGJSlJInZHNiJGJEYlRiUqJiIiJUYlRipGJSEiIkYlRi5GJSwsKiQpRipGLUYlRiUqJiIiKUYlRilGJUYlKiYiIidGJSlGKkYoRiVGJSomRihGJUYqRiVGJUYlRiVGJSwqRidGJSomRiRGJUY2RiVGJSomRjVGJUYqRiVGJUYlRiVGJUYl

Rof1sol:=Usoltv/w-t/3

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

n:=10:series(subs(w=wser(n),v=vser(n),Rof1sol)-subs(x=1,Rex(n)),t,n)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

Any simplifications? Nope... subs(troot=t,factor(evala(Normal(subs(t=troot,(1-8*t)*Usoltv)))))

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

Rof1sol := -(96*t*v^10+8*v^11+272*t*v^9+30*v^10+446*t*v^8+38*v^9+384*t*v^7-9*v^8+3*t*v^6-62*v^7-464*t*v^5-5*v^6-553*t*v^4+134*v^5-298*t*v^3+177*v^4-87*t*v^2+96*v^3-14*t*v+23*v^2-t+2*v)/((3*(2*v^3-4*v-1))*(v^4+8*v^3+6*v^2+2*v+1)*(2*v^3+3*v^2+6*v+1)*w)-(1/3)*t

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShSb2Yxc29sR0YoLCYqLiMiIiIiIiRGMSxOKigiIycqRjFJInRHRihGMSlJInZHRigiIzVGMUYxKiYiIilGMSlGOCIjNkYxRjEqKCIkcyNGMUY2RjEpRjgiIipGMUYxKiYiI0lGMUY3RjFGMSooIiRZJUYxRjZGMSlGOEY7RjFGMSomIiNRRjFGQEYxRjEqKCIkJVFGMUY2RjEpRjgiIihGMUYxKiZGQUYxRkZGMSEiIiooRjJGMUY2RjEpRjgiIidGMUYxKiYiI2lGMUZLRjFGTiooIiRrJUYxRjZGMSlGOCIiJkYxRk4qJkZXRjFGUEYxRk4qKCIkYCZGMUY2RjEpRjgiIiVGMUZOKiYiJE0iRjFGVkYxRjEqKCIkKUhGMUY2RjEpRjhGMkYxRk4qJiIkeCJGMUZlbkYxRjEqKCIjKClGMUY2RjEpRjgiIiNGMUZOKiZGNUYxRltvRjFGMSooIiM5RjFGNkYxRjhGMUZOKiYiI0JGMUZgb0YxRjFGNkZOKiZGYW9GMUY4RjFGMUYxLCgqJkZhb0YxRltvRjFGMSomRmZuRjFGOEYxRk5GMUZORk4sLCokRmVuRjFGMSomRjtGMUZbb0YxRjEqJkZRRjFGYG9GMUYxRmdvRjFGMUYxRk4sKkZpb0YxKiZGMkYxRmBvRjFGMSomRlFGMUY4RjFGMUYxRjFGTkkid0dGKEZORk4qJkYwRjFGNkYxRk43I0Yu

unassign('M'): eqM:=-t*(x*y^2+x-2*y)*M(0, 0)/(2*x*y^2)-(t*x*y^2+2*t*y^2+t*x+2*t*y-x*y+2*t)*M(0, y)/(2*x*y)-t*(x^2+x+1)*M(x, 0)/(x*y)+(t*x^2*y^2+t*x^2*y+t*x*y^2+t*x^2+t*y^2+t*x+t*y-x*y+t)*M(x, y)/(x*y)+t*(y^2+y+1)*M(y, 0)/(2*y^2)-t*(D[1](M))(0, 0)/(2*y)+(1/3)*x;

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

eqMof11:=subs(x=1,y=1,(D[1](M))(0, 0)=R1/t^2,M(0,1)=S(1)/t,M(1,0)=R(1)/t^2,eqM)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlcU1vZjExR0YoLCwjIiIiIiIkRjAqKiNGMCIiI0YwLCZGMCEiIiomIiIpRjBJInRHRihGMEYwRjAtSSJTR0YoNiNGMEYwRjlGNkY2KigjRjFGNEYwRjlGNi1JIlJHRihGPEYwRjYqJkY1RjAtSSJNR0YoNiRGMEYwRjBGMCooRjNGMEY5RjZJI1IxR0YoRjBGNjcjRi4=

We denote Mof11=M11norm/(1-8*t) subs(R1=R1w,R(1)=Rof1sol,S(1)=w*T-1/2,M(1,1)=Mof11,Mof11=M11norm/(1-8*t),eqMof11)

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

We have an expression, let us compute the degree res:=factor(1/(1-8*t)^2*resultant(numer(%),algwv,w)): nops(res); degree(res,M11norm)

IiQ5JA==

IiIj

res1:=factor(resultant(res,algTv3,T)): nops(res1)

IiIl

map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyY8IjwlSShNMTFub3JtRzYiSSJ0R0YmSSJ2R0YmPCNGKDwjRic=

res2:=op(2,res1): nops(%); degree(%%,M11norm)

IiV1OA==

IiIl

res3:=factor(rem(res2,algv,t)): nops(%)

IiIo

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyk8IjwjSSJ2RzYiRiRGJDwlSShNMTFub3JtR0YmSSJ0R0YmRiVGJEYk

res4:=op(5,res3): nops(%)

IiQwKA==

degree(res4,M11norm)

IiIl

res5:=factor(resultant(res4,algv,v)):nops(%)

IiIn

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Nyg8IjwjSSJ0RzYiRiRGJEYkPCRJKE0xMW5vcm1HRiZGJQ==

res6:=op(6,res5): nops(%)

IiUlcCM=

degree(res6,M11norm);

IiNb

algM11norm:=res6: nops(%)

IiUlcCM=

res7:=numer(factor(subs(M11norm=(1-8*t)*Mof11,res6))): nops(%)

IiIj

op(1,res7)

KiQpLCYiIiIhIiIqJiIiKUYlSSJ0RzYiRiVGJSIjQ0Yl

algMof11:=op(2,res7): nops(%)

IiUlcCM=

Let us check n:=10: series(subs(Mof11=subs(x=1,y=1,Mex(n)),algMof11),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

PexprM := M(x, y)/x-M(0, y)/x+M(y, x)/y-M(0, x)/y

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdQZXhwck1HRigsKiomLUkiTUdGKDYkSSJ4R0YoSSJ5R0YoIiIiRjMhIiJGNSomLUYxNiQiIiFGNEY1RjNGNkY2KiYtRjE2JEY0RjNGNUY0RjZGNSomLUYxNiRGOkYzRjVGNEY2RjY3I0Yu

eqPof11:=Pof11-subs(x=1,y=1,M(0,1)=S(1)/t,M(1,1)=Mof11,%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlcVBvZjExR0YoLChJJlBvZjExR0YoIiIiKiYiIiNGMEkmTW9mMTFHRihGMCEiIiooRjJGMC1JIlNHRig2I0YwRjBJInRHRihGNEYwNyNGLg==

eqMof11

LCwjIiIiIiIkRiQqKiNGJCIiI0YkLCZGJCEiIiomIiIpRiRJInRHNiJGJEYkRiQtSSJTR0YuNiNGJEYkRi1GKkYqKigjRiVGKEYkRi1GKi1JIlJHRi5GMUYkRioqJkYpRiQtSSJNR0YuNiRGJEYkRiRGJCooRidGJEYtRipJI1IxR0YuRiRGKg==

collect(subs(Mof11=solve(%,M(1,1)),eqPof11*(1-8*t)),[S,R1,Pof11,R],factor)

LCwqKCwmIiIiISIiKiYiIilGJUkidEc2IkYlRiVGJS1JIlNHRio2I0YlRiVGKUYmRiYqJkYpRiZJI1IxR0YqRiVGJSomLCZGJUYlRidGJkYlSSZQb2YxMUdGKkYlRiUjIiIjIiIkRiYqKEY1RiVGKUYmLUkiUkdGKkYtRiVGJQ==

subs(R1=R1w,R(1)=Rof1sol,S(1)=w*T-1/2,Pof11=P11norm/(1-8*t),%)

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

res:=numer(factor(1/(1-8*t)^2*resultant(numer(%),algwv,w))): nops(res); degree(res,P11norm)

IiQ5JA==

IiIj

res1:=factor(resultant(res,algTv3,T)): nops(res1)

IiIl

map(indets,[seq(op(i,res1),i=1..nops(res1))])

NyY8IjwlSShQMTFub3JtRzYiSSJ0R0YmSSJ2R0YmPCNGKDwjRic=

res2:=op(2,res1): nops(%); degree(%%,P11norm)

IiVwOA==

IiIl

res3:=factor(rem(res2,algv,t)): nops(%)

IiIo

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyk8IjwjSSJ2RzYiRiRGJDwlSShQMTFub3JtR0YmSSJ0R0YmRiVGJEYk

res4:=op(5,res3): nops(%)

IiQuKA==

degree(res4,P11norm)

IiIl

res5:=factor(resultant(res4,algv,v)):nops(%)

IiIn

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Nyg8IjwjSSJ0RzYiRiRGJEYkPCRJKFAxMW5vcm1HRiZGJQ==

res6:=op(6,res5): nops(%)

IiUicCM=

degree(res6,P11norm);

IiNb

algP11norm:=res6: nops(%)

IiUicCM=

res7:=numer(factor(subs(P11norm=(1-8*t)*Pof11,res6))): nops(%)

IiIj

op(1,res7)

KiQpLCYiIiIhIiIqJiIiKUYlSSJ0RzYiRiVGJSIjQ0Yl

algPof11:=op(2,res7): nops(%)

IiUicCM=

Let us check n:=10: series(subs(Pof11=subs(x=1,y=1,Pex(n)),algPof11),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

eqAof11:=Aof11-Pof11-2*Mof11

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlcUFvZjExR0YoLChJJkFvZjExR0YoIiIiSSZQb2YxMUdGKCEiIiomIiIjRjBJJk1vZjExR0YoRjBGMjcjRi4=

eqPof11

LChJJlBvZjExRzYiIiIiKiYiIiNGJUkmTW9mMTFHRiRGJSEiIiooRidGJS1JIlNHRiQ2I0YlRiVJInRHRiRGKUYl

%%+%

LChJJkFvZjExRzYiIiIiKiYiIiVGJUkmTW9mMTFHRiRGJSEiIiooIiIjRiUtSSJTR0YkNiNGJUYlSSJ0R0YkRilGJQ==

subs(M(1,1)=Mof11,eqMof11)

LCwjIiIiIiIkRiQqKiNGJCIiI0YkLCZGJCEiIiomIiIpRiRJInRHNiJGJEYkRiQtSSJTR0YuNiNGJEYkRi1GKkYqKigjRiVGKEYkRi1GKi1JIlJHRi5GMUYkRioqJkYpRiRJJk1vZjExR0YuRiRGJCooRidGJEYtRipJI1IxR0YuRiRGKg==

No S(1) here ! eqAof11:=collect((1-8*t)*%%-4*%,[R,R1,Aof11,A],factor)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShlcUFvZjExR0YoLCoqKCIiJyIiIkkidEdGKCEiIi1JIlJHRig2I0YxRjFGMSooIiIjRjFGMkYzSSNSMUdGKEYxRjEjIiIlIiIkRjMqJiwmRjFGMSomIiIpRjFGMkYxRjNGMUkmQW9mMTFHRihGMUYxNyNGLg==

subs(R1=R1w,R(1)=Rof1sol,Aof11=A11norm/(1-8*t),%)

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

collect(%,[A11norm,w],factor)

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

Let us work out te degree over Q(t) res:=numer(factor(resultant(numer(%),algwv,w))): nops(res); degree(res,A11norm)

IiRcIg==

IiIj

res3:=factor(rem(res,algv,t)): nops(%)

IiIo

map(indets,[seq(op(i,res3),i=1..nops(res3))])

Nyk8IjwjSSJ2RzYiRiRGJDwlSShBMTFub3JtR0YmSSJ0R0YmRiVGJEYk

res4:=op(5,res3): nops(%)

IiRgIg==

degree(res4,A11norm)

IiIj

res5:=factor(resultant(res4,algv,v)):nops(%)

IiIn

map(indets,[seq(op(i,res5),i=1..nops(res5))])

Nyg8IjwjSSJ0RzYiRiRGJEYkPCRJKEExMW5vcm1HRiZGJQ==

res6:=op(6,res5): nops(%)

IiRDJw==

degree(res6,A11norm);

IiND

algA11norm:=res6: nops(%)

IiRDJw==

res7:=numer(factor(subs(A11norm=(1-8*t)*Aof11,res6))): nops(%)

IiIj

op(1,res7)

KiQpLCYiIiIhIiIqJiIiKUYlSSJ0RzYiRiVGJSIjN0Yl

algAof11:=op(2,res7): nops(%)

IiRDJw==

Let us check n:=10: series(subs(Aof11=subs(x=1,y=1,Aex(n)),algAof11),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzY=

Closed form expression Aof11sol:=collect(solve(subs(R1=R1w,R(1)=Rof1sol,eqAof11),Aof11),w,factor)

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

That's better factor(subs(troot=t,evala(Normal(subs(t=troot,t*(1-2*t)*op(2,Aof11sol))))))

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

op(2,Aof11sol)

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

Aof11sol:=subsop(2=%%/t/(1-2*t),Aof11sol)

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

n:=10: series(subs(x=1,y=1,Aex(n))-subs(w=wser(n),v=vser(n),Aof11sol),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

Aof11sol:=op(1,Aof11sol)+op(2,Aof11sol)/(4*v^4+4*v^3-4*v-1)*(-w^2)

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

n:=10: series(subs(x=1,y=1,Aex(n))-subs(w=wser(n),v=vser(n),Aof11sol),t,n+1)

KyVJInRHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIzU=

collect(numer(op(2,Aof11sol))/w,t,factor)

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denom(op(2,Aof11sol))

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Aof11sol

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limit(limit(PexprM,x=0),y=0)

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n:=10:subs(x=0,y=0,Pex(n))

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series(subs(w=wser(n),v=vser(n),2*R1w/t^2),t,n)

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A00sol:=2*R1/t^2

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R1w

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factor(subs(S(x)=x*T,1/x*numer(eqScat)));; factor(series(%,x,2))

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

factor(discrim(algu,u)); factor(lcoeff(algu,u))

LCQqLCImJG8+IiIiKSwmSSJ0RzYiRiVGJUYlIiIjRiUpLCZGJSEiIiomIiIpRiVGKEYlRiVGKkYlKSwmKiYiIiVGJUYoRiVGJUYlRiVGM0YlKUYoRipGJUYt

LCQqKCIjRiIiIkkidEc2IkYlLCZGJkYlRiVGJUYlISIi

First possible singularity at tc=1/8 with(plots): user(4)

Ky1JInRHNiIiIiJGJUYlIiIjIiM1IiIkIiNZIiIlLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjRiUiIiY=

implicitplot(algu,t=-1/4..1/6,u=-1.2..1,numpoints=10000)

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with(gfun): Around 1/8, we see the two real branches. We denote epsilon=(1-8t) map(allvalues,algeqtoseries(subs(t=1/8*(1-epsilon),algu),epsilon,u,2));nops(%)

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IiIl

using:=op(3,map(allvalues,algeqtoseries(subs(t=1/8*(1-epsilon),algu),epsilon,u,8)))

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v is not singular when u=1/3, and has a larger radius of convergence (in u) factor(discrim(algvu,v));lcoeff(algvu,v);fsolve(%%)

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LCZJInVHNiIhIiIiIiJGJQ==

NiQkISsiSCskPSQqISM1JCIrXnFPLXRGJQ==

implicitplot(algvu,u=-1..1,v=-1..1,numpoints=10000)

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implicitplot(algv,t=-1..1/6,v=-1..1,numpoints=10000); implicitplot(algv,t=-1/4..1/7,v=-0.1..1,numpoints=10000)

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algvu;-numer(factor(subs(u=1/3,algvu))); fsolve(%)

LCYqJkkidUc2IiIiIiwoKiQpSSJ2R0YlIiIkRiYhIiIqJkYrRiZGKkYmRiZGJkYmRiZGJiomRipGJiwoKiQpRioiIiNGJkYmRipGJkYmRiZGJkYs

LCgqJiIiJSIiIilJInZHNiIiIiRGJUYlKiZGKUYlKUYnIiIjRiVGJUYlISIi

JCIrNi81YVghIzU=

The critical value of v alias(vs=RootOf(4*_Z^3+3*_Z^2-1))

NiVJJ3Ryb290dUc2IkkmdHJvb3RHRiRJI3ZzR0Yk

Now eta=1-3u vsingeta:=op(algeqtoseries(subs(u=1/3*(1-eta),algvu),eta,v,6))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSl2c2luZ2V0YUdGKCsxSSRldGFHRihJI3ZzR0YoIiIhLCYqJiMiIiIiIiNGNUYwRjUhIiIqJClGMEY2RjVGN0Y1LCYqJiNGNSIiKUY1RjBGNUY3KiYjRjUiIiVGNUY5RjVGN0Y2LCgqJiNGNSIjW0Y1RjBGNUY1KiYjIiImRkRGNUY5RjVGN0ZDRjUiIiQsKComIyIjRCIkJVFGNUYwRjVGNSomI0ZHIiQjPkY1RjlGNUY1I0Y1IiMnKkY1RkAsKComIyIjWiIkbyhGNUYwRjVGNSomIyIjTkZXRjVGOUY1RjUjRkdGV0Y1RkctSSJPR0YlNiNGNSIiJzcjRi4=

etasing:=simplify(series(1-3*using,epsilon,20))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShldGFzaW5nR0YoLDIqKCMiIiMiIiQiIiIpIiInI0YzRjJGMylJKGVwc2lsb25HRihGNkYzRjMqKCNGMyIiKkYzKUY1RjBGMylGOEYwRjMhIiIqJkY6RjNGOEYzRj4qKCMiI1QiJGkiRjNGNEYzKUY4IyIiJUYyRjNGMyooIyIjTiIkJ1tGM0Y8RjMpRjgjIiImRjJGM0Y+KiYjRkkiJEMkRjMpRjhGMUYzRj4qKCMiJEQoIiV1VkYzRjRGMylGOCMiIihGMkYzRjMtSSJPR0YlNiMqJClGOCMiIilGMkYzRjM3I0Yu

vsingepsilon:=map(factor,series(subs(eta=etasing,vsingeta),epsilon,20))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SS12c2luZ2Vwc2lsb25HRigsLkkjdnNHRigiIiIqLCNGMCIiJEYwRi9GMCwmRjBGMComIiIjRjBGL0YwRjBGMCkiIidGMkYwKUkoZXBzaWxvbkdGKEYyRjAhIiIqKCNGMCIjYUYwLCgqJiIiKUYwKUYvRjZGMEYwKiYiIzZGMEYvRjBGMEY2RjBGMEY6RjBGMCoqI0YwIiRDJEYwRjdGMCwoKiYiI09GMEZCRjBGMComIiM+RjBGL0YwRjBGNkYwRjApRjojIiIlRjNGMEY7KipGRkYwKUY4I0Y2RjNGMCwoKiRGQkYwRjAqJkZPRjBGL0YwRjBGMEYwRjApRjojIiImRjNGMEY7LUkiT0dGJTYjKiQpRjpGNkYwRjA3I0Yu

and w is not singular when v reaches v_sing subs(w=0,algwv); fsolve(%)

LCoqJiIiJSIiIilJInZHNiJGJEYlRiUqJkYkRiUpRiciIiRGJUYlKiZGJEYlRidGJSEiIkYlRi0=

NiQkIStuZXFNRSEjNSQiK10oXCQpUilGJQ==

wsingdelta:=simplify(subs(signum(-4*vs^4-4*vs^3+4*vs+1)=1,series(subs(v=vs*(1-delta),subs(w=0,sqrt(-algwv))),delta,10)))

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

deltasing:=simplify(series(1-vsingeta/vs,eta,30))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpkZWx0YXNpbmdHRigrL0kkZXRhR0YoLCYjIiIiIiIjRjJJI3ZzR0YoRjJGMiwmI0YyIiIpRjIqJiNGMiIiJUYyRjRGMkYyRjMsKComI0YyIiM3RjIpRjRGM0YyISIiKiYjRjIiI0NGMkY0RjJGMiNGMiIjW0ZAIiIkLCgqJkZCRjJGP0YyRkAqJiMiIzYiJCM+RjJGNEYyRkAjIiNEIiQlUUZARjosKComIyIiJkZMRjJGP0YyRkAqJkZNRjJGNEYyRkAjIiNaIiRvKEZARlMtSSJPR0YlNiNGMiIiJzcjRi4=

wsingeta:=map(simplify,map(factor,series(subs(delta=%,%%),eta,20)))

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

map(simplify,series(subs(eta=etasing,%),epsilon,20))

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

wsingepsilon:=map(factor,series(map(Z->evala(Normal(Z)),%),epsilon,20))

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

Now A(1,1) Aof11sol

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

We proceed in two steps (numerator, then denomnator) map(factor,map(Z->evala(Normal(Z)),map(simplify,series(subs(t=1/8*(1-epsilon), w=wsingepsilon,v=vsingepsilon,numer(Aof11sol)),epsilon,17))))

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

map(factor,map(Z->evala(Normal(Z)),map(simplify,series(subs(t=1/8*(1-epsilon), w=wsingepsilon,v=vsingepsilon,denom(Aof11sol)),epsilon,17))))

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

map(factor,map(Z->evala(Normal(Z)),map(simplify,series(%%/%,epsilon,17))))

LDQqLCMiIzsiJUZGIiIiKSwoKiYiIiRGJylJI3ZzRzYiIiIjRidGJyomIiM3RidGLUYnRidGK0YnI0YnRi9GJykiIicjRidGK0YnKUkoZXBzaWxvbkdGLiNGL0YrISIiLCgqJiIjR0YnRixGJ0YnKiYiI2hGJ0YtRidGJyIjJylGOUYnRjkjIiIpRitGOSooIyIlV2AiJyJHRSlGJ0YoRidGLEYnRjkqKCMiJytFVUZFRidGKEYnRi1GJ0YnKiYjIid3MURGRUYnRihGJ0YnKiwjIig/Xi8iIihIbFYoRidGKEYnRjNGJ0YsRicpRjdGNUYnRjkqLCMiKF96cCNGT0YnRihGJ0YzRidGLUYnRlBGJ0Y5KiojIihbRylIRk9GJ0YoRidGM0YnRlBGJ0YnLUkiT0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGLjYjKiRGNkYnRic=

Aof11ser:=map(factor,series(%,epsilon))

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

What is the degree of this number over Q? at most 18 co0:=op(1,Aof11ser)*epsilon^(2/3)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRjbzBHRigsJCoqIyIjOyIlRkYiIiIpLCgqJiIiJEYzKUkjdnNHRigiIiNGM0YzKiYiIzdGM0Y5RjNGM0Y3RjMjRjNGOkYzKSIiJyNGM0Y3RjMsKComIiNHRjNGOEYzRjMqJiIjaEYzRjlGM0YzIiMnKSEiIkYzRkc3I0Yu

res:=numer(factor(resultant(subs(vs=v,co0^2-c0^2), subs(t=1/8,algv),v)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRyZXNHRigsJComKSwqKigiKStjYVYiIiIpIiInIyIiIyIiJEY0KUkjYzBHRigiIiVGNEY0KiYiKShlNEIjRjQpRjtGNkY0RjQqKCIqT3pnNCZGNClGNiNGNEY5RjQpRjtGOEY0RjQiKydIblxIJSEiIkY5RjRGOkY0RkY3I0Yu

op(1,op(2,res)); subs(c0=6^(1/3)*co1,%); ifactor([coeffs(%/4)]); subs(co1= 2^(15/3)*co2/3^(3/2),%%/2^32);ifactor([coeffs(%)]);

LCoqKCIpK2NhViIiIikiIicjIiIjIiIkRiUpSSNjMEc2IiIiJUYlRiUqJiIpKGU0QiNGJSlGLEYnRiVGJSooIipPemc0JkYlKUYnI0YlRipGJSlGLEYpRiVGJSIrJ0huXEglISIi

LCoqJiIqS145LikiIiIpSSRjbzFHNiIiIidGJUYlKiYiKys7a246RiUpRiciIiVGJUYlKiYiKzt3a2RJRiUpRiciIiNGJUYlIisnSG5cSCUhIiI=

NyYqJiktSSFHNiI2IyIiJCIiKiIiIiktRiY2IyIkLCIiIiNGKyoqKS1GJjYjRjAiIzVGKylGJSIiKEYrKS1GJjYjIiImRjBGKy1GJjYjRjdGKyomKUYzIiM/RispRiUiIidGKywkKiQpRjMiI0lGKyEiIg==

LCoqJiImLC0iIiIiKUkkY28yRzYiIiInRiVGJSomIiREJkYlKUYnIiIlRiVGJSomIiNGRiUpRiciIiNGJUYlRiUhIiI=

NyYqJCktSSFHNiI2IyIkLCIiIiMiIiIqKC1GJjYjIiIkRispLUYmNiMiIiZGKkYrLUYmNiMiIihGKyokKUYtRi9GKyEiIg==

The degree over Q is really 18. Another way to write this Kexpr:=co0^6/2^32*3^7;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZLZXhwckdGKCwkKigjIiIiIjQ3cClRJj5uNHNMIkYxKSwoKiYiIiRGMSlJI3ZzR0YoIiIjRjFGMSomIiM3RjFGOEYxRjFGNkYxRjZGMSksKComIiNHRjFGN0YxRjEqJiIjaEYxRjhGMUYxIiMnKSEiIiIiJ0YxRjE3I0Yu

numer(factor(resultant(subs(vs=v,Ks-Kexpr),subs(t=1/8,algv),v)))

LCQqKCIzQCIqKnBITlk0XSIiIiIpSSNLc0c2IiIiI0YlKSwqKiYiLiwxOj86MSJGJSlGJyIiJEYlRiUqJiIqLmNGLCdGJUYmRiUhIiIqJiImNkcqRiVGJ0YlRiVGJUYyRi9GJUYl

algKs:=op(1,op(3,%)); [coeffs(%)]:ifactor(%)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdLc0dGKCwqKiYiLiwxOj86MSIiIiIpSSNLc0dGKCIiJEYxRjEqJiIqLmNGLCdGMSlGMyIiI0YxISIiKiYiJjZHKkYxRjNGMUYxRjFGOTcjRi4=

NyYqJCktSSFHNiI2IyIkLCIiIiciIiIsJComLUYmNiMiIiRGKy1GJjYjIiosX1UrI0YrISIiKiZGLkYrLUYmNiMiJlA0JEYrRjQ=

fsolve(1061520150601*Ks^3-601275603*Ks^2+92811*Ks-1)

JCIrI0dNTDsiISM5

Now A_{0,0} A00sol:=2*R1w/t^2

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdBMDBzb2xHRigsJCooIiIjIiIiLCgjRjEiIidGMSomI0YxIiIkRjFJInRHRihGMUYxKjBGM0YxLCYqJkYwRjFJInZHRihGMUYxRjFGMUYxLCZGMUYxKiZGMEYxRjhGMSEiIkYxLDAqJiIjO0YxKUY8RjRGMUYxKiYiI0NGMSlGPCIiJkYxRjEqJiIiKEYxKUY8IiIlRjFGMSomRkVGMSlGPEY3RjFGPyomIiNJRjEpRjxGMEYxRj8qJiIjNUYxRjxGMUY/RjFGP0YxSSJ3R0YoRj8sKComRjBGMUZNRjFGPyomRktGMUY8RjFGMUYxRjFGPywsKiRGSkYxRjEqJiIiKUYxRk1GMUYxKiZGNEYxRlBGMUYxRjtGMUYxRjFGP0YxRjEpRjhGMEY/RjE3I0Yu

map(factor,map(Z->evala(Normal(Z)),map(simplify,series(subs(t=1/8*(1-epsilon), w=wsingepsilon,v=vsingepsilon,numer(A00sol)),epsilon,17))))

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

map(factor,map(Z->evala(Normal(Z)),map(simplify,series(subs(t=1/8*(1-epsilon), w=wsingepsilon,v=vsingepsilon,denom(A00sol)),epsilon,17))))

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

map(factor,map(Z->evala(Normal(Z)),map(simplify,series(%%/%,epsilon,17))))

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

A00sing:=map(factor,series(%,epsilon))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SShBMDBzaW5nR0YoLDQqKCMiJktTIyIlRkYiIiIpLCgqJiIiJEYzKUkjdnNHRigiIiNGM0YzKiYiIzdGM0Y5RjNGM0Y3RjMjRjNGOkYzRjlGMyEiIiooIyIla1tGMkYzRjRGM0Y4RjNGMyomIyImM0siRjJGM0Y0RjNGPiMiIyEpRjdGMyosIyIkYyMiJyJHRSlGM0Y0RjMpIiInI0Y6RjdGMywoKiYiJTtuRjNGOEYzRjMqJiIlbEBGM0Y5RjNGMyIlI2UiRj5GMylJKGVwc2lsb25HRihGTUYzRj4qKCMiIikiKFYpeUNGMywqIillSShbIkYzKigiJzN1KClGM0Y0RjNGOEYzRjMqKCIoR3N5JUYzRjRGM0Y5RjNGPiomIihCaGEjRjNGNEYzRj5GM0ZVRjNGMyosIyIkRyIiKlZKT10jRjNGNEYzKUZMI0YzRjdGMylGVSMiIiVGN0YzLCgqJiInZ1lNRjNGOEYzRjMqJiInTiYpb0YzRjlGM0YzIidZJj0oRj5GM0YzKiwjIiVbPyIrKEdvS0QjRjNGNEYzRktGMylGVSMiIiZGN0YzLCgqJiIoJTNsW0YzRjhGM0YzKiYiKCZvazpGM0Y5RjNGMyIoV2NCIkY+RjNGPi1JIk9HRiU2IyokKUZVRjpGM0YzNyNGLg==

subs(sqrt(3*vs^2+12*vs+3)=wc,epsilon=(1-8*t),vs=vc,%)

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

1/GAMMA(-2/3)

LCQqKiMiIiIiIiRGJUkjUGlHJSpwcm90ZWN0ZWRHISIiKUYmI0YlIiIjRiUtSSZHQU1NQUc2JEYoSShfc3lzbGliRzYiNiMjRixGJkYlRik=

degree at most 18 again d0:=-op(5,A00sing)/epsilon^(2/3)/sqrt(3); evalf(d0)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNkMEdGKCwkKiwjIiRjIyIoVil5QyIiIiksKComIiIkRjMpSSN2c0dGKCIiI0YzRjMqJiIjN0YzRjlGM0YzRjdGMyNGM0Y6RjMpIiInI0Y6RjdGMywoKiYiJTtuRjNGOEYzRjMqJiIlbEBGM0Y5RjNGMyIlI2UiISIiRjMpRjdGPUYzRjM3I0Yu

JCIrMChlKD05ISIq

res:=numer(factor(resultant(subs(vs=v,d^6-d0^6),subs(t=1/8,algv),v)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRyZXNHRigqKClJImRHRigiIzciIiIpLCoqJiI4Ll1zNyMpUTJkKFE1NkYyKUYwIiIqRjJGMiomIjolKSpIIlxZISpbenB4UmEiRjIpRjAiIidGMkYyKiYiOzNRXU9qNy52VUVWXWVGMilGMCIiJEYyRjIiPEcwUmlWYHMxIlxdVVo6RjJGQEYyKSwqRjVGMkY5ISIiRj1GMkZBRkRGQEYyNyNGLg==

In fact, d0 has degree 9 only algd0:=op(1,op(3,res))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdkMEdGKCwqKiYiOC5dczcjKVEyZChRNTYiIiIpSSJkR0YoIiIqRjFGMSomIjolKSpIIlxZISpbenB4UmEiRjEpRjMiIidGMSEiIiomIjszUV1PajcudlVFVl1lRjEpRjMiIiRGMUYxIjxHMFJpVmBzMSJcXVVaOkY5NyNGLg==

algKK:=factor(subs(d=D0^(1/3),D0=2^29/3^7*KK,algd0/2^87))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdLS0dGKCwqKiYiLiwxOj86MSIiIiIpSSNLS0dGKCIiJEYxRjEqJiIqLmNGLCdGMSlGMyIiI0YxISIiKiYiJjZHKkYxRjNGMUYxRjFGOTcjRi4=

Same equation as before algKs

LCoqJiIuLDE6PzoxIiIiIilJI0tzRzYiIiIkRiVGJSomIiouY0YsJ0YlKUYnIiIjRiUhIiIqJiImNkcqRiVGJ0YlRiVGJUYu

The next coefficient 1/GAMMA(-4/3)

LCQqJiMiIiUiIioiIiItSSZHQU1NQUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIyIiIyIiJCEiIkYn

d1:=-op(7,A00sing)/epsilon^(4/3)/9*4; evalf(d1)

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNkMUdGKCwkKiojIiQ3JiIrKEdvS0QjIiIiKSwoKiYiIiRGMylJI3ZzR0YoIiIjRjNGMyomIiM3RjNGOUYzRjNGN0YzI0YzRjpGMykiIicjRjNGN0YzLCgqJiInZ1lNRjNGOEYzRjMqJiInTiYpb0YzRjlGM0YzIidZJj0oISIiRjNGRzcjRi4=

JCIrPywmNDolISM1

degree 18 res:=numer(factor(resultant(subs(vs=v,d^6-d1^6),subs(t=1/8,algv),v)))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRyZXNHRigqJilJImRHRigiIzciIiIpLCoqJiJccEIwdEApZUheZzhocmZyOUlSeTsoM3gjXEFMLCQpbyJwdilcSCpRZyNIOnk9R0YyKUYwIiM9RjJGMiomIlxwP0Z5NS9seEA5NDtKZiNSVSkzOz8udF1VKTNkW3ZtTV0hM2NWIkhMJUgnPmdGMkYvRjIhIiIqJiJccEtHLjJrIVElPWowSTJUKFJFdD9sUGFSbyRRNVglbzJ3eVElPXkuSUctIj1MRjIpRjAiIidGMkYyImpvYz1nR3FqXlIkZjk6Ikd1NXB0X2g5JiozWjtAYyxrT1VZOEFfXDJcO28iRjsiIiRGMjcjRi4=

algd1:=op(1,op(2,res))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZhbGdkMUdGKCwqKiYiXHBCMHRAKWVIXmc4aHJmcjlJUnk7KDN4I1xBTCwkKW8icHYpXEgqUWcjSDp5PUciIiIpSSJkR0YoIiM9RjFGMSomIlxwP0Z5NS9seEA5NDtKZiNSVSkzOz8udF1VKTNkW3ZtTV0hM2NWIkhMJUgnPmdGMSlGMyIjN0YxISIiKiYiXHBLRy4yayFRJT1qMEkyVChSRXQ/bFBhUm8kUTVYJW8yd3lRJT15LklHLSI9TEYxKUYzIiInRjFGMSJqb2M9Z0dxal5SJGY5OiJHdTVwdF9oOSYqM1o7QGMsa09VWThBX1wyXDtvIkY5NyNGLg==

algL:=factor(subs(d=(2^(62)*L/3^(31))^(1/6),algd1/2^186))

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVhbGdMR0YoLCoqJiJGLD1gPG8pKlw1eWdbbSdvdnU5Jz4iIiIiKUkiTEdGKCIiJEYxRjEqJiJCcVpyPz9NaDklUmlZdiUzOFUkRjEpRjMiIiNGMSEiIiomIj5UT29ULkFWTFMhPkMoZV8jRjFGM0YxRjEiOC8ya0lrW1p5dFhyIkY5NyNGLg==

ifactor([coeffs(algL)])

NyYqJCktSSFHNiI2IyIkLCIiIz0iIiIsJCouLUYmNiMiIiNGKy1GJjYjIiIkRistRiY2IyIiJkYrLUYmNiMiIzhGKy1GJjYjIiNIRistRiY2IyI+blpHIVtoJ2VROCIpZkhdLSRGKyEiIiouRjFGKy1GJjYjIig0cmEnRistRiY2IyIsKmZNNSJcIkYrLUYmNiMiJiwjR0YrLUYmNiMiJUA8RistRiY2IyIleDxGKywkKiYpRi4iIidGKyktRiY2IyIlUkRGVEYrRkA=

JSFH