Determination of the series c_i (and more): an equation with 4 unknown additional series
(counting near-triangulations with outer degree 1,3,5,7)
> |
> | factor(series(normal(eqinv),y,1)); |
> | c6sol:=factor(solve(coeff(%,y,-12),c[6])); |
> | factor(series(subs(c[6]=c6sol,normal(eqinv)),y,3)); |
> | c5sol:=factor(solve(coeff(%,y,-10),c[5])); |
> | factor(series(subs(c[6]=c6sol,c[5]=c5sol,normal(eqinv)),y,5)); |
> | c4sol:=factor(solve(coeff(%,y,-8),c[4])); |
> | factor(series(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,normal(eqinv)),y,6)); |
> | subs(Q(0)=1,factor(series(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,normal(eqinv)),y,7))); |
> | c3sol:=collect(factor(solve(coeff(%,y,-6),c[3])),[Q,t],factor); |
> | res:=factor(subs(Q(0)=1,factor(series(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,c[3]=c3sol,normal(eqinv)),y,9)))); |
> | D2Qsol:=factor(solve(coeff(res,y,-5),`@@`(D,2)(Q)(0))); |
> | c2sol:=collect(solve(subs(`@@`(D,2)(Q)(0)=D2Qsol,coeff(res,y,-4)),c[2]),[Q,t],factor); |
> | res:=factor(subs(Q(0)=1,`@@`(D,2)(Q)(0)=D2Qsol,factor(subs(series(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,normal(eqinv)),y,11))))); |
> | D4Qsol:=collect(factor(solve(coeff(res,y,-3),`@@`(D,4)(Q)(0))),[Q,t],factor); |
> | c1sol:=collect(solve(subs(`@@`(D,4)(Q)(0)=D4Qsol,`@@`(D,2)(Q)(0)=D2Qsol,coeff(res,y,-2)),c[1]),[Q,t],factor); |
> | res:=factor(subs(Q(0)=1,`@@`(D,2)(Q)(0)=D2Qsol,`@@`(D,4)(Q)(0)=D4Qsol,factor(series(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,normal(eqinv)),y,13)))); |
> | D6Qsol:=map(factor,collect(factor(solve(coeff(res,y,-1),`@@`(D,6)(Q)(0))),[Q,t],factor)); |
> | c0sol:=collect(solve(subs(`@@`(D,4)(Q)(0)=D4Qsol,`@@`(D,2)(Q)(0)=D2Qsol,`@@`(D,6)(Q)(0)=D6Qsol,coeff(res,y,0)),c[0]),[Q,t],factor); |
> | eqcat:=map(factor,collect(factor(subs(c[6]=c6sol,c[5]=c5sol,c[4]=c4sol,c[3]=c3sol,c[2]=c2sol,c[1]=c1sol,c[0]=c0sol,eqinv/t^3)),Q,distributed)): |
> | factor(subs(t=0,%)); |
> | res:=factor(eqcat): |
> | nops(res); |
> | op(1,res);op(2,res);op(4,res);op(5,res); |
> | eqcatQ:=collect(op(3,res),Q,factor); |
> |