The case q=3 (m=6,k=1) : an equation with a single catalytic variable (Section 13.1)
> | T:=proc(m) subs(cos(x)=x,expand(cos(m*x))): end: |
> | T(6); |
> | m:=6: k:=1: 2+2*cos(2*k*Pi/m); |
> | I2:=normal(subs(C=CC,II=I1,q=3,yinv=1/y,M(1,y)=M(y),normal(sqrt(C)^m*subs(x=xsubs,T(m))))): |
> | indets(I2); |
> | factor(series(normal(I2),y=1,1)); |
> | eqinv:=subs(M(1,y)=M(y),q=3,I2-add(c[i]*I1^i,i=0..6)): |
> | indets(eqinv); |
> |
> |
Determination of the series c_i. An equation with a single catalytic variable and 4 additional unknown series, M(1), M'(1),...,M'''(1)
> |
> | eqinvM; |
> |
The case nu=0 and w=1 (properly 3-coloured maps by edges) : the equation with one catalytic variable
> |
> |