b^b^x with base 0exp(-e), the two periodic fixed points are complex conjugate pairs. Code:/* formal period2 fixed point for generic function with slope=-1,  2-cyclic solution  */ /* gs=formalperiod2(-exp(x)+1,30)[1]; */ /* returns [series,x2term] */ \ps 31 kf(a)=log(-log(a))-1; fixedaaz(a,n) = {   if (n<>-1, n=1);  return((subst(gs,x,n*sqrt(kf(a)*6))-kf(a)-1)/log(a)); } formalperiod2(gf,n) = {   local(i,gs,savegs,zs,z,zt,x2term,m2,s2,r2);   savegs=0;   gs = x+aecoeff*x^2+O(x^4);   z = subst(gf,x,gs)-subst(gs,x,-x)+acoeff*x^2;   zs = subst(polcoeff(z,3),aecoeff,x);   zt = -polcoeff(zs,0)/polcoeff(zs,1);   savegs = x + zt*x^2;   gs=savegs;   z = subst(gf,x,gs)-subst(gs,x,-x)+acoeff*x^2;   zs = subst(polcoeff(z,2),acoeff,x);   zt = -polcoeff(zs,0)/polcoeff(zs,1);   x2term = zt;   m2 = matrix(2,2);   s2 = matrix(2,1);   forstep (i=3,n,2,     gs = savegs + aocoeff*x^i + aecoeff*x^(i+1)+O(x^(i+3));     z  = subst(gf,x,gs) - subst(gs,x,-x) + x2term*x^2;     zs = subst(polcoeff(z,i+1),aecoeff,x);     zs = subst(zs,aocoeff,0);     m2[1,1] =  polcoeff(zs,1);     zs = subst(polcoeff(z,i+1),aocoeff,x);     zs = subst(zs,aecoeff,0);     m2[1,2] =  polcoeff(zs,1);     s2[1,1] = -polcoeff(zs,0);     zs = subst(polcoeff(z,i+2),aecoeff,x);     zs = subst(zs,aocoeff,0);     m2[2,1] =  polcoeff(zs,1);     zs = subst(polcoeff(z,i+2),aocoeff,x);     zs = subst(zs,aecoeff,0);     m2[2,2] =  polcoeff(zs,1);     s2[2,1] = -polcoeff(zs,0);     r2 = matsolve(m2,s2);     savegs = savegs + r2[2,1]*x^i + r2[1,1]*x^(i+1);   );   return([savegs,x2term]); } gs = formalperiod2(-exp(x)+1,30)[1]; - Sheldon « Next Oldest | Next Newest »

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