Some new GP features
serdiffdep
Let S be a power series, seralgdep(S,p,r) finds a
polynomial equation of degree p with polynomial coefficients of
degree < r. satisfied by S, serdiffdep(S,p,r) finds an
(inhomogenous) linear equation of degree p with polynomial
coefficients of degree < r satisfied by S.
? S = sum(i=0,100,binomial(2*i,i)/(i+1)*T^(i+1))\
+ O(T^101);
? seralgdep(S,3,3)
%70 = x^2-x+T
? S^2-S+T
%71 = 0
? serdiffdep(S,3,3)
%72 = [(4*T-1)*x-2,-1]
? (4*T-1)*S’-2*S==-1
%73 = 1