Re: Introduction, Curve Algorithm

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Oct 09, 2018 at 02:40:25PM -0500, Brad Klee wrote:
> \\ Genus 2,  parity symmetric sextic ( Cf. OEIS: A006480 ).
> \\ 2F1 parameters: (a,b,c) = (1/3,2/3,1).
> PFData = HyperellipticPicardFuchs(-(1/4)*(18*x^2+48*x^4+32*x^6));
> [-PFData[3],CheckCertificate(PFData)]
> T=sum(n=0,100,(3*n)!/(n!)^3*(z/27)^n);
> [T,T',T'']*PFData[3]
> \\ [ [2, 18*z - 9, 9*z^2 - 9*z]~, 0]
> \\ BigInt*z^100
> \\ time delta = 8ms, fast!

Hello Brad,

If you want to define power series, do
T=sum(n=0,100,(3*n)!/(n!)^3*(z/27)^n)+O(z^101);
so you get
? [T,T',T'']*PFData[3]
%16 = O(z^100)

Using the numerical version:

Eqn=-PFData[3]
T(z)=hypergeom([1/3,2/3],[1],z);
h(z)=[T(z),T'(z),T''(z)]*subst(Eqn,'z,z);
sum(i=1,100,abs(h(i/1000)))
%24 = 5.450207108236383428E-37

Cheers,
Bill.