|Bill Allombert on Mon, 17 Nov 2014 17:24:15 +0100|
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|New GP functions for modular polynomials|
Dear PARI developers, We have recently added three new GP functions in PARI GIT 2.8, implemented by Hamish Ivey-Law, using Sutherland algorithm: polmodular(l): return the canonical modular polynomial of level l prime. (unfortunately limited to l<=31 in 32bit) polclass(D): return the Hilbert class polynomial for the imaginary order. ellissupersingular(E): test whether E is supersingular (faster than ellap). Also this was the last missing piece for polynomial time point counting function for elliptic curve over GF(p^n) (ellcard). We use 5 different algorithms depending on n and p: - if p==2, we use Satoh-Mestre-Harley AGM algorithm - if p==3,5,7,13 we use Satoh-Harley-Kohel algorithm. otherwise: - if n<=p/2, we use SEA (Joux-Lercier variant). - if p/2<n<7/10*p we use Kedlaya algorith (following Gaudry-Gürel). - if n>=7/10*p, we use Satoh-Mestre-Harley algorithm (which requires polmodular(p)) So, please test (in 64bit). Cheers, Bill.