| 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.