Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time

Abstract

We present an efficient algorithm to compute the Hasse-Witt matrix of a hyperelliptic curve C/Q modulo all primes of good reduction up to a given bound N, based on the average polynomial-time algorithm recently introduced by Harvey. An implementation for hyperelliptic curves of genus 2 and 3 is more than an order of magnitude faster than alternative methods for N = 2^26.

17 pages

References in corpus (1)

• Kedlaya's algorithm in larger characteristic

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