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

We present an efficient algorithm to compute the Hasse–Witt matrix of a hyperelliptic curve $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}C/Q$ modulo all primes of good reduction up to a given bound $N$ , based on the average polynomial-time algorithm recently proposed by the first author. An implementation for hyperelliptic curves of genus 2 and 3 is more than an order of magnitude faster than alternative methods for N = 2²⁶ .