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

(with Andrew Sutherland)

LMS J. Comput. Math. **17** (2014), Special Issue A, 257–273 (DOI).

(Proceedings of 11th Algorithmic Number Theory Symposium)

arXiv preprint (February 2014).

## 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}.

## Erratum

In step 2 of the RemainderTree algorithm, the variable *i* should go down to zero, not 1. (Thanks to Maike Massierer for catching this.)

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