Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
2014 ◽
Vol 17
(A)
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pp. 257-273
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Keyword(s):
Genus 2
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AbstractWe present an efficient algorithm to compute the Hasse–Witt matrix of a hyperelliptic curve $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}C/\mathbb{Q}$ 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 $N = 2^{26}$.
2007 ◽
Vol 17
(02)
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pp. 289-328
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Keyword(s):
2011 ◽
Vol 22
(05)
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pp. 1197-1209
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Keyword(s):
Keyword(s):
Keyword(s):
2014 ◽
Vol 61
(1)
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pp. 51-78
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