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1999 Sieving in function fields
Ralf Flassenberg, Sachar Paulus
Experiment. Math. 8(4): 339-349 (1999).

Abstract

We present the first implementation of sieving techniques in the context of function fields. More precisely, we compute in class groups of quadratic congruence function fields by combining the algorithm of Hafner and McCurley with sieving ideas known from factoring. We apply our methods to the computation of generators and relations of the Jacobian variety of hyperelliptic curves over finite fields.

The algorithms introduced here were implemented in C++ with the help of LEDA and LiDIA. We provide examples of running times and comparisons with earlier algorithms.

Citation

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Ralf Flassenberg. Sachar Paulus. "Sieving in function fields." Experiment. Math. 8 (4) 339 - 349, 1999.

Information

Published: 1999
First available in Project Euclid: 9 March 2003

zbMATH: 0942.11047
MathSciNet: MR1737230

Subjects:
Primary: 11R65
Secondary: 11R58 , 11Y16

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 4 • 1999
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