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TitleAn extension of Kedlaya’s algorithm for hyperelliptic curves
Author(s) Michael Harrison
TypeArticle in Journal
AbstractIn this paper we describe a generalisation and adaptation of Kedlaya’s algorithm for computing the zeta-function of a hyperelliptic curve over a finite field of odd characteristic that the author used for the implementation of the algorithm in the Magma library. We generalise the algorithm to the case of an even degree model. We also analyse the adaptation of working with the x^i d x / y^3 rather than the x^i d x / y differential basis. This basis has the computational advantage of always leading to an integral transformation matrix whereas the latter fails to in small genus cases. There are some theoretical subtleties that arise in the even degree case where the two differential bases actually lead to different redundant eigenvalues that must be discarded.
KeywordsKedlaya’s algorithm, Monsky–Washnitzer cohomology, Magma
URL http://www.sciencedirect.com/science/article/pii/S0747717111001313
JournalJournal of Symbolic Computation
Pages89 - 101
Translation No
Refereed No