A relative van Hoeij algorithm over number fields
نویسنده
چکیده
Van Hoeij’s algorithm for factoring univariate polynomials over the rational integers rests on the same principle as Berlekamp-Zassenhaus, but uses lattice basis reduction to improve drastically on the recombination phase. His ideas give rise to a collection of algorithms, differing greatly in their efficiency. We present two deterministic variants, one of which achieves excellent overall performance. We then generalize these ideas to factor polynomials over number fields.
منابع مشابه
Factoring Polynomials over Number Fields
The purpose of these notes is to give a substantially self-contained introduction to the factorization of polynomials over number fields. In particular, we present Zassenhaus’ algorithm and a factoring algorithm using lattice reduction, which were, respectively, the best in practice and in theory, before 2002. We give references for the van Hoeij-Novocin algorithm, currently the best both in pr...
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 37 شماره
صفحات -
تاریخ انتشار 2004