Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants

Autor:	Hyun, Seung Gyu, Neiger, Vincent, Schost, Éric
Rok vydání:	2019
Předmět:	Computer Science - Symbolic Computation
Druh dokumentu:	Working Paper
Popis:	Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of the practical impact of these algorithms, e.g. on applications such as decoding some error-correcting codes and solving polynomial systems or structured linear systems. In this paper, we discuss implementation aspects for most fundamental operations: multiplication, truncated inversion, approximants, interpolants, kernels, linear system solving, determinant, and basis reduction. We focus on prime fields with a word-size modulus, relying on Shoup's C++ library NTL. Combining these new tools to implement variants of Villard's algorithm for the resultant of generic bivariate polynomials (ISSAC 2018), we get better performance than the state of the art for large parameters. Comment: ISSAC 2019, 8 pages on 2 columns
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.04356 Zobrazit plný text záznamu View this record from Arxiv