Computing the Determinant of a Dense Matrix over Z
Number Theory
2024-04-15 v1
Abstract
We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The algorithm uses randomness internally, but the result is guaranteed correct. The main new idea is to use a modular HNF in cases where the Pauderis--Storjohann HCOL method performs poorly. The algorithm is implemented in OSCAR~1.0.
Cite
@article{arxiv.2404.08358,
title = {Computing the Determinant of a Dense Matrix over Z},
author = {John Abbott and Claus Fieker},
journal= {arXiv preprint arXiv:2404.08358},
year = {2024}
}
Comments
8 pages, subnitted as extended abtract to ICMS 2024 (Durham)