Algorithms for the Computing Determinants in Commutative Rings

TL;DR

This paper compares existing and a new algorithm for computing determinants over integral domains, demonstrating that the new method outperforms previous ones across various rings.

Contribution

Introduces a novel determinant computation method for integral domains and evaluates its efficiency against existing algorithms.

Findings

The new method is faster than existing algorithms across tested rings.

Performance varies depending on the ring, but the new method consistently outperforms others.

The paper provides a comprehensive comparison of three determinant computation methods.

Abstract

Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the best.