Year: 2007
Type: preprint
Abstract: We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We compare features of the algorithm with several other algorithms in the literature. In addition we present a deterministic verification procedure which is similarly efficient in most cases but has a worst-case complexity of $O(n^4)$. Finally, we report the results of practical experiments with an implementation of our algorithms in comparison with the current algorithms in the {\sf GAP} library.
Source: arXiv (Cornell University)
Authors: Neunhoeffer, Max, Praeger, Cheryl E.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2057577558