English

A simple, polynomial-time algorithm for the matrix torsion problem

Discrete Mathematics 2009-09-08 v3 Data Structures and Algorithms

Abstract

The Matrix Torsion Problem (MTP) is: given a square matrix M with rational entries, decide whether two distinct powers of M are equal. It has been shown by Cassaigne and the author that the MTP reduces to the Matrix Power Problem (MPP) in polynomial time: given two square matrices A and B with rational entries, the MTP is to decide whether B is a power of A. Since the MPP is decidable in polynomial time, it is also the case of the MTP. However, the algorithm for MPP is highly non-trivial. The aim of this note is to present a simple, direct, polynomial-time algorithm for the MTP.

Keywords

Cite

@article{arxiv.0806.2068,
  title  = {A simple, polynomial-time algorithm for the matrix torsion problem},
  author = {Francois Nicolas},
  journal= {arXiv preprint arXiv:0806.2068},
  year   = {2009}
}

Comments

6 pages. Not intended to be submitted

R2 v1 2026-06-21T10:49:57.426Z