Cyclic matrices and the MEATAXE (Q2759637)

The MEATAXE by \textit{R. A. Parker} [Computational group theory, Proc. Symp., Durham/Engl. 1982, 267-274 (1984; Zbl 0555.20001)] is a principal tool for studying representations of finite groups. The authors propose a variant of this algorithm that uses cyclic matrices (that is matrices with the same characteristic and minimal polynomial). While the performance of this variant should be no worse than the ``classical'' algorithm, its particular value to the authors is a better analyzability, using the authors work on the probability that a given matrix is cyclic [J. Algebra 234, No. 2, 367-418 (2000; Zbl 1020.20032)]. In this paper the authors study only irreducibility test and centralizer algebra. Variants of other MEATAXE procedures will be given in a forthcoming paper [Exploiting cyclic matrices in computer algebra: sharpening the MEATAXE] by the authors.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00030].