Fast randomized algorithms for the structure of matrix algebras over finite fields (extended abstract)

Authors:
Gábor Ivanyos
Affiliations:
Computer and Automation Research Institute, Hungarian Academy of Sciences, Lágymányosi u. 11. H-1111 Budapest, Hungary
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

We discuss randomized algorithms which compute algebra generators of a Wedderburn complement as well as ideal generators of the radical of a matrix algebra over a finite field given by algebra generators. The cost of the algorithms is comparable to that of a poly-logarithmic number of matrix multiplications.