Deterministic distinct-degree factorization of polynomials over finite fields

Authors:
Shuhong Gao;Erich Kaltofen;Alan G. B. Lauder
Affiliations:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA;Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA;Mathematical Institute, Oxford University, Oxford OX1 3LB, UK
Venue:
Journal of Symbolic Computation
Year:
2004

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Abstract

A deterministic polynomial time algorithm is presented for finding the distinct-degree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of polynomials over finite fields in deterministic polynomial time, thus resolving a theoretical open problem of Kaltofen from 1987.