Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
A new polynomial factorization algorithm and its implementation
Journal of Symbolic Computation
An introduction to pseudo-linear algebra
Selected papers of the conference on Algorithmic complexity of algebraic and geometric models
Subquadratic-time factoring of polynomials over finite fields
Mathematics of Computation
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A new deterministic algorithm for factoring polynomials over finite fields is presented. This algorithm makes use of linear algebra methods and is an improvement of the Berlekamp algorithm, as well as that of Niederreiter, in the case of nontrivial algebraic extensions. The improvement is achieved by a new method of computing a basis of the so-called Berlekamp primitive subalgebra that makes use of an idea related to the field of Grobner bases. Finally, some comparative running times show how this new deterministic algorithm performs better than other probabilistic algorithms in some practical cases.