Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

Details Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

2009-12-17

arxiv.org/abs/0912.3312v1

Mathematics

Commutative Algebra

Scientific paper

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one a combinatorial method. They yield approximations with relative errors that essentially decrease exponentially in the input size.

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