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arXiv · 0912.3312

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

Joachim von zur Gathen·Alfredo Viola·Konstantin Ziegler
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Abstract

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 uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.

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Joachim von zur Gathen, Alfredo Viola, Konstantin Ziegler. 2009-12-17. Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields. https://doi.org/10.1137/110854680

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