Counting decomposable multivariate polynomials

Details Counting decomposable multivariate polynomials Counting decomposable multivariate polynomials

2008-11-28

arxiv.org/abs/0811.4726v2

Mathematics

Commutative Algebra

v2: 21 pages, simplification in the proof of Theorem 4.1

Scientific paper

A polynomial f (multivariate over a field) is decomposable if f = g(h) with g
univariate of degree at least 2. We determine the dimension (over an
algebraically closed field) of the set of decomposables, and an approximation
to their number over a finite field. The relative error in our approximations
is exponentially decaying in the input size.

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