Counting decomposable multivariate polynomials
Commutative Algebra
2009-07-02 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.0811.4726,
title = {Counting decomposable multivariate polynomials},
author = {Joachim von zur Gathen},
journal= {arXiv preprint arXiv:0811.4726},
year = {2009}
}
Comments
v2: 21 pages, simplification in the proof of Theorem 4.1