Date: 07 May 2011

Counting decomposable multivariate polynomials

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Abstract

A polynomial f (multivariate over a field) is decomposable if \({f=g \circ h}\) 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.