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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.

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  1. B-IT, Universität Bonn, 53113, Bonn, Germany

    Joachim von zur Gathen

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  1. Joachim von zur Gathen
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von zur Gathen, J. Counting decomposable multivariate polynomials. AAECC 22, 165–185 (2011). https://doi.org/10.1007/s00200-011-0141-9

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  • DOI: https://doi.org/10.1007/s00200-011-0141-9

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