Applicable Algebra in Engineering, Communication and Computing

, 22:165

Counting decomposable multivariate polynomials

Authors

Original Paper

DOI: 10.1007/s00200-011-0141-9

Cite this article as:
von zur Gathen, J. AAECC (2011) 22: 165. doi:10.1007/s00200-011-0141-9
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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.

Keywords

Computer algebraPolynomial decompositionMultivariate polynomialsFinite fieldsCombinatorics on polynomials

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© Springer-Verlag 2011