Counting decomposable multivariate polynomials
classification
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fielddecomposablemultivariatealgebraicallyapproximationapproximationsclosedcounting
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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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