Computing the Degree of Black-Box Polynomials, with Applications

Eduardo S. Zeron () and Jesús A. De Loera ()
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Eduardo S. Zeron: CINVESTAV del IPN, Departamento de Matemáticas
Jesús A. De Loera: University of California, Department of Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 777-792 from Springer

Abstract: Abstract This note presents simple techniques to recover the total degree of a black-box polynomial and the value of its leading coefficients, relying only on few evaluations of the polynomial or its derivatives, the knowledge of basic bounds for the size of the coefficients, and classical properties of complex-valued polynomials. We apply the techniques to discrete optimization problems.

Keywords: Black-box polynomials; Laurent polynomials; Convex rational polytopes; Barvinok and Pommersheim decomposition; Discrete optimization; Integer programming (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_54

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DOI: 10.1007/978-3-032-16368-4_54

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