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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.

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Computing the Degree of Black-Box Polynomials, with Applications

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  • 发表日期：

    2025年

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  • Eduardo S. Zeron,
  • Jesús A. De Loera

摘要

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.