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On systems of algebraic equations with parametric exponents II

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Abstract

We deal with ideals generated by polynomials with parametric exponents, and discuss certain stability of forms of Gröbner bases of those ideals. Based on the author’s previous work, we investigate techniques by “slack variables” and succeed in obtaining further useful notions and new techniques using elimination ideals and ring homomorphisms. We also apply those techniques to cases, where a single parameter appears only on a single variable as its exponent, with help of univariate GCD computation of polynomials with parametric exponent. Moreover, as the original method for GCD computation could not handle some subcase and so it was not complete, we complete the method by adding a concrete procedure for handling the subcase.

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  1. Department of Mathematics, Rikkyo University, 3-34-1 Nishi Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Kazuhiro Yokoyama

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  1. Kazuhiro Yokoyama
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Correspondence to Kazuhiro Yokoyama.

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Yokoyama, K. On systems of algebraic equations with parametric exponents II. AAECC 18, 603–630 (2007). https://doi.org/10.1007/s00200-007-0055-8

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  • DOI: https://doi.org/10.1007/s00200-007-0055-8

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