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Gröbner Systems Conversion

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Abstract

In this paper, we consider the problem of converting parametric Gröbner bases. More precisely, given a (comprehensive) Gröbner system w.r.t. a given monomial ordering, we present an efficient method to convert this system into a Gröbner system w.r.t. another monomial ordering. For this purpose, we develop the parametric variant of the generic Gröbner walk algorithm due to Fukuda et al. This new algorithm takes as input a monomial ordering and a Gröbner basis w.r.t. a set of parametric constraints, and outputs a decomposition of the given space of parameters as a finite set of (parametric) cells and for each cell a Gröbner basis w.r.t. the target monomial ordering.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Amir Hashemi

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    Amir Hashemi

  3. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, 14155-6455, Iran

    Mahdi Dehghani Darmian

  4. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Marzieh Barkhordar

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  1. Amir Hashemi
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  2. Mahdi Dehghani Darmian
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  3. Marzieh Barkhordar
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Correspondence to Amir Hashemi.

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Hashemi, A., Dehghani Darmian, M. & Barkhordar, M. Gröbner Systems Conversion. Math.Comput.Sci. 11, 61–77 (2017). https://doi.org/10.1007/s11786-017-0295-3

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  • DOI: https://doi.org/10.1007/s11786-017-0295-3

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