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Invariant G2V algorithm for computing SAGBI-Gröbner bases

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Abstract

Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G 2 V algorithm, to compute SAGBI-Gröbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Gröbner bases. We have implemented our new algorithm in Maple, and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm.

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Authors and Affiliations

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

    Amir Hashemi

  2. Young Researchers Club, Science and Research Branch, Islamic Azad University, Tehran, 461/15655, Iran

    Benyamin M.-Alizadeh

  3. Department of Mathematics, Damghan University, Damghan, 36716-41167, Iran

    Monireh Riahi

Authors
  1. Amir Hashemi
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  2. Benyamin M.-Alizadeh
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  3. Monireh Riahi
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Correspondence to Amir Hashemi.

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Hashemi, A., M.-Alizadeh, B. & Riahi, M. Invariant G2V algorithm for computing SAGBI-Gröbner bases. Sci. China Math. 56, 1781–1794 (2013). https://doi.org/10.1007/s11425-012-4506-8

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