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Linear algebra to compute syzygies and Gröbner bases

Daniel Cabarcas Dept. of Mathematical Sciences, University of Cincinnati, 2600 Clifton ave. Cincinnati, OH 45221 Jintai Ding Dept. of Mathematical Sciences, University of Cincinnati, 2600 Clifton ave. Cincinnati, OH 45221; South China University of Technology, China

TBD mathscidoc:2207.43055

ISSAC 2011, 67–74, 2011.6
In this paper, we introduce a new method to avoid zero reductions in Gröbner basis computation. We call this method LASyz, which stands for Lineal Algebra to compute Syzygies. LASyz uses exhaustively the information of both principal syzygies and non-trivial syzygies to avoid zero reductions. All computation is done using linear algebra techniques. LASyz is easy to understand and implement. The method does not require to compute Gröbner bases of subsequences of generators incrementally and it imposes no restrictions on the reductions allowed. We provide a complete theoretical foundation for the LASyz method and we describe an algorithm to compute Gröbner bases for zero dimensional ideals based on this foundation. A qualitative comparison with similar algorithms is provided and the performance of the algorithm is illustrated with experimental data.
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@inproceedings{daniel2011linear,
  title={Linear algebra to compute syzygies and Gröbner bases},
  author={Daniel Cabarcas, and Jintai Ding},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714134840057588632},
  booktitle={ISSAC 2011},
  pages={67–74},
  year={2011},
}
Daniel Cabarcas, and Jintai Ding. Linear algebra to compute syzygies and Gröbner bases. 2011. In ISSAC 2011. pp.67–74. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220714134840057588632.
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