@inproceedings{d88b85ddceae4375b2a714bdbf64b7ab,
title = "Linear algebra to compute Syzygies and Gr{\"o}bner bases",
abstract = "In this paper, we introduce a new method to avoid zero reductions in Gr{\"o}bner 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 Gr{\"o}bner 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 Gr{\"o}bner 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.",
keywords = "Gr{\"o}bner bases, linear algebra, syzygy",
author = "Daniel Cabarcas and Jintai Ding",
year = "2011",
doi = "10.1145/1993886.1993902",
language = "English",
isbn = "9781450306751",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
pages = "67--74",
booktitle = "ISSAC 2011 - Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation",
note = "36th International Symposium on Symbolic and Algebraic Computation, ISSAC 2011 ; Conference date: 08-06-2011 Through 11-06-2011",
}