Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences

@article{Berthomieu2015LinearAF,
  title={Linear Algebra for Computing Gr{\"o}bner Bases of Linear Recursive Multidimensional Sequences},
  author={J{\'e}r{\'e}my Berthomieu and Brice Boyer and Jean-Charles Faug{\`e}re},
  journal={J. Symb. Comput.},
  year={2015},
  volume={83},
  pages={36-67}
}
Sakata generalized the Berlekamp--Massey algorithm to n dimensions in~1988. The Berlekamp--Massey--Sakata (BMS) algorithm can be used for finding a Grbner basis of a 0-dimensional ideal of relations verified by a table. We investigate this problem usingö linear algebra techniques, with motivations such as accelerating change of basis algorithms (FGLM) or improving their complexity. We first define and characterize multidimensional linear recursive sequences for 0-dimensional ideals. Under… CONTINUE READING