Guessing Linear Recurrence Relations of Sequence Tuplesand P-recursive Sequences with Linear Algebra

@inproceedings{Berthomieu2016GuessingLR,
  title={Guessing Linear Recurrence Relations of Sequence Tuplesand P-recursive Sequences with Linear Algebra},
  author={J{\'e}r{\'e}my Berthomieu and Jean-Charles Faug{\`e}re},
  booktitle={ISSAC},
  year={2016}
}
Given several n-dimensional sequences, we first present an algorithm for computing the Grobner basis of their module of linear recurrence relations. A P-recursive sequence (u<sub>i</sub>)<sub>i</sub> ∈ N<sup>n</sup> satisfies linear recurrence relations with polynomial coefficients in i, as defined by Stanley in 1980. Calling directly the aforementioned algorithm on the tuple of sequences ((i<sup>j</sup>, u<sub>i</sub>)<sub>i</sub> ∈ N<sup>n</sup>)<sub>j</sub> for retrieving the relations… CONTINUE READING