Computing syzygies in finite dimension using fast linear algebra

V Neiger, É Schost - Journal of Complexity, 2020‏ - Elsevier
We consider the computation of syzygies of multivariate polynomials in a finite-dimensional
setting: for a K [X 1,…, X r]-module M of finite dimension D as a K-vector space, and given …

Guessing with little data

M Kauers, C Koutschan - … of the 2022 International Symposium on …, 2022‏ - dl.acm.org
Guessing with Little Data Page 1 Guessing with Little Data∗ Manuel Kauers Institute for
Algebra, Johannes Kepler University A4040 Linz, Austria manuel.kauers@jku.at Christoph …

Guessing Gröbner bases of structured ideals of relations of sequences

J Berthomieu, MS El Din - Journal of Symbolic Computation, 2022‏ - Elsevier
Assuming sufficiently many terms of an n-dimensional table defined over a field are given,
we aim at guessing the linear recurrence relations with either constant or polynomial …

A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension

S Naldi, V Neiger - Proceedings of the 45th International Symposium on …, 2020‏ - dl.acm.org
Let f 1,..., fm be elements in a quotient R n/N which has finite dimension as a K-vector space,
where R= K [X 1,..., Xr] and N is an R-submodule of R n. We address the problem of …

On Recurrence Relations of Multi-dimensional Sequences

H Rahkooy - arxiv preprint arxiv:2410.17208, 2024‏ - arxiv.org
In this paper, we present a new algorithm for computing the linear recurrence relations of
multi-dimensional sequences. Existing algorithms for computing these relations arise in …

Algorithms for linearly recurrent sequences of truncated polynomials

SG Hyun, V Neiger, É Schost - … of the 2021 International Symposium on …, 2021‏ - dl.acm.org
Linear recurrent sequences are those whose elements are defined as linear combinations of
preceding elements, and finding recurrence relations is a fundamental problem in computer …

In-depth comparison of the Berlekamp–Massey–Sakata and the Scalar-FGLM algorithms: the adaptive variants

J Berthomieu, JC Faugère - Journal of Symbolic Computation, 2020‏ - Elsevier
Abstract The Berlekamp–Massey–Sakata algorithm and the Scalar-FGLM algorithm both
compute the ideal of relations of a multidimensional linear recurrent sequence. Whenever …

[PDF][PDF] Contributions to polynomial system solving: Recurrences and Gröbner bases

J Berthomieu - 2023‏ - hal.sorbonne-universite.fr
This habilitation thesis deals with polynomial system solving through Gröbner bases
computations. It focuses on the link between multivariate polynomials and linear recurrence …

Quasi-Linear Guessing of Minimal Lexicographic Gröbner Bases of Ideals of C-Relations of Random Bi-Indexed Sequences

J Berthomieu, R Lebreton, K Tran - 2025‏ - hal.sorbonne-universite.fr
Computing recurrence relations for sequences is a central problem in computer algebra,
with applications in error-correcting codes, Gröbner basis computation, and sparse …

On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms

C Mou, X Fan - Computer Algebra in Scientific Computing: 21st …, 2019‏ - Springer
Abstract The Berlekamp–Massey and Berlekamp–Massey–Sakata algorithms compute a
minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional …