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Computing syzygies in finite dimension using fast linear algebra
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 …
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
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 …
Algebra, Johannes Kepler University A4040 Linz, Austria manuel.kauers@jku.at Christoph …
Guessing Gröbner bases of structured ideals of relations of sequences
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 …
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
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 …
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
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 …
multi-dimensional sequences. Existing algorithms for computing these relations arise in …
Algorithms for linearly recurrent sequences of truncated polynomials
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 …
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
Abstract The Berlekamp–Massey–Sakata algorithm and the Scalar-FGLM algorithm both
compute the ideal of relations of a multidimensional linear recurrent sequence. Whenever …
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 …
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 …
with applications in error-correcting codes, Gröbner basis computation, and sparse …
On Berlekamp–Massey and Berlekamp–Massey–Sakata Algorithms
Abstract The Berlekamp–Massey and Berlekamp–Massey–Sakata algorithms compute a
minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional …
minimal polynomial or polynomial set of a linearly recurring sequence or multi-dimensional …