Inspired by Faugère and Mou's sparse FGLM algorithm, we show how using linear recurrent
multi-dimensional sequences can allow one to perform operations such as the primary …

Consider a zero-dimensional ideal I in K [X 1,…, X n]. Inspired by Faugère and Mou's Sparse
FGLM algorithm, we use Krylov sequences based on multiplication matrices of I in order to …

Given a zero-dimensional ideal I⊂ K [x 1,…, xn] of degree D, the transformation of the
ordering of its Gröbner basis from DRL to LEX is a key step in polynomial system solving …

Let K be an infinite perfect computable field and let I⊆ K [x] be a zero-dimensional ideal
represented by a Gröbner basis. We derive a new algorithm for computing the reduced …

Our goal is to present an algorithm for computing a primary decomposition of a zero-
dimensional ideal. We compute the decomposition of the radical ideal of the zero …

We present an algorithm for computing the corners of a monomial ideal. The corners are a
set of multidegrees that support the numerical information of a monomial ideal such as Betti …

The paper presents two algorithms for finding irreducible decomposition of monomial ideals.
The first one is recursive, derived from staircase structures of monomial ideals. This …

We describe a version of the FGLM algorithm that can be used to compute generic fibers of
positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting …

We introduce the notion of regular decomposition of an ideal and present a first algorithm to
compute it. Designed to avoid generic perturbations and eliminations of variables, our …

We present a linear algebra algorithm, which, given a zero-dimensional ideal via a “good”
representation, produces a separating linear form, its radical, again given via the same …