In latest years, several advancements have been made in symbolic-numerical eigenvalue
techniques for solving polynomial systems. In this article, we add to this list. We design an …

We consider the problem of computing homogeneous coordinates of points in a zero-
dimensional subscheme of a compact, complex toric variety $ X $. Our starting point is a …

Effective computation of resultants is a central problem in elimination theory and polynomial
system solving. Commonly, we compute the resultant as a quotient of determinants of …

We present a new eigenvalue method for solving a system of Laurent polynomial equations
defining a zero-dimensional reduced subscheme of a toric compactification X of (C∖{0}) n …

Twenty years after the discovery of the F5 algorithm, Gröbner bases with signatures are still
challenging to understand and to adapt to different settings. This contrasts with Buchberger's …

Solving polynomial systems is one of the oldest and most important problems in
computational mathematics and has many applications in several domains of science and …

Solving systems of polynomial equations is a central problem in nonlinear and
computational algebra. Since Buchberger's algorithm for computing Gröbner bases in the …

We study polynomial systems with prescribed monomial supports in the Cox ring of a toric
variety built from a complete polyhedral fan. We present combinatorial formulas for the …

We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For
homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has …