14 citations · 20 across the 6 of their papers we have counts for
11 papers
The Moment Method for Computing Real Points of Sparse Polynomial Systems
Tom Baumbach, Matías Bender
One of the most important problems in computational algebra is the computation of real solutions of a polynomial system. Lasserre, Laurent, and Rostalski introduced a numerical met…
Dimension Results for Extremal-Generic Polynomial Systems over Complete Toric Varieties
Matías Bender, Pierre-Jean Spaenlehauer
We study polynomial systems with prescribed monomial supports in the Cox rings of toric varieties built from complete polyhedral fans. We present combinatorial formulas for the dim…
Solving sparse polynomial systems using Groebner bases and resultants
Matías R. Bender
Solving systems of polynomial equations is a central problem in nonlinear and computational algebra. Since Buchberger's algorithm for computing Gröbner bases in the 60s, there has…
Classifier construction in Boolean networks using algebraic methods
Robert Schwieger, Matías R. Bender, Heike Siebert +1
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even mo…
Koszul-type determinantal formulas for families of mixed multilinear systems
Matías R. Bender, Jean-Charles Faugère, Angelos Mantzaflaris +1
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 ma…
Yet another eigenvalue algorithm for solving polynomial systems
Matías R. Bender, Simon Telen
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…
Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
Matías R. Bender, Simon Telen
We consider the problem of computing homogeneous coordinates of points in a zero-dimensional subscheme of a compact, complex toric variety . Our starting point is a homogeneous…
Gr{ö}bner Basis over Semigroup Algebras: Algorithms and Applications for Sparse Polynomial Systems
Matías Bender, Jean-Charles Faugère, Elias Tsigaridas
Gr{ö}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential i…
A nearly optimal algorithm to decompose binary forms
Matías Bender, Jean-Charles Faugère, Ludovic Perret +1
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. I…
Towards Mixed Gr{ö}bner Basis Algorithms: the Multihomogeneous and Sparse Case
Matías Bender, Jean-Charles Faugère, Elias Tsigaridas
One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{ö}bner basis computations that take into account the sparsity of the input po…
Bilinear systems with two supports: Koszul resultant matrices, eigenvalues, and eigenvectors
Matías Bender, Jean-Charles Faugère, Angelos Mantzaflaris +1
A fundamental problem in computational algebraic geometry is the computation of the resultant. A central question is when and how to compute it as the determinant of a matrix. whos…