5 papers · 1 filter
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…
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…