4 papers
Positive Univariate Polynomials: SOS certificates, algorithms, bit complexity, and T-systems
MatÃas Bender, Philipp Di Dio, Elias Tsigaridas
We consider certificates of positivity for univariate polynomials with rational coefficients that are positive over (an interval of)~. Such certificates take the form o…
Certificates for nonnegativity of multivariate integer polynomials under perturbations
MatÃas R Bender, Khazhgali Kozhasov, Elias Tsigaridas +1
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their…
Solving bihomogeneous polynomial systems with a zero-dimensional projection
MatÃas Bender, Laurent Busé, Carles Checa +1
We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points.…
Bigraded Castelnuovo-Mumford regularity and Gröbner bases
MatÃas Bender, Laurent Busé, Carles Checa +1
We study the relation between the bigraded Castelnuovo-Mumford regularity of a bihomogeneous ideal in the coordinate ring of the product of two projective spaces and the bidegr…