29 citations · 88 across the 9 of their papers we have counts for
9 papers
On the Pythagoras number for polynomials of degree 4 in 5 variables
Santiago Laplagne
We give an example of a polynomial of degree 4 in 5 variables that is the sum of squares of 8 polynomials and cannot be decomposed as the sum of 7 squares. This improves the curren…
Strictly positive polynomials in the boundary of the SOS cone
Santiago Laplagne, Marcelo Valdettaro
We study the boundary of the cone of real polynomials that can be decomposed as a sum of squares (SOS) of real polynomials. This cone is included in the cone of nonnegative polynom…
Facial reduction for exact polynomial sum of squares decompositions
Santiago Laplagne
We study the problem of decomposing a non-negative polynomial as an exact sum of squares (SOS) in the case where the associated semidefinite program is feasible but not strictly fe…
Bad Primes in Computational Algebraic Geometry
Janko Boehm, Wolfram Decker, Claus Fieker +2
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and…
Local to global algorithms for the Gorenstein adjoint ideal of a curve
Janko Boehm, Wolfram Decker, Santiago Laplagne +1
We present new algorithms for computing adjoint ideals of curves and thus, in the planar case, adjoint curves. With regard to terminology, we follow Gorenstein who states the adjoi…
Computing integral bases via localization and Hensel lifting
Janko Boehm, Wolfram Decker, Santiago Laplagne +1
We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic…
Prediction of residue-residue contacts from protein families using similarity kernels and least squares regularization
Massimo Andreatta, Santiago Laplagne, Shuai Cheng Li +1
One of the most challenging and long-standing problems in computational biology is the prediction of three-dimensional protein structure from amino acid sequence. A promising appro…
Parallel algorithms for normalization
Janko Boehm, Wolfram Decker, Santiago Laplagne +3
Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization \bar{A} of A. Our starting point is the algorithm of Greuel, La…
Normalization of Rings
Gert-Martin Greuel, Santiago Laplagne, Frank Seelisch
We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where…