29 citations · 88 across the 9 of their papers we have counts for
5 papers · 1 filter
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…