8 papers · 1 filter
Quadrature rules with few nodes supported on algebraic curves
Cordian Riener, Ettore Teixeira Turatti
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we min…
Symbolic Computation with Symmetric Polynomials in Real Algebraic Geometry
Cordian Riener, Thi Xuan Vu
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inhere…
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and sym…
Constructively describing orbit spaces of finite groups by few inequalities
Philippe Moustrou, Cordian Riener, Robin Schabert
Let be a finite group acting linearly on . A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space as a…
On nonnegative invariant quartics in type A
Sebastian Debus, Charu Goel, Salma Kuhlmann +1
The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification…
Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő theorem
Sebastian Debus, Cordian Riener, Robin Schabert
Univariate polynomials are called stable with respect to a domain if all of their roots lie in . We study linear slices of the space of stable univariate polynomials with re…