8 papers
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…
Symmetric and Isotypic Hilbert Series for Symmetric Ideals
Henri Breloer, Cordian Riener
An ideal in a polynomial ring is symmetric if it is invariant under any permutation of variables. In this paper, we define and study the symmetric and isotypic Hilbert series for s…
#P-hardness proofs of matrix immanants evaluated on restricted matrices
Istvan Miklos, Cordian Riener
We establish the -hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing -immanants…
Slices of Stable Polynomials and Connections to the Grace-Walsh-SzegÅ 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…
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…
A semidefinite programming hierarchy for covering problems in discrete geometry
Cordian Riener, Jan Rolfes, Frank Vallentin
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed prim…