10 citations · 27 across the 8 of their papers we have counts for
8 papers
Tautological systems and local cohomology
Paul Görlach, Thomas Reichelt, Christian Sevenheck +1
We discuss the connections between tautological systems and the local cohomology of cones over homogeneous spaces. We study a derived version of tautological systems, related to th…
Connection Matrices in Macaulay2
Paul Görlach, Joris Koefler, Anna-Laura Sattelberger +4
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of fini…
Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument
Paul Görlach, Christian Lehn, Anna-Laura Sattelberger
In this article, we investigate Muirhead's classical system of differential operators for the hypergeometric function 1F1 of a matrix argument. We formulate a conjecture for the co…
Computing zero-dimensional tropical varieties via projections
Paul Görlach, Yue Ren, Leon Zhang
We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gröbner bases. We prov…
Detecting tropical defects of polynomial equations
Paul Görlach, Yue Ren, Jeff Sommars
We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine space…
Coordinate-wise Powers of Algebraic Varieties
Papri Dey, Paul Görlach, Nidhi Kaihnsa
We introduce and study coordinate-wise powers of subvarieties of , i.e. varieties arising from raising all points in a given subvariety of to the -t…
Rational invariants of even ternary forms under the orthogonal group
Paul Görlach, Evelyne Hubert, Théo Papadopoulo
In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group on the space $\mathbb{R}[x,y,z]_{2…
Deciding positivity of multisymmetric polynomials
Paul Görlach, Cordian Riener, Tillmann Weißer
The question how to certify non-negativity of a polynomial function lies at the heart of Real Algebra and also has important applications to Optimization. In this article we invest…