Matroids in OSCAR

Daniel Corey, Lukas Kühne, Benjamin Schröter

Published 2023-11-15Version 1

OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number theory). Here, we present parts of the module handeling matroids in OSCAR, which will appear as a chapter of the upcoming OSCAR book. A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear dependency in vector spaces as well as many aspects of graph theory. Moreover, matroids form a cornerstone of tropical geometry and a deep link between algebraic geometry and combinatorics. Our focus lies in particular on computing the realization space and the Chow ring of a matroid.