English

Matroids in OSCAR

Combinatorics 2025-05-21 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.2311.08792,
  title  = {Matroids in OSCAR},
  author = {Daniel Corey and Lukas Kühne and Benjamin Schröter},
  journal= {arXiv preprint arXiv:2311.08792},
  year   = {2025}
}

Comments

13 pages, 1 figure

R2 v1 2026-06-28T13:21:49.340Z