Matroids in OSCAR
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915294004379648 |
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| author | Corey, Daniel Kühne, Lukas Schröter, Benjamin |
| author_facet | Corey, Daniel Kühne, Lukas Schröter, Benjamin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_08792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matroids in OSCAR Corey, Daniel Kühne, Lukas Schröter, Benjamin Combinatorics Algebraic Geometry 05-04 (05-02, 05E14) 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. |
| title | Matroids in OSCAR |
| topic | Combinatorics Algebraic Geometry 05-04 (05-02, 05E14) |
| url | https://arxiv.org/abs/2311.08792 |