{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computing-all-minimal-markov-bases-in","title":"Computing all minimal Markov bases in Macaulay2","arxiv_id":"2502.19031","date":"2025-02-26","proceeding":null,"authors":["Oliver Clarke","Alexander Milner"],"abstract":"We introduce the package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by producing the fiber graph of the toric ideal. The package uses this graph to compute other properties of the toric ideal such as its indispensable set of binomials as well as its universal Markov basis.","url_abs":"https://arxiv.org/abs/2502.19031v1","url_pdf":"https://arxiv.org/pdf/2502.19031v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computing-all-minimal-markov-bases-in","repo_url":"https://github.com/ollieclarke8787/WorkshopDurham2024/tree/main/ToricIdeals","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}