{"id":19084787,"url":"https://github.com/ryu577/groebnerbasis","last_synced_at":"2025-04-30T09:26:03.765Z","repository":{"id":54260429,"uuid":"79706338","full_name":"ryu577/GroebnerBasis","owner":"ryu577","description":"Buchbergers algorithm for computing Groebner basis of polynonmial ideals","archived":false,"fork":false,"pushed_at":"2023-12-02T01:27:51.000Z","size":117,"stargazers_count":13,"open_issues_count":0,"forks_count":3,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-04-23T14:52:34.346Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"https://ryu577.github.io/jekyll/update/2017/01/23/buchbergers_algo_groebner_basis.html","language":"C#","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ryu577.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":".github/FUNDING.yml","license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null},"funding":{"github":"ryu577","patreon":null,"open_collective":null,"ko_fi":null,"tidelift":null,"community_bridge":null,"liberapay":null,"issuehunt":null,"otechie":null,"lfx_crowdfunding":null,"custom":null}},"created_at":"2017-01-22T09:02:12.000Z","updated_at":"2025-04-01T01:41:41.000Z","dependencies_parsed_at":"2024-11-09T02:52:41.483Z","dependency_job_id":null,"html_url":"https://github.com/ryu577/GroebnerBasis","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ryu577%2FGroebnerBasis","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ryu577%2FGroebnerBasis/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ryu577%2FGroebnerBasis/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ryu577%2FGroebnerBasis/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ryu577","download_url":"https://codeload.github.com/ryu577/GroebnerBasis/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":251675755,"owners_count":21625884,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-11-09T02:52:37.637Z","updated_at":"2025-04-30T09:26:03.721Z","avatar_url":"https://github.com/ryu577.png","language":"C#","funding_links":["https://github.com/sponsors/ryu577"],"categories":[],"sub_categories":[],"readme":"Buchbergers algorithm for computing Groebner Basis\r\n\r\nPolynomial bases are a generalization of systems of linear equations. If we have a system of linear equations, say - \r\n\r\nIn \u003ca href=\"http://mathworld.wolfram.com/GaussianElimination.html\"\u003eGaussian elimination\u003c/a\u003e, we take a system of linear equations and convert them to a basis where the solution becomes obvious.\r\n\r\nA framework is provided for defining polynomial ideals. The various objects that are a part of this solution form a hierarchical structure:\r\n\r\nPolynomialBasis -\u003e Polynomial -\u003e Monomial\r\n\r\nThe code starts with the building blocks like LCM, polynomial division, S-polynomials and builds up to Groebner basis. Some applications \r\nof Groebner basis are also provided. \r\n\r\nYou can execute the code via Program.cs. \r\n\r\nAll algorithms are based on the book - \u003ca href=\"http://www.dm.unipi.it/~caboara/Misc/Cox,%20Little,%20O'Shea%20-%20Ideals,%20varieties%20and%20algorithms.pdf\"\u003eIdeals, Varieties and Algorithms by Cox, Little and O'Shea\u003c/a\u003e \r\n\r\nIn comments and documentation, \"CLO\" referes to this book (Cox, Little and O'Shea). I wrote a \u003ca href=\"https://medium.com/@rohitpandey576/solving-systems-of-polynomial-equations-with-object-oriented-programming-797eb8add0fc\"\u003eblog\u003c/a\u003e on this topic providing some background.\r\n\r\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fryu577%2Fgroebnerbasis","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fryu577%2Fgroebnerbasis","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fryu577%2Fgroebnerbasis/lists"}