https://github.com/ryu577/groebnerbasis
Buchbergers algorithm for computing Groebner basis of polynonmial ideals
https://github.com/ryu577/groebnerbasis
Last synced: 3 months ago
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Buchbergers algorithm for computing Groebner basis of polynonmial ideals
- Host: GitHub
- URL: https://github.com/ryu577/groebnerbasis
- Owner: ryu577
- Created: 2017-01-22T09:02:12.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2023-12-02T01:27:51.000Z (over 1 year ago)
- Last Synced: 2025-04-23T14:52:34.346Z (3 months ago)
- Language: C#
- Homepage: https://ryu577.github.io/jekyll/update/2017/01/23/buchbergers_algo_groebner_basis.html
- Size: 114 KB
- Stars: 13
- Watchers: 1
- Forks: 3
- Open Issues: 0
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Metadata Files:
- Readme: README.md
- Funding: .github/FUNDING.yml
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README
Buchbergers algorithm for computing Groebner Basis
Polynomial bases are a generalization of systems of linear equations. If we have a system of linear equations, say -
In Gaussian elimination, we take a system of linear equations and convert them to a basis where the solution becomes obvious.
A framework is provided for defining polynomial ideals. The various objects that are a part of this solution form a hierarchical structure:
PolynomialBasis -> Polynomial -> Monomial
The code starts with the building blocks like LCM, polynomial division, S-polynomials and builds up to Groebner basis. Some applications
of Groebner basis are also provided.
You can execute the code via Program.cs.
All algorithms are based on the book - Ideals, Varieties and Algorithms by Cox, Little and O'Shea
In comments and documentation, "CLO" referes to this book (Cox, Little and O'Shea). I wrote a blog on this topic providing some background.