https://github.com/ryu577/groebnerbasis

Buchbergers algorithm for computing Groebner basis of polynonmial ideals
https://github.com/ryu577/groebnerbasis

Last synced: 7 days 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 (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2023-12-02T01:27:51.000Z (12 months ago)
• Last Synced: 2024-05-01T16:24:32.028Z (7 months ago)
• Language: C#
• Homepage: https://ryu577.github.io/jekyll/update/2017/01/23/buchbergers_algo_groebner_basis.html
• Size: 114 KB
• Stars: 10
• Watchers: 1
• Forks: 3
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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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.