https://github.com/chakravala/fieldalgebra.jl

Field-algebra based on Group / Ring symbolic vector module extension
https://github.com/chakravala/fieldalgebra.jl

algebra algebraic-data-types algebraic-structures commutative-algebra computer-algebra group-theory julia math mathematics multivariate-polynomials polynomial-arithmetic polynomials vector

Last synced: about 3 hours ago
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Field-algebra based on Group / Ring symbolic vector module extension

• Host: GitHub
• URL: https://github.com/chakravala/fieldalgebra.jl
• Owner: chakravala
• License: agpl-3.0
• Created: 2022-09-19T14:36:08.000Z (about 2 years ago)
• Default Branch: master
• Last Pushed: 2024-04-23T18:53:09.000Z (7 months ago)
• Last Synced: 2024-09-02T19:17:48.596Z (3 months ago)
• Topics: algebra, algebraic-data-types, algebraic-structures, commutative-algebra, computer-algebra, group-theory, julia, math, mathematics, multivariate-polynomials, polynomial-arithmetic, polynomials, vector
• Language: Julia
• Homepage:
• Size: 36.1 KB
• Stars: 9
• Watchers: 4
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# FieldAlgebra.jl

*Field-algebra based on Group / Ring symbolic vector module extension*

[![DOI](https://zenodo.org/badge/538546202.svg)](https://zenodo.org/badge/latestdoi/538546202)

[![Build status](https://ci.appveyor.com/api/projects/status/p8yu8cth0eoctd54?svg=true)](https://ci.appveyor.com/project/chakravala/fieldalgebra-jl)

Work in progress of abelian `Group` implementation which is extended to `Field` algebra.

```Julia

julia> @ring xyz x y z

julia> x*y^2

xy²

julia> ans/x

y²

julia> x+y^2

x + y²

```

There are more undocumented features which will be explained once the design matures.

Fundamental principle of design is to construct `Field` algebra from an abelian `Group` algebra construction built on a vector space module.

Used in [Similitude.jl](https://github.com/chakravala/Similitude.jl) and [MeasureSystems.jl](https://github.com/chakravala/MeasureSystems.jl) to implement dimensional group algebra.