The computational-algebra package

Dependently-typed computational algebra libray for Groebner basis.

Properties

Versions	0.0.1.0, 0.0.1.1, 0.0.2.0, 0.0.3.0, 0.0.3.1, 0.0.3.2, 0.1.0.0, 0.1.0.1, 0.1.1.0, 0.1.2.0, 0.1.3.0, 0.1.3.1, 0.1.3.5, 0.1.3.6, 0.2.0.0, 0.3.0.0
Dependencies	algebra (==3.), base (>=2.0 && <5), containers (>=0.4 && <0.6), equational-reasoning (==0.0.), heaps (==0.2.), lens (==3.), monad-loops (>=0.3 && <0.5), monomorphic (==0.0.), peggy (==0.3.), singletons (>=0.8), sized-vector (==0.0.), tagged (>=0.4 && <1), type-natural (==0.0.3.) [details]
License	BSD3
Copyright	(C) Hiromi ISHII 2013
Author	Hiromi ISHII
Maintainer	konn.jinro_at_gmail.com
Stability	Unknown
Category	Math
Home page	https://github.com/konn/computational-algebra
Source repository	head: git clone git://github.com/konn/computational-algebra.git
Uploaded	Sat Sep 28 17:12:47 UTC 2013 by HiromiIshii
Distributions	NixOS:0.3.0.0
Downloads	3213 total (26 in the last 30 days)
Votes	0 []
Status	Docs available [build log] Successful builds reported [all 1 reports]

For package maintainers and hackage trustees

$ cabal install computational-algebra

If you once installed the same version of this package and want to reinstall, please run cabal clean first to avoid the GHC's bug.

This library provides data-types and functions to manipulate polynomials. This is built up with GHC's nice type features.

It contains following things:

Compute Groebner basis using Buchberger Algorithm
Ideal membership problem
Elimination ideal calculation
- This library provides the monomial orders of l-th elimination type other than lex order, such as elimination order, product order,...
Ideal operations
- Saturation Ideal, Quotient ideal,...

There are two interfaces:

Dependently-typed I/F
- Arity-paramaterized polynomials. It uses vector representations for monomials. Algebra.Ring.Polynomial and Algebra.Algorithms.Groebner.
Monomorphic wrapper I/F
- Not-so-dependently-typed interface to wrap dependently-typed ones. Algebra.Ring.Polynomial.Monomorphic and Algebra.Algorithms.Groebner.Monomorphic.

For more information, please read examples/polymorphic.hs and examples/monomorphic.hs.

Due to GHC 7.4.*'s bug, this library contains extra modules and functionalities as follows:

Monomorphic data-type and his friends
- This is completely separeted as monomorphic package. But due to GHC 7.4.1, which is shipped with latest Haskell Platform, I include the functionality from this library for a while.
Singleton types and functions
- Because the singletons package is not available in GHC 7.4.1, I provide limited version of the functionalities of that package in Algebra.Internal module. After new HP released, I will entirely rewrite all source codes using singletons.
Type-level natural numbers and size-parameterized vectors
- For the similar reason, I include SNat and Vector data-type in Algebra.Internal module, which is separated as sized-vector package. Their proofs are so messy, so I will entirely rewrite these after new HP released with my unreleased package equational-reasoning, which provides the functionalities similar to Agda's EqReasoning.