computational-algebra: Well-kinded computational algebra library, currently supporting Groebner basis.

[ bsd3, library, math ] [ Propose Tags ]

Dependently-typed computational algebra libray for Groebner basis.

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Versions [RSS]	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, 0.4.0.0, 0.5.0.0, 0.5.1.0
Dependencies	algebra (>=3 && <4), base (>=2.0 && <5), containers (>=0.4 && <0.6), heaps (>=0.2 && <0.3), lens (>=3 && <4), monad-loops (>=0.3 && <0.4), monomorphic (>=0.0 && <0.1), peggy (>=0.3 && <0.4), tagged (>=0.4 && <1) [details]
License	BSD-3-Clause
Copyright	(C) Hiromi ISHII 2013
Author	Hiromi ISHII
Maintainer	konn.jinro_at_gmail.com
Category	Math
Home page	https://github.com/konn/computational-algebra
Source repo	head: git clone git://github.com/konn/computational-algebra.git
Uploaded	by HiromiIshii at 2013-05-02T18:50:46Z
Distributions
Reverse Dependencies	1 direct, 0 indirect [details]
Downloads	15388 total (60 in the last 30 days)
Rating	2.25 (votes: 2) [estimated by Bayesian average]
Your Rating	λ λ λ
Status	Docs not available [build log] All reported builds failed as of 2016-12-21 [all 8 reports]

$ 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.