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https://github.com/konn/computational-algebra

General-Purpose Computer Algebra System as an EDSL in Haskell
https://github.com/konn/computational-algebra

algorithm computational-algebra groebner-basis haskell ideal math mathematics polynomial

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General-Purpose Computer Algebra System as an EDSL in Haskell

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README 

        
Computational Algebra Library

==============================

[![pipeline status](https://gitlab.com/konn/computational-algebra/badges/master/pipeline.svg)](https://gitlab.com/konn/computational-algebra/commits/master) 

[![coverage report](https://gitlab.com/konn/computational-algebra/badges/master/coverage.svg)](https://gitlab.com/konn/computational-algebra/commits/master)



**For more detail, please read [Official Project Site](http://konn.github.io/computational-algebra/)**.



Overview

--------

The `computational-algebra` is the computational algebra system, implemented as a Embedded Domain Specific Language (*EDSL*) in [Haskell](https://www.haskell.org).

This library provides many functionality for computational algebra, especially ideal computation such as Groebner basis calculation.



Thanks to Haskell's powerful language features, this library achieves the following goals:



Type-Safety

:   Haskell's static type system enforces **static correctness** and prevents you from violating invariants. 



Flexibility

:   With the powerful type-system of Haskell,

    we can write **highly abstract program** resulted in **easy-to-extend** system.



Efficiency

:   Haskell comes with many **aggressive optimization mechanism** and **parallel computation features**,

    which enables us to write efficient program.



This package currently provides the following functionalities:



* Groebner basis calculation w.r.t. arbitrary monomial ordering

    * Currently using Buchberger's algorithm with some optimization

    * Faugere's F_4 algorithms is experimentally implemented,

	  but currently not as fast as Buchberger's algorithm 

* Computation in the (multivariate) polynomial ring over arbitarary field and its quotient ring

    * Ideal membership problem

    * Ideal operations such as intersection, saturation and so on.

    * Zero-dimensional ideal operation and conversion via FGLM algorithm

    * Variable elimination

* Find numeric solutions for polynomial system with real coefficient



Requirements and Installation

------------------------------

Old version of this package is uploaded on [Hackage](http://hackage.haskell.org/package/computational-algebra), but it's rather outdated.

Most recent version of `computational-algebra` is developed on GitHub.



It uses the most agressive language features recently implemented in [Glasgow Haskell Compiler](https://www.haskell.org/ghc/), so it requires at least GHC 8.0.1 and

also it depends on many packages currently not available on Hackage, but you can install it fairly easily with help of [The Haskell Tool Stack](https://docs.haskellstack.org/en/stable/README/).



```zsh

$ curl -sSL https://get.haskellstack.org/ | sh

  # if you haven't install Stack yet

$ git clone https://github.com/konn/computational-algebra

$ cd computational-algebra

$ stack build

```



In addition, you may need to install GSL and LAPACK (for matrix computation) beforehand.

You can install them via Homebrew (OS X), `apt-get`, or other major package management systems.



Paper

-----

* Hiromi Ishii, _A Purely Functional Computer Algebra System Embedded in Haskell_.

  Computer Algebra in Scientific Computing, pp. 288-303. 20th International Workshop, CASC 2018, Lille, France, September 17-21, 2018, Proceedings ([arXiv][arXiv]).



### [Read More in Official Project Site](http://konn.github.io/computational-algebra/)



[arXiv]: https://arxiv.org/abs/1807.01456