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README
Computational Algebra Library
For more detail, please read Official Project Site.
Overview
The computationalalgebra
is the computational algebra system, implemented as a Embedded Domain Specific Language (EDSL) in Haskell.
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:
TypeSafety : Haskell's static type system enforces static correctness and prevents you from violating invariants.
Flexibility : With the powerful typesystem of Haskell, we can write highly abstract program resulted in easytoextend 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.
 Zerodimensional 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Old version of this package is uploaded on Hackage, but it's rather outdated.
Most recent version of computationalalgebra
is developed on GitHub.
It uses the most agressive language features recently implemented in Glasgow Haskell Compiler, 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.
$ curl sSL https://get.haskellstack.org/  sh
# if you haven't install Stack yet
$ git clone https://github.com/konn/computationalalgebra
$ cd computationalalgebra
$ stack build
In addition, you may need to install GSL and LAPACK (for matrix computation) beforehand.
You can install them via Homebrew (OS X), aptget
, or other major package management systems.
Paper
 Hiromi Ishii, A Purely Functional Computer Algebra System Embedded in Haskell. Computer Algebra in Scientific Computing, pp. 288303. 20th International Workshop, CASC 2018, Lille, France, September 1721, 2018, Proceedings (arXiv).