Applications and libraries/Mathematics

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This page contains a list of libraries and tools in a certain category. For a comprehensive list of such pages, see Applications and libraries.

Libraries for numerical algorithms and mathematics

Linear algebra

High level functional interface to standard linear algebra computations and other numerical algorithms based on the GNU Scientific Library. Alternative download site.
Wrapper to CLAPACK
Digital Signal Processing
Modules for matrix manipulation, digital signal processing, spectral estimation, and frequency estimation.
Index-aware linear algebra
Frederik Eaton's library for statically checked matrix manipulation in Haskell
Indexless linear algebra
algorithms by Jan Skibinski, see below

See also: Design discussions

Number representations

Decimal arithmetic library
An implementation of real decimal arithmetic, for cases where the binary floating point is not acceptable (for example, money).
Exact real arithmetic
is an interesting area: it is a deep connection between numeric methods and deep theoretic fondations of algorithms (and mathematics). Its topic: computable real numbers raise a lot of interesting questions rooted in mathematical analysis, arithmetic, but also computability theory (see numbers-as-programs approaches). Computable reals can be achieved by many approaches -- it is not one single theory.

Type class hierarchies

There are several approaches to improve the numeric type class hierarchy.

Dylan Thurston and Henning Thielemann's Numeric Prelude
Experimental revised framework for numeric type classes. Needs hiding of Prelude, overriding hidden functions like fromInteger and multi-parameter type classes. Probably restricted to GHC.
Jerzy Karczmarczuk's approach
Serge D. Mechveliani's Basic Algebra proposal
Andrew Frank's approach
The proposal:
Haskell Prime
Ongoing efforts for the language revision


Geometric Algorithms
A small Haskell library, containing algorithms for two-dimensional convex hulls, triangulations of polygons, Voronoi-diagrams and Delaunay-triangulations, the QEDS data structure, kd-trees and range-trees.
Papers by Jerzy Karczmarczuk
Some interesting uses of Haskell in mathematics, including functional differentiation, power series, continued fractions.
DoCon - Algebraic Domain Constructor
A Computer Algebra System
The HaskellMath library is a sandbox for experimenting with mathematics algorithms. So far I've implemented a few quantitative finance models (Black Scholes, Binomial Trees, etc) and basic linear algebra functions. Next I might work on either computer algebra or linear programming. All comments welcome!
Haskell for Maths
David Amos' collection of math libraries in Haskell - including number theory, commutative algebra, combinatorics, permutation groups and more.
Various math stuff by Henning Thielemann
This is some unsorted mathematical stuff including: GNUPlot wrapper, portable grey map (PGM) image reader and writer, simplest numerical integration, differentiation, zero finding, interpolation, solution of differential equations, combinatorics, some solutions of math riddles, computation of fractal dimensions of iterated function systems (IFS)
Adaptive Simulated Annealing
A Haskell interface to Lester Ingber's adaptive simulating annealing code.
Number Theory Library
Andrew Bromage's Haskell number theory library, providing operations on primes, fibonacci sequences and combinatorics.
Hmm: Haskell Metamath
Hmm is a small Haskell library to parse and verify Metamath databases.
Probabilistic Functional Programming
The PFP library is a collection of modules for Haskell that facilitates probabilistic functional programming, that is, programming with stochastic values. The probabilistic functional programming approach is based on a data type for representing distributions. A distribution represent the outcome of a probabilistic event as a collection of all possible values, tagged with their likelihood. A nice aspect of this system is that simulations can be specified independently from their method of execution. That is, we can either fully simulate or randomize any simulation without altering the code which defines it.
Sinc function
A general boolean algebra class and some instances for Haskell.
HODE is a binding to the Open Dynamics Engine. ODE is an open source, high performance library for simulating rigid body dynamics.
An haskell implementation of Brendan McKay's algorithm for graph canonic labeling and automorphism group. (aka Nauty)
Mirror of the following numeric modules by Jan Skibinski