Difference between revisions of "Applications and libraries/Mathematics"

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.
Wrapper to CLAPACK
Digital Signal Processing
Modules for matrix manpulation, 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

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.

other

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!
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, interpolation, solution of differential equations, combinatorics, some solutions of math riddles, computation of fractal dimensions of iterated function systems (IFS)
Numeric Prelude
Experimental revised framework for numeric type classes.