# Software for Mathematics

This page lists software for mathematics, some commercial and some shared. There is an additional on the Portal page for Software companies.

#### Collections of Software

GAMS – Guide to Available Mathematical Software from NIST
A cross-index and virtual repository of mathematical and statistical software components of use in computational science and engineering.
Netlib:
a collection of mathematical software, papers, and databases. The major source of all numerical software, including LINPACK, EISPACK, etc. (at UTK and ORNL)
AT&T Software Tools:
software tools appearing on this page that have been developed by AT&T Labs researchers.
Mathematical and Statistical Software List
at Pittsburgh Supercomputing Center

#### Specific Packages

Derive (1999-2003)
GAP (Groups, Algorithms, Programs) (Version 4.4.12: Dec 2008)
GAP: – Groups, Algorithms, Programming – a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. See also the overview and the description of the mathematical capabilities. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. Coordinated by CIRCA at St. Andrews, UK.
MACSYMA
At Scientek Inc. — This venerable computer algebra system, in an obvious sense probably the first commercial such, went out of business: but it’s back at version 2.4 in Korea! [See also further information
MAGMA
The Magma System for Algebra, Number Theory and Geometry
MAPLE resources
Maple User Group at the Symbolic Computation Group (U Waterloo, ON CA)
from Parametric Technology Corporations; used to be MathSoft (http://www.mathsoft.com)
Mathematica resources

MathSource
Stephan Kaufmann’s Mathematica Info
MATCOM (Matlab to C++ compiler)
MATLAB: The MathWorks produces software for technical computing and Model-Based Design for engineers, scientists, mathematicians, and researchers. Our two core products are MATLAB®, used for performing mathematical calculations, analyzing and visualizing data, and writing new software programs; and Simulink®, used for modeling and simulating complex dynamic systems, such as a vehicle’s automatic transmission system. We also produce more than 90 additional tools for specialized tasks such as processing images and signals and analyzing financial data. Since its founding in 1984, The MathWorks has become the leading global provider of software for technical computing and Model-Based Design. Headquartered in Natick, Massachusetts, The MathWorks currently employs more than 2,000 people worldwide.
MAXIMA: a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. [a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology.]
MicroMath

MLAB:
Civilized Software Inc.
NMATH: .NET Math and Statistics Libraries (was the first .NET commercial math library in March, 2003)
Center Space Software
PARI-GP Number Theory and Algebra program: a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves…), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computation.
PARI’s FTP service (Bordeaux, France)

REDUCE: a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations but also provides a full programming language, with a syntax similar to other modern programming languages. implemented in Standard Lisp expressed in an intuitive imperative-style notation called RLISP. The latter is used as a basis for REDUCE’s user-level language.
SAGE: free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface, which grew out of its early version as Software for Algebra and Geometry Experimentation.

#### Software by Subject

Combinatorics
DISCRETA [by Anton Betten, Evi Haberberger, Reinhard Laue, Alfred Wassermann at Universität Bayreuth]
A program to construct t-designs with prescribed automorphism groups.
DISCRETAQ [by Michael Braun at Universität Bayreuth]
Systematic construction of q-analogs of designs.
Geometry Programs
Windows (95/98/NT), Macintosh, Linux, and BeOS ports of this fractal drowing program with extensive features, freeware fractal generator created for IBMPC’s and compatible computers.
Xfractint 20.2.04
The BSD X11 port of the program Fractint

Geomview
[an interactive 3D viewing program for Unix;written at the Geometry Center at the University of Minnesota between 1992 and 1996 used by thousands of people around the world. Through the volunteer work of the original authors and other volunteers, Geomview continues to evolve. Runs on most Unix platforms, including GNU/Linux]
Kaleido
Uniform Polyhedra – Computation and 3D Display. Runs on Unix and various other platforms and the algorithms have been ported to Mathematica.
Knot Theory
CBraid [by Jae Choon Cha at Korean Advanced Institute of Science and Technology]
A C++ library for computations in braid groups; also used for braid cryptography.
Number Theory
KASH/KANT (version 3, Jun 2004) (Institut für Mathematik, TU Berlin])
Package for algebraic number theory. It is a tool for sophisticated computations in number fields, global function fields, and local fields.
LiDIA (version 2.1.3, Dec 2004) (at TU Darmstadt, Germany)
C++ Library for Number Theory
Magma Computational Algebra System (at V2.12) (at University of Sydney), Australia)
“Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric and geometric objects.”
Mersenne Prime Freeware
many variations, inlcuding links to GIMPS
SIMATH (at Tokyo Metropolitan University)
(A computer algebra system, especially for number theoretic purpose: Number Theory, Elliptic Curves, Compiler)

Numerical Software
Interactive Environment for the Taylor Integration of ODEs
(PC, Windows) [by Alexander Gofen]