Mathematical software is software used to model

Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

, analyze or calculate numeric, symbolic or geometric data.

Computer algebra systems

Many mathematical suites are computer algebra system

Computer algebra system

A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...

s that use symbolic mathematics. They are designed to solve classical algebra equations and problems in human readable notation.

Statistics

Many tools are available for statistical analysis of data. See also Comparison of statistical packages

Comparison of statistical packages

The following tables compare general and technical information for a number of statistical analysis packages.-General information:Basic information about each product...

.

Geometry

Numerical analysis

The Netlib

Netlib

Netlib is a repository of software for scientific computing maintained by AT&T, Bell Laboratories, the University of Tennessee and Oak Ridge National Laboratory. Netlib comprises a large number of separate programs and libraries...

 repository contains various collections of software routines for numerical problems, mostly in Fortran

Fortran

Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...

 and C

C (programming language)

C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....

. Commercial products implementing many different numerical algorithms include the IMSL

IMSL Numerical Libraries

IMSL is a commercial collection of software libraries of numerical analysis functionality that are implemented in the computer programming languages of C, Java, C#.NET, and Fortran...

, NMath

NMath

NMath is a numerical package for the Microsoft .NET Framework. It is developed by CenterSpace Software. Version 1.0 was released in March, 2003 as NMath Core...

 and NAG libraries

NAG Numerical Libraries

NAG Numerical Libraries is a software product sold by The Numerical Algorithms Group Ltd . The product is a software library of numerical analysis routines. It comprises a collection of 1500 mathematical and statistical algorithms. Areas covered include linear algebra, optimization, quadrature,...

; a free alternative is the GNU Scientific Library

GNU Scientific Library

In computing, the GNU Scientific Library is a software library written in the C programming language for numerical calculations in applied mathematics and science...

. A different approach is taken by the Numerical Recipes

Numerical Recipes

Numerical Recipes is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul Teukolsky, William Vetterling and Brian Flannery. In various editions, the books have been in print since 1986...

 library, where emphasis is placed on clear understanding of algorithms.

Many computer algebra system

Computer algebra system

A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...

s (listed above) can also be used for numerical computations.

See also Comparison of numerical analysis software

Comparison of numerical analysis software

The following tables provide a comparison of numerical analysis software.- General :- Operating system support :The operating systems the software can run on natively .- Language features :Colors indicate features available as...

.

Programming libraries

Low-level mathematical libraries intended for use within other programming languages:

• GMP
  GNU Multi-Precision Library
  The GNU Multiple Precision Arithmetic Library, also known as GMP, is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers...
  
  , the GNU Multi-Precision Library
  GNU Multi-Precision Library
  The GNU Multiple Precision Arithmetic Library, also known as GMP, is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers...
  
   for extremely fast arbitrary precision arithmetic.
• Class Library for Numbers
  Class Library for Numbers
  CLN is a free library for arbitrary precision arithmetic. It operates on signed integers, rational numbers, floating point numbers, complex numbers, modular numbers, and univariate polynomials...
  
  , a high-level C++
  C++
  C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
  
   library for arbitrary precision arithmetic.
• Boost.Math

External links

• Mathstore published reviews of packages by United Kingdom Higher Education Academy
  Higher Education Academy
  The Higher Education Academy is an independent organisation in the United Kingdom that supports higher education institutions with strategies for the development of research and evaluation to improve the learning experience for students.-History:...
  
  's Maths, Stats & OR Network.
• CTI-Maths Older reviews.