Mathematical software is

software Software is a set of computer programs and associated documentation and data. This is in contrast to hardware, from which the system is built and which actually performs the work. At the lowest programming level, executable code consists ...

used to model, analyze or calculate numeric, symbolic or geometric data.

Evolution of mathematical software

Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods t ...

and symbolic computation had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as

algorism Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system ...

which exist before the

invention An invention is a unique or novel device, method, composition, idea or process. An invention may be an improvement upon a machine, product, or process for increasing efficiency or lowering cost. It may also be an entirely new concept. If an i ...

of electronic computer, helped to mathematical software developing. On the other hand, by the growth of

computing power In computing, computer performance is the amount of useful work accomplished by a computer system. Outside of specific contexts, computer performance is estimated in terms of accuracy, efficiency and speed of executing computer program instruction ...

(such as seeing on

Moore's law Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empir ...

), the new treatment (for example, a new kind of technique such as

data assimilation Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – for example, to determine the optimal state es ...

which combined numerical analysis and

statistics Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...

) needing conversely the progress of the

mathematical science The mathematical sciences are a group of areas of study that includes, in addition to mathematics, those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper. Statisti ...

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical ...

.
The progress of mathematical information presentation such as TeX or

MathML Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide We ...

will demand to evolution form ''formula manipulation language'' to true ''mathematics manipulation language'' (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called ''one purpose software'' which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be kept.

Software calculator

A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.

Computer algebra systems

Many mathematical suites are

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

s that use

symbolic mathematics In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

. 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 The following tables compare general and technical information for a number of statistical analysis packages. General information Operating system support ANOVA Support for various ANOVA Analysis of variance (ANOVA) is a collection of sta ...

Theorem provers and proof assistants

Optimization software

Geometry

Numerical analysis

TK Solver TK Solver (originally TK!Solver) is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc. History Invented by Milos Konopasek in the late 1 ...

is a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc.. The

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 many separate programs and libraries. Most of the code is written in ...

repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL,

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. The current version is called NMath 7.1, released in December, 2019. NMath is built on ...

and NAG libraries; a free alternative is the

GNU Scientific Library The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science. The GSL is written in C; wrappers are available for other programming languages. The GSL is part of the GNU Project and is d ...

. A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms. Many

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

Music mathematics software

''Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns.'' * Musimat (by

Gareth Loy Gareth Loy is an American author, composer, musician and mathematician. Loy is the author of the two volume series on the intersection of music and mathematics titled ''Musimathics''. Loy was an early practitioner of music synthesis at Stanford ...

)

Websites

A growing number of mathematical software is available in web browsers, without the need to download or install any code.Internet Accessible Mathematical Computation
Institute for Computational Mathematics,

Kent State University Kent State University (KSU) is a public research university in Kent, Ohio. The university also includes seven regional campuses in Northeast Ohio and additional facilities in the region and internationally. Regional campuses are located in A ...

, retrieved 2015-02-15.

Programming libraries

Low-level mathematical libraries intended for use within other programming languages: * GMP, the

GNU Multi-Precision Library GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones imp ...

for high-performant

arbitrary precision arithmetic In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are lim ...

. *

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. Its implementation pr ...

, a high-level C++ library for

. * AMD Core Math Library, a software development library released by AMD * Boost.Math

References

{{reflist

External links

swMATH
Database on mathematical software