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Mathematical software is
software Software is a collection of instructions Instruction or instructions may refer to: Computing * Instruction, one operation of a processor within a computer architecture instruction set * Computer program, a collection of instructions Music * I ...

software
used to
model In general, a model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. ...
, 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 computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis ...
and
symbolic computation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
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 Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Anci ...
which exist before the
invention An invention is a unique or novelty (patent), novel machine, device, method, composition or process. The invention process is a process within an overall engineering and product development process. It may be an improvement upon a machine or p ...

invention
of
electronic computer Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor *Electronics (magazine), ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic ...

electronic computer
, helped to mathematical software developing. On the other hand, by the growth of
computing power In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes and development of both computer hardware , hardware and softwar ...
(such as seeing on
Moore's law Moore's law is the observation that Transistor count, the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and Forecasting, projection of a historical trend. Rather than a ph ...
), 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 estim ...
which combined numerical analysis and
statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ...

statistics
) needing conversely the progress of the
mathematical science The mathematical sciences are a group of areas of study that includes, in addition to mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algeb ...
or
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and be ...
.
The progress of mathematical information presentation such as
TeX TeX (, see below), stylized within the system as TeX, is a typesetting system which was designed and mostly written by Donald Knuth and released in 1978. TeX is a popular means of typesetting complex mathematical formulae; it has been noted ...
or
MathML Mathematical Markup Language (MathML) is a mathematical markup language, an application of XML for describing mathematics, mathematical notations and capturing both its structure and content. It aims at integrating mathematical formulae into Wo ...
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 Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of applica ...

computer algebra system
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 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 methods Regression Support for various Regression anal ...
.


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 1970s ...
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 Computational science, also known as scientific computing or scientific computation (SC), is a field that uses advanced computing Computing is any goal-oriented activity requiring, bene ...
repository contains various collections of software routines for numerical problems, mostly in
Fortran Fortran (; formerly FORTRAN) is a general-purpose, compiled language, compiled imperative programming, imperative programming language that is especially suited to numerical analysis, numeric computation and computational science, scientific com ...

Fortran
and C. Commercial products implementing many different numerical algorithms include the IMSL, NMath 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 Applied mathematics is the application of mathematical methods by different fields such as physics Physics (from grc, φυσ ...
. A different approach is taken by the
Numerical Recipes ''Numerical Recipes'' is the generic title of a series of books on algorithm In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algori ...
library, where emphasis is placed on clear understanding of algorithms. Many
computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of applica ...

computer algebra system
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)


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 In public relations Public relations (PR) is the practice of managing and disseminating information from an individual or an organization An organization, or organisation (English in t ...
, 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 integer An integer (from the Latin wikt:integer#Latin, ''integer'' meaning "whole") is colloquially defined as a numb ...
for extremely fast arbitrary precision arithmetic. * Class Library for Numbers, a high-level
C++ C++ () is a general-purpose programming language In computer software, a general-purpose programming language is a programming language dedicated to a general-purpose, designed to be used for writing software in a wide variety of application ...

C++
library for arbitrary precision arithmetic. * AMD Core Math Library, a software development library released by AMD * Boost.Math


References

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External links


swMATH
Database on mathematical software :