List of open-source software for mathematics

This is a list of open-source software to be used for high-order mathematical calculations. This software has played an important role in the field of mathematics.^[1] Open-source software in mathematics has become pivotal in education because of the high cost of textbooks.^[2]

Computer algebra systems

A

procedures

.

Axiom

Axiom is a general-purpose

BSD license

.

Cadabra

A

physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra

. However, Cadabra has been expanded for a wider range of uses, it is no longer restricted to physicists.

CoCoA

CoCoA (COmputations in COmmutative Algebra) is

multivariate polynomials and initiated in 1987. Originally written in Pascal, CoCoA was later translated into C

.

GAP

GAP was initiated by RWTH Aachen University in 1986. This was the case until in 1997 when they decided to co-develop GAP further with CIRCA (Centre for Research in Computational Algebra). Unlike MAXIMA and Axiom, GAP is a system for computational discrete algebra with particular emphasis on computational group theory. In March 2005 the GAP Council and the GAP developers have agreed that status and responsibilities of "GAP Headquarters" should be passed to an equal collaboration of a number of "GAP Centres", where there is permanent staff involvement and an element of collective or organizational commitment, while fully recognizing the vital contributions of many individuals outside those centers.

Mathics

Mathics is an open-source GPL3 license version of the Wolfram Language.

Maxima

This

GNU General Public license and the source code

was released later that year. Since his death in 2001, a group of Maxima enthusiasts have continued to provide technical support.

PARI/GP

PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials,

GPL

software. The gp interactive shell allows GP-language scripting; the gp2c compiler compiles GP scripts into C; and the PARI C library allows C programs to use PARI/GP functions.

Sympy

Sympy is a computer algebra system written in Python.

Xcas

Xcas/Giac is an open-source project developed at the

Voyage 200 calculators. The system was chosen by Hewlett-Packard as the CAS for their HP Prime

calculator, which utilizes the Giac/Xcas 1.1.2 engine under a dual-license scheme.

Geometry

Geogebra

Geogebra (Geometry and Algebra)

- combines geometric objects like circles and graphs of functions with its algebraic representation e.g.

x^{2}+y^{2}=r^{2}

representing a circle with the radius

r

. Designed for use in schools and educational settings.

Numerical analysis

arbitrary function

does not have a closed form as its solution, there would not be any analytical tools present to evaluate the desired solutions, hence an approximation method is employed instead.

FreeMat

FreeMat is an alternative to MATLAB.

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 and wrappers are available for other programming languages. The GSL is part of the GNU Project and is distributed under the GNU General Public License.

Octave

Octave (aka GNU Octave) is an alternative to

numerical computation

.

Modelica

Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems including algebraic and differential equations. OpenModelica and Jmodelica are some of the opensource implementations of the language.

Scilab

Inspired by

GPL

compatible. In 2010, Scilab Enterprise was founded to provide even more support to the software.

SciPy

SciPy is a python programming language library to take advantage of Python's ability to handle large data sets.^[4]

Statistics

Inferential statistics

sample

to draw conclusions about the Population.

Alternatives to SPSS

GNU-R Statistics Software has a large community that maintains R packages

also beyond statistical analysis.

R

GNU project

.

Demetra+

Demetra is a program for

EUPL

license.

Multipurpose mathematics software

Such

Mathematica. They contain multiple other free software

and hence have more features than the rest of the software mentioned.

SageMath

SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.

SageMath was initiated by

Mathematica

.

Theorem provers

Recreational mathematics software

Golly

References

^ David Joyner; William Stein (November 2007). "Open Source Mathematical Software" (PDF). American Mathematical Society. Retrieved 11 June 2013.
^ Russell Herman; Gabriel Lugo (24 May 2008). "Open Source Resources for Teaching and Research in Mathematics" (PDF). University of North Carolina Wilmington. Retrieved 11 June 2013.
^ "PARI/GP home page". Archived from the original on 2019-09-29. Retrieved 2016-12-28.
^ "Visualizing big data".

[1] David Joyner; William Stein (November 2007). "Open Source Mathematical Software" (PDF). American Mathematical Society. Retrieved 11 June 2013.

[2] Russell Herman; Gabriel Lugo (24 May 2008). "Open Source Resources for Teaching and Research in Mathematics" (PDF). University of North Carolina Wilmington. Retrieved 11 June 2013.

[3] "PARI/GP home page". Archived from the original on 2019-09-29. Retrieved 2016-12-28.

[4] "Visualizing big data".

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[2]

[4]