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This is a list ofopen-sourcesoftware 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]
Acomputer algebra system (CAS) is a software product designed for manipulation ofmathematical formulae. The principal objective of a computer algebra system is to systematize monotonous and sometimes problematicalgebraic manipulation tasks. The primary difference between a computer algebra system and a traditionalcalculator is the ability to deal with equationssymbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation ofsymbolic equations. Computer algebra systems often include facilities forgraphing equations and provide aprogramming language for the users' ownprocedures.
Axiom is a general-purpose CAS. It has been in development since 1971 byIBM, and was originally namedscratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took over the project. It was eventually sold to theNumerical Algorithms Group (NAG) and was renamed Axiom. After a failure to launch as a product, NAG decided to release it as afree software in 2001 with more than 300 man-years worth of research involved. Axiom is licensed under a ModifiedBSD license.
A CAS designed for the solution of problems inphysical field theory. An unpublished computational program written inPascal called Abra inspired thisopen-source software.Abra was originally designed forphysicists to compute problems present inquantum mechanics. Kespers Peeters then decided to write a similar program inC computing language rather than Pascal, which he renamedCadabra. However, Cadabra has been expanded for a wider range of uses, it is no longer restricted to physicists.
CoCoA (COmputations in COmmutative Algebra) isopen-source software used for computingmultivariate polynomials and initiated in 1987. Originally written inPascal,CoCoA was later translated intoC.
GAP was initiated byRWTH 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 computationaldiscrete algebra with particular emphasis oncomputational 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.
Mathomatic isportablegeneral-purposecomputer algebra system capable of performing symboliccalculus, algebraic simplification, and equation solving.
Mathics is an open-source GPL3 license version of theWolfram Language.
Thisfree software had an earlier incarnation,Macsyma. Developed byMassachusetts Institute of Technology in the 1960s, it was maintained byWilliam Schelter from 1982 to 2001. In 1998, Schelter obtained permission to release Maxima asopen-source software under theGNU General Public license and thesource code was released later that year. Since his death in 2001, a group of Maxima enthusiasts have continued to provide technical support.
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,power series, algebraic numbers, andtranscendental functions.[3] Originally developed by Henri Cohen et al at Université Bordeaux I, France, it now isGPL 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 is a computer algebra system written inPython.
Xcas/Giac is an open-source project developed at theJoseph Fourier University ofGrenoble since 2000. Written inC++, maintained byBernard Parisse's [fr] et al. and available forWindows,Mac,Linux and many others platforms. It has a compatibility mode withMaple,Derive andMuPAD software andTI-89,TI-92 andVoyage 200 calculators. The system was chosen byHewlett-Packard as the CAS for theirHP Prime calculator, which utilizes the Giac/Xcas 1.1.2 engine under a dual-license scheme.
Geogebra (Geometry and Algebra) - combines geometric objects like circles and graphs of functions with its algebraic representation e.g. representing a circle with the radius. Designed for use in schools and educational settings.
Numerical analysis is an area of mathematics that creates and analyzesalgorithms for obtainingnumerical approximations to problems involvingcontinuousvariables. When anarbitraryfunction 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.
Euler Mathematical Toolbox is an open-sourcenumerical software system combining matrix language, symbolic algebra (viaMaxima), and plotting capabilities.
FreeMat is an alternative toMATLAB.
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 (aka GNU Octave) is an alternative toMATLAB. Originally conceived in 1988 by John W. Eaton as a companion software for an undergraduate textbook, Eaton later opted to modify it into a more flexible tool. Development began in 1992 and thealpha version was released in 1993. Subsequently, version 1.0 was released a year after that in 1994. Octave is a high levellanguage with the primary intention innumerical computation.
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.
Inspired byMATLAB, Scilab was initiated in the mid-1980s at theINRIA (French national Institute for computer science and control). François Delebecque and Serge Steer developed it and it was released byINRIA in 1994 as an open-source software. Since 2008,Scilab has been distributed under theCeCILL license, which isGPL compatible. In 2010, Scilab Enterprise was founded to provide even more support to the software.
SciPy is apython programming language library to take advantage of Python's ability to handle large data sets.[4]
Statistics is the study of how to collate and interpret numerical information from data. It is the science of learning from data and communicating uncertainty. There are two branches instatistics: ‘Descriptive statistics’’ and ‘’Inferential statistics
Descriptive statistics involves methods of organizing, picturing and summarizing information from data.Inferential statistics involves methods of using information from asample to draw conclusions about the Population.
R Statistics Software,SOFA Statistics,PSPP andJASP are open source software competitors toSPSS, widely used for statistical analysis of sampled data. PSPP is maintained by the GNU project.SOFA Statistics is addressing beginners with basic features, whileGNU-R Statistics Software has a large community that maintainsR packages also beyond statistical analysis.
R is both alanguage andsoftware used forstatistical computing andgraphing.R was originally developed byBell Laboratories (Currently known asLucent Technologies) byJohn Chambers. SinceR is largely written inC language, users can useC orC++ commands to manipulate R-objects directly. Also,R runs on mostUNIX platforms.R is currently part of theFree Software FoundationGNU project.
Demetra is a program forseasonal adjustments that was developed and published byEurostat –European Commission under theEUPL license.
Suchsoftware were created with the original intent of providing amath platform that can be compared toproprietary software such asMATLAB andMathematica. They contain multiple otherfree software and hence have more features than the rest of the software mentioned.
SageMath is designed partially as a free alternative to the general-purpose mathematics productsMaple andMATLAB. 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 byWilliam Stein, ofHarvard University in 2005 for his personal project innumber theory. It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted ofPari,GAP,Singular andMaxima with aninterface that rivals that ofMathematica.
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