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This article is a summary of the available open source software use for mathematics. It is for web viewers (more so for mathematicians) to be aware of these available mathematical open source software in the global market. For more detailed information of each individual software, please refer to their respective web pages.

This is a list of open source software to be used for high order mathematical calculations. This software has played a huge role in the field of mathematics. Open source software in mathematics has become pivotal in education because of the high cost of textbooks.

Computer algebra systems

A computer algebra system is a type of software set that is used in manipulation of mathematical formulae. The principal objective of a computer algebra system is to systematize monotonous and sometimes problematic algebraic manipulation tasks. The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically 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 of symbolic equations. Computer algebra system often include facilities for graphing equations and provide a programming language for the users' own procedures.

Axiom	Axiom is general-purpose computer algebra system. It has been in development since 1971 by IBM, originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took the project. Project scratchpad was eventually sold to a numerical group called Numerical Algorithms Group (NAG) and was renamed Axiom. After a failure to launch as a product, NAG decided to release it as a free software in 2001 with more than 300 man-years worth of research involved. Axiom is licensed under a Modified BSD license.	File:Axiomlogo.jpg
MAXIMA	This free software had an earlier incarnation, Macsyma. Developed by Massachusetts Institute of Technology in 1960's, it was maintained by William Schelter from 1982 to 2001. In 1998, Schelter obtained the permission to release MAXIMA as an open source software under the GNU General Public license. Subsequently, he released the source code to the world later that year. Since his passing in 2001, a group of MAXIMA enthusiasts have continued to provide technical support.	File:MAXIMAScreenShot1.png
GAP	GAP was initiated by RWTH Aachen university, a research university of technology located in Germany 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.	File:GAPScreenShot1.jpg
Cadabra	A Computer Algebra System designed for the solution of the field theory problems. An unpublished computational program written in pascal called Abra inspired this open source software. Abra was originally designed for physicists to compute problems present in Quantum Mechanics. It's original author, a man named Kespers Peeters then decided to write a similar program in C computing language rather in pascal, in which he renamed it Cadabra. However, Cadabra has been written for a wider range of uses, it is no longer restricted to physicists.	File:CadabraScreenShot1.png
CoCoA	CoCoA (COmputations in COmmutative Algebra) is an open source software use for computing multivariate polynomials initiated in 1987. Originally written in Pascal, CoCoA was translated into C language.	File:CoCoAlogo.jpg

Numerical analysis

Numerical analysis is an area of mathematics that creates and analyzes algorithms for obtaining numerical approximations to problems involving continuous variables. When an arbitrary function does not 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.

Octave	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 begun in 1992 and the alpha version was released in 1993. Subsequently, version 1.0 was released a year after that in 1994. Octave is a high level language with the primary intention in numerical computation.	File:OctaveScreenShots1.jpg
Scilab	Inspired by the software named MATLAB, Scilab was initiated in the mid 1980's at the INRIA (French national Institute for computer science and control). François Delebecque and Serge Steer developed it and it was released by INRIA in 1994 as an open source software. Since 2008, Scilab has been distributed under the CeCILL license, which is GPL compatible. In 2010, Scilab Enterprise was founded to provide even more supported to the software.	File:ScilabScreenShots1.jpg
SciPy	SciPy was developed in the python programming language to take advantage of Python's ability to handle large data sets.

Statistics

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 in statistics ‘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 a sample to draw conclusions about the Population.

R

R is both a language and software used for statistical computing and graphing. R was originally developed by Bell Laboratories (Currently known as Lucent Technologies) by John Chambers. Since R is largely written in C language, users can use C or C++ commands to manipulate R-objects directly. Also, R runs on most UNIX platforms. Currently, R has been part of Free Software Foundation GNU project.

File:RScreenShot1.jpg

Multipurpose mathematics software

Such softwares were created with the original intent of providing a math platform that can be compared to proprietary software such as MATLAB and MATHEMATICA. They contain multiple other free softwares and hence have more features than the rest of the softwares mentioned.

Sage	Sage was initiated by William Stein, of Harvard University in 2005 for his personal project in Number 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 on 2005 and almost year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and MAXIMA with an interface that rivals that of Mathematica.	File:Sage ScreenShot.png
MathBuntu	Developed as an alternative to Sage, MathBuntu is for the Ubuntu or Kubuntu operating system.

Basic Definitions

Open Source

Open Source are programs that is available to the general public for use or modification from its original design for free.

Open Source Software

Open Source Software is computer software that is distributed along with its source code.

Mathematics

Mathematics is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.

List of Open Source Software for Mathematics

Sage

Sage is an open source mathematical software which features many mathematical aspects such as algebra, graphs (commonly use in statistics and analytics), number theory, calculus, etc. The software is mostly written in Python and Cython.

Gap

Gap the acronym for (Group, Algorithms, Programming) is an open source software for computing algebraic system commonly associated with the use of graph theory.

KASH

KASH is an associated command line interface associated with KANT. It is an open source software for really pure mathematicians for the usage of pure mathematics especially in the field of number theory and algebraic number theory.

LaTeX

LaTeX is a commonly used open source document by mathematicians to write mathematical formula and mathematical symbols. Most mathematics professor in the colleges or universities would love this software as it helps them to write their lecture notes, set tutorial questions and examination script easier.

References

• http://www.sagemath.org/

• http://www.gap-system.org/

• http://www.sagemath.org/doc/reference/interfaces/sage/interfaces/kash.html

• http://page.math.tu-berlin.de/~kant/kash.html

• http://dlmf.nist.gov/LaTeXML/

• http://www.latex-project.org/