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Computer algebra systems and TeXmacs
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1.Axiom

Axiom is a general purpose Computer Algebra system. It is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.

Axiom has been in development since 1973 and was sold as a commercial product. It has been released as free software (under a BSD-like license).

Efforts are underway to extend this software to

Axiom web page : http://www.nongnu.org/axiom/

Axiom project : http://savannah.nongnu.org/projects/axiom

2.Giac

Giac Is A Computer algebra system. The system has been designed by Bernard Parisse and is under active development.

3.GTybalt

GTybalt is a free computer algebra system which is built on top of GiNaC, CLN and a program to interpret C and C++ commands. gTybalt, which is still in an experimental stage, is maintained by Stefan Weinzierl. Some of the main features of gTybalt are the following:

4.Macaulay 2

Macaulay 2 is a new software system devoted to supporting research in algebraic geometry and commutative algebra. The software is available now in source code for porting, and in compiled form for Linux, SunOS, Solaris, Windows, and a few other Unix machines. An interface with TeXmacs is currently being implemented.

5.Maxima

Maxima is not only one of the oldest and best computer algebra systems around, it is also one of the only general purpose systems for which there is a free implementation. The current free Maxima implementation was started by William F. Schelter. It is dedicated to his memory. Here follow some features of Maxima:

6.Pari

Pari-gp is a software package for computer-aided number theory. It consists of a C library, libpari (with optional assembler cores for some popular architectures), and of the programmable interactive gp calculator. While you can write your own libpari-based programs, many people just start up a gp session, or have gp execute their scripts. Pari sessions can now be started inside TeXmacs.

Originally developed at Bordeaux by a team led by Henri Cohen, PARI-GP is now maintained by Karim Belabas at the Université Paris-Sud Orsay with the help of many volunteer contributors.

7.Reduce

Reduce is one of the oldest computer algebra systems. It is powerful, stable and highly efficient. Its TeXmacs interface is described in the arXiv article.

8.Sage

Sage is an open source system for mathematical computations. It is written in Python and provides interfaces for a wide variety of other systems, such as Axiom, Gap, Pari GP, Macaulay 2, Maxima, Octave, and Singular. The system was started by William Stein.

9.Yacas

Yacas is, as it's name suggest, yet another computer algebra system. Things implemented include: arbitrary precision, rational numeric, vector, complex, and matrix computations (including inverses and determinants and solving matrix equations), derivatives, solving, Taylor series, numerical solving (Newtons method), and a lot more non-mathematical algorithms. The language natively supports variables and user-defined functions. There is basic support for univariate polynomials, integrating functions and tensor calculations. Yacas is still under development.

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