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Computers > Algorithms > Computational Algebra (60)
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A Tutorial Introduction To AXIOM - http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/axiom.html
By Martin N. Dunstan.

Algebra Cheat - http://www.bacsoftware.co.uk/algebra/
Program solves variable equations and gives explanations of steps used.

Algebra Helper - http://www.algebra-answer.com/
Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.

Algebra Problem Solver - http://www.cyberedinc.com/
Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.

Algebra Word Problem Tutor:Miss Lindquist - http://www.cs.cmu.edu/~neil/
The world's first web-delivered self-improving intelligent tutoring system able to tutor students in writing expressions for algebra word problems.

Axiom Computer Algebra System - http://savannah.nongnu.org/projects/axiom
Savannah Free Software project for revival of Axiom as open source.

Combinatorial Representation Theory (CREP) - http://www.mathematik.uni-bielefeld.de/~sek/crep.html
CREP is designed to deal with categories whose morphism spaces are finite-dimensional over a field k. The main example of a category with this property is the category of finite-dimensional representations of an associative unital k-algebra.

Comparison of Polynomial-Oriented Computer Algebra Systems - http://www.fordham.edu/lewis/cacomp.html
By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.

Computer Algebra and Problem Solving Environments - http://math.unm.edu/~wester/aca96/Steinberg_abstract.html
Abstract for Stanly Steinberg's article in "Comparative CAS Reviews and Philosophy", suggesting 6 ways in which computer algebra systems could be improved.

Computer Algebra Benchmarks - http://krum.rz.uni-mannheim.de/cafgbench.html
Collated by Computer Algebra Fachgruppe, Mannheim.

Computer Algebra Pages and Servers - http://krum.rz.uni-mannheim.de/cabench/cawww.html
A collection of links.

FRISCO - A Framework for Integrated Symbolic/Numeric Computation - http://www.nag.co.uk/projects/FRISCO.html
The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.

Galois Field Arithmetic Library - http://www.partow.net/projects/galois/
A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.

GAP - Groups, Algorithms and Programming - http://www-history.mcs.st-and.ac.uk/~gap/
A free system for computational discrete algebra.

GB and FGB - http://www-calfor.lip6.fr/~jcf/
Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.

http://cocoa.dima.unige.it/ - http://cocoa.dima.unige.it/
A special-purpose system for computations in Commutative Algebra.

http://fchabaud.free.fr/English/ZEN/ - http://fchabaud.free.fr/English/ZEN/
A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.

http://felix.hgb-leipzig.de/ - http://felix.hgb-leipzig.de/
Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.

http://groups.yahoo.com/group/finitas/ - http://groups.yahoo.com/group/finitas/
Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.

http://maxima.sourceforge.net/ - http://maxima.sourceforge.net/
A GPL CAS based on DOE-MACSYMA. A GPL project.

http://ring.perisic.com/ - http://ring.perisic.com/
A Java package for multivariate polynomials over polymorphic rings.

http://smc.vnet.net/Schur.html - http://smc.vnet.net/Schur.html
A package for Lie groups by Brian G. Wybourne. DOS, Win32, Unix. Ordering information.

http://swissnet.ai.mit.edu/~jaffer/JACAL.html - http://swissnet.ai.mit.edu/~jaffer/JACAL.html
An interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. Linux RPM distribution.

http://www-fourier.ujf-grenoble.fr/~parisse/english.html - http://www-fourier.ujf-grenoble.fr/~parisse/english.html
Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.

http://www.aldor.org/ - http://www.aldor.org/
Originally an extension to Axiom, now a separate product. Binaries are available free for non-profit use, with documentation, tips, projects and links.

http://www.bway.net/~lewis/ - http://www.bway.net/~lewis/
Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.

http://www.cs.clemson.edu/~dpj/albertstuff/albert.html - http://www.cs.clemson.edu/~dpj/albertstuff/albert.html
Albert is an interactive program to assist the specialist in the study of nonassociative algebra: the main problem addressed is the recognition of polynomial identities in varieties of nonassociative algebras. Download source code in C.

http://www.ginac.de/ - http://www.ginac.de/
An open framework for symbolic computation within the C++ programming language. The name GiNaC is an iterated and recursive abbreviation for "GiNaC is Not a CAS", where CAS stands for Computer Algebra System. Its design is revolutionary in a sense that contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities. It is published under the GNU Public License (GPL).

http://www.math.sci.kobe-u.ac.jp/KAN/ - http://www.math.sci.kobe-u.ac.jp/KAN/
Rings and Computer algebra software, part of OpenXM.

http://www.nag.co.uk/symbolic_software.asp - http://www.nag.co.uk/symbolic_software.asp
Symbolic solver complete with a high-level interactive language, user extensible library and visualisation tool for the manipulation of graphical output. For Unix and Windows. No longer produced: support ceases at the end of 2001.

http://www.numbertheory.org/cmat/krm_cmat.html - http://www.numbertheory.org/cmat/krm_cmat.html
A matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p.

LAPACK -- Linear Algebra PACKage - http://netlib2.cs.utk.edu/lapack/
written in Fortran77; provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems.

LAPACK++: Linear Algebra Package in C++ - http://math.nist.gov/lapack++/
(v. 1.1a) a software library for numerical linear algebra; however, it does not include all of the capabilities of original f77 LAPACK.

Macaulay - http://www.math.columbia.edu/~bayer/Macaulay/index.html
Macaulay is a computer algebra system for mathematical computations in algebraic geometry and commutative algebra. At its core is a carefully tuned implementation of Grobner basis methods for manipulating systems of polynomial equations.

Macaulay 2 - http://www.math.uiuc.edu/Macaulay2/
A new software system devoted to supporting research in algebraic geometry and commutative algebra.

MAS - The Modula-2 Algebra System - http://www.fmi.uni-passau.de/algebra/projects/mas.php3
MAS is an experimental computer algebra system with algebraic specification capabilities for the design and study of algebraic algorithms. Downloads, documentation.

Math Forum - Algebra Software - http://mathforum.org/algebra/alg.software.html
Algebra software resources compiled by The Math Forum.

Math Symbolic Library - http://www.cdrnet.net/projects/nmath/
Evaluate, calculate, simplify and derive symbolic scalar, complex or vector expression. [OpenSource]

MathPad - Scientific Matrices Calculator - http://www.mathpad.com/public/htmls/main/left/matrix/MatrixInfo.html
Java applet based online Matrix calculation program for analyzing various simultaneous equations.

Mathscribe - http://www.mathscribe.com/
Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included.

Matrix Expression Templates (MET) - http://met.sourceforge.net/
C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.

Online Gröbner Basis Calculations - http://grobner.nuigalway.ie/grobner/basis.html
Online computation of reduced ideal bases.

SINGULAR - http://www.singular.uni-kl.de/
Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.

Software for Computing Primitive Polynomials. - http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/overview.html
Free C software for computing primitive polynomials of degree n modulo p for p^n up to about 2^60.

SymbolicNet - http://www.symbolicnet.org/
Directory of links on Symbolic Algebraic Computation: Frequently Asked Questions, Live Demos, software for download, events, bibliography, research groups, and researcher directory.

Symmetrica - http://www.mathe2.uni-bayreuth.de/axel/symneu_engl.html
A collection of routines, written in C, for computing in the representation theory of classical and symmetric groups, and related areas. Public domain.

Yet Another Computer Algebra System - http://yacas.sourceforge.net/
A general purpose easy program for It is built on top of its own programming language designed for symbolic manipulation of math symbols. Includes information on how to use the software.

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