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Macaulay
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.
http://www.math.columbia.edu/~bayer/Macaul...
HartMath
Java computer algebra applet. Some features are: EPOC32 Java version, big rational number arithmetic, symbolic differentiation, linear algebra functions, 2D plot functions, numeric computations, pattern matching, transformation rules, functional programming, pure functions. [Open Source, GPL]
http://www.hartmath.com/
Math Forum - Algebra Software
Algebra software resources compiled by The Math Forum.
http://mathforum.org/algebra/alg.software....
FINITAS
Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.
http://groups.yahoo.com/group/finitas/
gTybalt
An experimental free computer algebra system built on top of GiNaC, CLN and a program to interpret C and C++ commands.
http://www.fis.unipr.it/~stefanw/gtybalt.h...
Axiom Computer Algebra System
Savannah Free Software project for revival of Axiom as open source.
http://savannah.nongnu.org/projects/axiom
perisic
A Java package for multivariate polynomials over polymorphic rings.
http://ring.perisic.com/
Software for Computing Primitive Polynomials.
Free C software for computing primitive polynomials of degree n modulo p for p^n up to about 2^60.
http://www.seanerikoconnor.freeservers.com...
AXIOM
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.nag.co.uk/symbolic_software.asp
LAPACK -- Linear Algebra PACKage
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.
http://netlib2.cs.utk.edu/lapack/
Online Gröbner Basis Calculations
Online computation of reduced ideal bases.
http://grobner.nuigalway.ie/
CMAT
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.
http://www.numbertheory.org/cmat/krm_cmat....
Math Symbolic Library
Evaluate, calculate, simplify and derive symbolic scalar, complex or vector expression. [OpenSource]
http://www.cdrnet.net/projects/nmath/
Computer Algebra and Problem Solving Environments
Abstract for Stanly Steinberg's article in "Comparative CAS Reviews and Philosophy", suggesting 6 ways in which computer algebra systems could be improved.
http://math.unm.edu/~wester/aca96/Steinber...
CoCoA
A special-purpose system for computations in Commutative Algebra.
http://cocoa.dima.unige.it/
Maxima
A GPL CAS based on DOE-MACSYMA. A GPL project.
http://maxima.sourceforge.net/
Miss Lindquist: The Online Algebra Tutor for Word Problems
An intelligent tutoring system funded through a grant from the National Science Foundation to build software that is more like human tutors. This program will tutor students presenting them with progressivly harder problems and will help me when needed.
http://www.cs.cmu.edu/~neil/
MathPad - Scientific Matrices Calculator
Java applet based online Matrix calculation program for analyzing various simultaneous equations.
http://www.mathpad.com/public/htmls/main/l...
Aldor
Functional language in which types are first class values. Normal functions returning types reproduce the features of template classes of other languages. Links to many projects around the world based on Aldor.
http://www.aldor.org/
Computer Algebra Benchmarks
Collated by Computer Algebra Fachgruppe, Mannheim.
http://krum.rz.uni-mannheim.de/cafgbench.h...
Matrix Expression Templates (MET)
C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.
http://met.sourceforge.net/
Combinatorial Representation Theory (CREP)
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.
http://www.mathematik.uni-bielefeld.de/~se...
Mathscribe
Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included.
http://www.mathscribe.com/
Albert
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.cs.clemson.edu/~dpj/albertstuff...
JACAL
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://swissnet.ai.mit.edu/~jaffer/JACAL.h...
Yet Another Computer Algebra System
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.
http://yacas.sourceforge.net/
Macaulay 2
A new software system devoted to supporting research in algebraic geometry and commutative algebra.
http://www.math.uiuc.edu/Macaulay2/
A Tutorial Introduction To AXIOM
By Martin N. Dunstan.
http://www.dcs.st-and.ac.uk/~mnd/documenta...
Algebra Problem Solver
Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.
http://www.cyberedinc.com/
Galois Field Arithmetic Library
A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.
http://www.partow.net/projects/galois/
Fermat
Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.
http://www.bway.net/~lewis/
Symmetrica
A collection of routines, written in C, for computing in the representation theory of classical and symmetric groups, and related areas. Public domain.
http://www.mathe2.uni-bayreuth.de/axel/sym...
LAPACK++: Linear Algebra Package in C++
(v. 1.1a) a software library for numerical linear algebra; however, it does not include all of the capabilities of original f77 LAPACK.
http://math.nist.gov/lapack++/
KAN
Rings and Computer algebra software, part of OpenXM.
http://www.math.sci.kobe-u.ac.jp/KAN/
Schur
A package for Lie groups by Brian G. Wybourne. DOS, Win32, Unix. Ordering information.
http://smc.vnet.net/Schur.html
Computer Algebra Pages and Servers
A collection of links.
http://krum.rz.uni-mannheim.de/cabench/caw...
GB and FGB
Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.
http://www-calfor.lip6.fr/~jcf/
ZEN
A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
http://fchabaud.free.fr/English/ZEN/
SymbolicNet
Information centre for symbolic mathematical computation. Links to research and software.
http://www.symbolicnet.org/
WinCoCoA Home Page
A version of CoCoA for Windows.
http://www.physik.uni-regensburg.de/~krm03...
GAP - Groups, Algorithms and Programming
A free system for computational discrete algebra.
http://www-history.mcs.st-and.ac.uk/~gap/
Algebra Helper
Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.
http://www.algebra-answer.com/
SINGULAR
Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.
http://www.singular.uni-kl.de/
MAS - The Modula-2 Algebra System
MAS is an experimental computer algebra system with algebraic specification capabilities for the design and study of algebraic algorithms. Downloads, documentation.
http://www.fmi.uni-passau.de/algebra/proje...
GiNaC
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.ginac.de/
FRISCO - A Framework for Integrated Symbolic/Numeric Computation
The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.
http://www.nag.co.uk/projects/FRISCO.html
Algebra Cheat
Program solves variable equations and gives explanations of steps used.
http://www.bacsoftware.co.uk/algebra/
Comparison of Polynomial-Oriented Computer Algebra Systems
By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.
http://www.fordham.edu/lewis/cacomp.html
GIAC
Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.
http://www-fourier.ujf-grenoble.fr/~pariss...
Felix
Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.
http://felix.hgb-leipzig.de/
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2006