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Computer software (or simply software) is the programs and procedures that enable a computer to perform a specific task, as opposed to the physical components of the system (hardware). This includes application software such as a word processor, which enables a user to perform a task, and system software such as an operating system, which enables other software to run properly, by interfacing with hardware and with other software.
The term "software" was first used in this sense by John W. Tukey in 1957. In computer science and software engineering, computer software is all information processed by computer systems, programs and data. The concept of reading different sequences of instructions into the memory of a device to control computations was invented by Charles Babbage as part of his difference engine. The theory that is the basis for most modern software was first proposed by Alan Turing in his 1935 essay Computable numbers with an application to the Entscheidungsproblem. Hally, Mike (2005:79). Electronic brains/Stories from the dawn of the computer age. British Broadcasting Corporation and Granta Books, London. ISBN 1-86-207663-4.
Relationship to hardware
Computer software is so called in contrast to computer hardware, which encompasses the physical interconnections and devices required to store and execute (or run) the software. In computers, software is loaded into RAM and executed in the central processing unit. At the lowest level, software consists of a machine language specific to an individual processor. A machine language consists of groups of binary values signifying processor instructions (object code), which change the state of the computer from its preceding state. Software is an ordered sequence of instructions for changing the state of the computer hardware in a particular sequence. It is generally written in high-level programming languages that are easier and more efficient for humans to use (closer to natural language) than machine language. High-level languages are compiled or interpreted into machine language object code. Software may also be written in an assembly language, essentially, a mnemonic representation of a machine language using a natural language alphabet. Assembly language must be assembled into object code via an assembler. More on [ Computer software ]
Computational Algebra :: Algorithms
Software :: Math
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A Tutorial Introduction To AXIOM - By Martin N. Dunstan.
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.
Aldor - Originally an extension to Axiom, now a separate product. Binaries are available free for non-profit use, with documentation, tips, projects and links.
Algebra Cheat - Program solves variable equations and gives explanations of steps used.
Meta Description: [ Algebra Cheat 1 Enter an Algebra expression or equation and press the simplify button, immediately the simplified version of expression is shown. A great tool for polynomial multiplication, Algebra Cheat 1 is even capable of polynomial division, try it and see. To help you learn and understand Al... ]
Algebra Helper - Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.
Algebra Problem Solver - Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.
Meta Description: [ PAT - Solves and graphs YOUR algebra problems step-by-step with explanations; Solves equations and inequalities, factors and simplifies expressions and polynomials, radical expressions; Graphs rational functions, parabolas, quadratic functions. ]
Algebra Word Problem Tutor:Miss Lindquist - The world's first web-delivered self-improving intelligent tutoring system able to tutor students in writing expressions for algebra word problems.
Meta Description: [ An intelligent tutoring system thatteaches student how to translate algebra word problems into algebraexpressions. ]
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.
Meta Description: [ AXIOM is a powerful computer algebra system which provides a complete environment for anyone needing to manipulate and solve mathematical formulae. Its application is wide-ranging, from pure mathematics research through branches of physics, chemistry, biology and engineering to financial modellin... ]
Axiom Computer Algebra System - Savannah Free Software project for revival of Axiom as open source.
Meta Description: [ Savannah is a central point for development, distribution and maintainance of Free Software. It allows contributors to easily join existing Free Software projects. ]
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.
CoCoA - A special-purpose system for computations in Commutative Algebra.
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.
Comparison of Polynomial-Oriented Computer Algebra Systems - By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.
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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.
Computer Algebra Benchmarks - Collated by Computer Algebra Fachgruppe, Mannheim.
Computer Algebra Pages and Servers - A collection of links.
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Edu2000 Visual Algebra - Designed to ease the difficulties many students experience during the transition from arithmetic into the world of algebra using visualization. Covers linear and quadratic equations.
Meta Description: [ Visual Algebra 1 helps overcome the difficulties experienced when making the transition from arithmetic into algebra, insuring success in algebra studies and improved test performance. ]
Felix - Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.
Fermat - Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.
FINITAS - Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.
Meta Description: [ finitas: FINITAS ]
FRISCO - A Framework for Integrated Symbolic/Numeric Computation - The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.
Galois Field Arithmetic Library - A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.
Meta Description: [ A simple library in C++ for performing arithmetic between elements and polynomials over Galois fields ]
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GAP - Groups, Algorithms and Programming - A free system for computational discrete algebra.
Meta Description: [ GAP system for computational discrete algebra, especially computational group theory ]
GB and FGB - Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.
GIAC - Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.
Meta Description: [ semi-classical mechanics, free computer algebra system ]
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).
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gTybalt - An experimental free computer algebra system built on top of GiNaC, CLN and a program to interpret C and C++ commands.
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HartMath - An experimental computer algebra system written in Java and available free under GPL.
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.
Meta Description: [ JACAL is 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. ]
KAN - Rings and Computer algebra software, part of OpenXM.
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.
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.
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LOWX - Parallel low-index subgroups algorithm software by Peter Dobcsányi for finding all subgroups up to given index in a finitely-presented group. Download documentation and binary distribution for Linux/i386 and Sparc/Solaris platforms.
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.
Macaulay 2 - A new software system devoted to supporting research in algebraic geometry and commutative algebra.
Meta Description: [ Macaulay 2 home page ]
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.
Math Forum - Algebra Software - Algebra software resources compiled by The Math Forum.
Math Symbolic Library - Evaluate, calculate, simplify and derive symbolic scalar, complex or vector expression. [OpenSource]
Meta Description: [ Math.NET is a framework written in C# for symbolic mathematical operations in an object oriented way (opensource), supporting scalar & complex Linear Algebra (Vector, Matrix, Tensor), Complex Expressions, Hyperbolics and Trigonometry, Logic Algebra, 3D geometry with vectors and plains, digital ci... ]
MathPad - Scientific Matrices Calculator - Java applet based online Matrix calculation program for analyzing various simultaneous equations.
Mathscribe - 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) - C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.
Maxima - A GPL CAS based on DOE-MACSYMA. A GPL project.
Meta Description: [ Homepage of the Maxima Project. ]
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Online Gröbner Basis Calculations - Online computation of reduced ideal bases.
perisic - A Java package for multivariate polynomials over polymorphic rings.
Meta Description: [ This Java class package features multivarite polynomials over the rings Z, Q, R, C, finite prime fields, cyclotomic fields, algebraic extensions and more.. ]
Schur - A package for Lie groups by Brian G. Wybourne. DOS, Win32, Unix. Ordering information.
SINGULAR - Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.
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.
Meta Description: [ Free C software for computing primitive polynomials of
degree n modulo p for p^n up to about 2^60. ]
SymbolicNet - Directory of links on Symbolic Algebraic Computation: Frequently Asked Questions, Live Demos, software for download, events, bibliography, research groups, and researcher directory.
Meta Description: [ Information center for researchers and professionals in the field of symbolic computation, computer algebra, mathematical computation, software, systems, conferences, jobs, calendar, announcements, literature, books, research groups, email directory, live demos ]
Symmetrica - A collection of routines, written in C, for computing in the representation theory of classical and symmetric groups, and related areas. Public domain.
WinCoCoA Home Page - A version of CoCoA for Windows.
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.
ZEN - A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
Meta Description: [ Mathematical library for fast computation in finite extension over finite rings. ]
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