symbolic computation


1 Symbolic Computation

Also called formula manipulation or algebraic computation.

Symbolic computationMathworldPlanetmath refers to the automatic transformationPlanetmathPlanetmath of mathematical expressions in symbolic form, hence in an exact way, as opposed to numerical and hence limited-precision floating-point computation. Typical operationsMathworldPlanetmath include differentiation and integration, linear algebra and matrix calculus, operations with polynomials, or the simplification of algebraic expressions.

Programs or systems in this area which provide a languagePlanetmathPlanetmath interface are called Computer Algebra Systems (or CASes). There are also symbolic computation libraries for existing programming languages.

Primarily designed for applications in theoretical physics or mathematics, these systems (which are often interactive in the case of CASes) can be used in any area where straightforward but tedious or lengthy calculations with formulae are required.

2 Systems

Some well known, general symbolic computation CASes are:

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    http://www.axiom-developer.orgAxiom

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    http://www.scientek.com/macsyma/mxmain.htmMacsyma

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    http://maxima.sourceforge.net/GNU Maxima

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    http://www.maplesoft.com/productsPlanetmathPlanetmathPlanetmath/maple/Maple

  • •

    http://www.wolfram.com/products/mathematica/index.htmlMathematica

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    http://www.uni-koeln.de/REDUCE/Reduce

These systems have different scope and facilities, and some are easier to use or to access than others. There is a trend away from generalized CAS systems to more specialized, application-specific systems, such as:

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    http://www.singularPlanetmathPlanetmath.uni-kl.de/SINGULAR (algebraic geometryMathworldPlanetmathPlanetmath, esp. singular varietiesMathworldPlanetmathPlanetmath)

  • •

    http://pari.math.u-bordeaux.fr/PARI-GP (computations on curves)

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    http://www-gap.dcs.st-and.ac.uk/ gap/GAP (group theory)

Some non-CAS symbolic computation libraries, with their supported languages, are:

  • •

    http://www.ginac.de/GiNaC (C++)

References

  • 1 Based on content from the http://rkb.home.cern.ch/rkb/titleA.htmlData Analysis Briefbook
Title symbolic computation
Canonical name SymbolicComputation
Date of creation 2013-03-22 12:04:20
Last modified on 2013-03-22 12:04:20
Owner akrowne (2)
Last modified by akrowne (2)
Numerical id 18
Author akrowne (2)
Entry type Topic
Classification msc 33F99
Classification msc 17-08
Classification msc 16Z05
Classification msc 13P99
Classification msc 12Y05
Classification msc 11Y40
Classification msc 14Q99
Classification msc 68W30
Synonym formula manipulation
Synonym algebraic computation
Defines CAS
Defines computer algebra systems