symbolic computation
1 Symbolic Computation
Also called formula manipulation or algebraic computation.
Symbolic computation^{} refers to the automatic transformation^{} of mathematical expressions in symbolic form, hence in an exact way, as opposed to numerical and hence limitedprecision floatingpoint computation. Typical operations^{} 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 language^{} 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.axiomdeveloper.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/products^{}/maple/Maple

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

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http://www.unikoeln.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, applicationspecific systems, such as:

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http://www.singular^{}.unikl.de/SINGULAR (algebraic geometry^{}, esp. singular varieties^{})

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http://pari.math.ubordeaux.fr/PARIGP (computations on curves)

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http://wwwgap.dcs.stand.ac.uk/ gap/GAP (group theory)
Some nonCAS symbolic computation libraries, with their supported languages, are:

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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  20130322 12:04:20 
Last modified on  20130322 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 1708 
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 