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symbolic computation
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(Topic)
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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 limited-precision floating-point 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.
Some well known, general symbolic computation CASes are:
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:
Some non-CAS symbolic computation libraries, with their supported languages, are:
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- Based on content from the Data Analysis Briefbook
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"symbolic computation" is owned by akrowne.
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(view preamble)
| Other names: |
formula manipulation, algebraic computation |
| Also defines: |
CAS, computer algebra systems |
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Cross-references: theory, group, curves, varieties, singular, algebraic geometry, scope, language, area, algebraic, polynomials, Calculus, matrix, linear algebra, differentiation, operations, expressions, transformation
There are 18 references to this entry.
This is version 14 of symbolic computation, born on 2001-12-25, modified 2005-12-05.
Object id is 1139, canonical name is AlgebraicComputation.
Accessed 10094 times total.
Classification:
| AMS MSC: | 68W30 (Computer science :: Algorithms :: Symbolic computation and algebraic computation) | | | 14Q99 (Algebraic geometry :: Computational aspects in algebraic geometry :: Miscellaneous) | | | 11Y40 (Number theory :: Computational number theory :: Algebraic number theory computations) | | | 12Y05 (Field theory and polynomials :: Computational aspects of field theory and polynomials) | | | 13P99 (Commutative rings and algebras :: Computational aspects of commutative algebra :: Miscellaneous) | | | 16Z05 (Associative rings and algebras :: Computational aspects of associative rings) | | | 17-08 (Nonassociative rings and algebras :: Computational methods) | | | 33F99 (Special functions :: Computational aspects :: Miscellaneous) |
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Pending Errata and Addenda
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