Computer algebra system: Difference between revisions
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imported>Igor Grešovnik (added types of symbolic manipulation) |
imported>Jitse Niesen m (spelling) |
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A '''computer algebra system''' ('''CAS''') is a [[ | {{subpages}} | ||
A '''computer algebra system''' ('''CAS''') is a [[software program]] that facilitates [[symbolic mathematics]]. The core functionality of any computer algebra systems is manipulation of mathematical expressions in symbolic form. Most of such systems incorporate their own programming languages. | |||
Typical symbolic manipulations that can be performed by ''computer algebra systems'' include: | Typical symbolic manipulations that can be performed by ''computer algebra systems'' include: | ||
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*[[factorization]] | *[[factorization]] | ||
*[[Closed-form solution|solution]] of linear and some non-linear equations | *[[Closed-form solution|solution]] of linear and some non-linear equations | ||
*solution of some [[Differential equation|differential | *solution of some [[Differential equation|differential equations]] | ||
*taking [[limit of a function|limits]] | *taking [[limit of a function|limits]] | ||
*some [[antidifferentiation|indefinite]] and [[integral|definite integration]] | *some [[antidifferentiation|indefinite]] and [[integral|definite integration]] | ||
*integral transforms | *integral transforms | ||
*[[arbitrary precision|arbitrary precision numeric]] operations | *[[arbitrary precision|arbitrary precision numeric]] operations | ||
*[[mathematical series| | *[[mathematical series|series]] operations such as expansion, summation and products | ||
*matrix operations | *matrix operations | ||
*display of mathematical expressions in different forms | *display of mathematical expressions in different forms | ||
*[[Gröbner basis]] calculations | |||
Latest revision as of 14:01, 18 January 2008
A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of any computer algebra systems is manipulation of mathematical expressions in symbolic form. Most of such systems incorporate their own programming languages.
Typical symbolic manipulations that can be performed by computer algebra systems include:
- simplification of expressions to some standard form or to the smallest possible expression; assumptions and constraints can be defined used in simplification.
- substitution of symbolic or numeric values for expressions
- change of form of expressions, e.g. expanding products and powers, writing trigonometric functions as exponentials, etc.
- partial differentiation and total differentiation
- factorization
- solution of linear and some non-linear equations
- solution of some differential equations
- taking limits
- some indefinite and definite integration
- integral transforms
- arbitrary precision numeric operations
- series operations such as expansion, summation and products
- matrix operations
- display of mathematical expressions in different forms
- Gröbner basis calculations