Editing Computer algebra system (section)

==Symbolic manipulations==
The symbolic manipulations supported typically include:
*simplification to a smaller expression or some [[Canonical form|standard form]], including automatic simplification with assumptions and simplification with constraints
*[[substitution (algebra)|substitution]] of symbols or numeric values for certain expressions
*change of form of expressions: expanding products and powers, partial and full [[factorization]], rewriting as [[partial fraction]]s, [[constraint satisfaction]], rewriting [[trigonometric functions]] as exponentials, transforming logic expressions, etc.
*[[partial differentiation|partial]] and [[total differentiation]]
*some [[antidifferentiation|indefinite]] and [[integral|definite integration]] (see [[symbolic integration]]), including multidimensional integrals
*symbolic constrained and unconstrained global optimization
*[[Closed-form solution|solution]] of linear and some non-linear equations over various domains
*solution of some [[differential equation|differential]] and [[difference equation]]s
*taking some [[limit of a function|limit]]s
*integral transforms
*[[mathematical series|series]] operations such as expansion, summation and products
*matrix operations including [[Direct product (Matrix)|products]], [[matrix inversion|inverses]], etc.
*[[List of statistical packages|statistical computation]]
*[[theorem proving]] and [[proof verification|verification]] which is very useful in the area of [[experimental mathematics]]
*[[Automatic programming#Implementations|optimized code generation]]

In the above, the word ''some'' indicates that the operation cannot always be performed.