# Computer algebra system

From Citizendium, the Citizens' Compendium

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