Editing Computer algebra system (section)

{{Short description|Mathematical software}}
{{Use dmy dates|date=April 2019|cs1-dates=y}}
{{Redirect|Symbolic algebra|the algebra of logic|Symbolical algebra}}
A '''computer algebra system''' ('''CAS''') or '''symbolic algebra system''' ('''SAS''') is any [[mathematical software]] with the ability to manipulate [[mathematical expressions]] in a way similar to the traditional manual computations of [[mathematician]]s and [[scientist]]s. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "[[computer algebra]]" or "symbolic computation", which has spurred work in [[algorithm]]s over [[mathematical object]]s such as [[polynomial]]s.

Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as [[number theory]], [[group theory]], or teaching of [[elementary mathematics]].

General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as:
*a [[user interface]] allowing a user to enter and display mathematical formulas, typically from a keyboard, menu selections, mouse or stylus.
*a [[programming language]] and an [[interpreter (computing)|interpreter]] (the result of a computation commonly has an unpredictable form and an unpredictable size; therefore user intervention is frequently needed),
*a [[Symbolic computation#Simplification|simplifier]], which is a [[rewrite system]] for simplifying mathematics formulas,
*a [[memory management|memory manager]], including a [[garbage collector (computing)|garbage collector]], needed by the huge size of the intermediate data, which may appear during a computation,
*an [[arbitrary-precision arithmetic]], needed by the huge size of the integers that may occur,
*a large library of mathematical [[algorithm]]s and [[special functions]].

The library must not only provide for the needs of the users, but also the needs of the simplifier. For example, the computation of [[polynomial greatest common divisor]]s is systematically used for the simplification of expressions involving fractions.

This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems. Significant systems include [[axiom (computer algebra system)|Axiom]], [[GAP_(computer_algebra_system)|GAP]], [[Maxima (software)|Maxima]], [[Magma (computer algebra system)|Magma]], [[Maple (software)|Maple]], [[Mathematica]], and [[SageMath]].