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Added citations for Mathematica and Maple's usage of the GMP library and internal data storage methods. |
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Therefore, the basic numbers used in computer algebra are the integers of the mathematicians, commonly represented by an unbounded signed sequence of [[numerical digit|digits]] in some [[radix|base of numeration]], usually the largest base allowed by the [[machine word]]. These integers allow to define the [[rational number]]s, which are [[irreducible fraction]]s of two integers.
Programming an efficient implementation of the arithmetic operations is a hard task. Therefore, most free [[computer algebra system]]s and some commercial ones such as [[Mathematica]] and [[Maple (software)]],<ref>[https://library.wolfram.com/infocenter/Conferences/7518/Macalester_talk.txt "The Mathematica Kernel: Issues in the Design and Implementation"]. October 2006. Retrieved 2023-11-29.</ref><ref>[https://www.maplesoft.com/support/help/AddOns/view.aspx?path=GMP "The GNU Multiple Precision (GMP) Library"]. [[Maplesoft]]. Retrieved 2023-11-29.</ref> use the [[GNU Multiple Precision Arithmetic Library|GMP library]], which is thus a ''de facto'' standard.
==== Expressions ====
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This process of delayed evaluation is fundamental in computer algebra. For example, the operator "=" of the equations is also, in most computer algebra systems, the name of the program of the equality test: normally, the evaluation of an equation results in an equation, but, when an equality test is needed, either explicitly asked by the user through an "evaluation to a Boolean" command, or automatically started by the system in the case of a test inside a program, then the evaluation to a boolean result is executed.
As the size of the operands of an expression is unpredictable and may change during a working session, the sequence of the operands is usually represented as a sequence of either [[Pointer (computer programming)|pointers]] (like in [[Macsyma]])<ref>{{Cite book |url=https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf |title=Macsyma Mathematics and System Reference Manual |publisher=[[Macsyma]] |year=1996 |pages=419}}</ref> or entries in a [[hash table]] (like in [[Maple (software)|Maple]]).
=== Simplification ===
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