Computer algebra: Difference between revisions

Revision as of 20:40, 28 December 2022

Revision as of 11:50, 29 December 2022

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Except for [[number]]s and [[variable (mathematics)|variables]], every [[Expression (mathematics)|mathematical expression]] may be viewed as the symbol of an operator followed by a [[sequence]] of operands. In computer algebra software, the expressions are usually represented in this way. This representation is very flexible, and many things that seem not to be mathematical expressions at first glance, may be represented and manipulated as such. For example, an equation is an expression with "=" as an operator, a matrix may be represented as an expression with "matrix" as an operator and its rows as operands.

Even programs may be considered and represented as expressions with operator "procedure" and, at least, two operands, the list of parameters and the body, which is itself an expression with "body" as an operator and a sequence of instructions as operands. Conversely, any mathematical expression may be viewed as a program. For example, the expression {{math|''a'' + ''b''}} may be viewed as a program for the addition, with {{math|''a''}} and {{math|''b''}} as parameters. Executing this program consists in ''evaluating'' the expression for given values of {{math|''a''}} and {{math|''b''}}; if they are not given antany values, the result of the evaluation is simply its input.

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.