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solvelib::preImage

Preimage of a set under a mapping

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

solvelib::preImage(a, x, S)

Description

solvelib::preImage(a, x, S) returns the set of all numbers y such that substituting y for x in a gives an element of S.

S can be a set of any type (finite or infinite).

Examples

Example 1

In case of a finite set S, the preimage of S is just the union of all sets solve(a=s, x), where s ranges over the elements of S.

solvelib::preImage(x^2+2, x, {11, 15});

Note that computing this set may take a long time for large finite sets:

time(solvelib::preImage(x, x, 
           Z_ intersect Dom::Interval(0, 1000000)))

Example 2

For intervals, the preimage is usually an interval or a union of intervals.

solvelib::preImage(x^2+2, x, Dom::Interval(3..7));

Parameters

a

Arithmetic expression

x

Identifier

S

Set

Return Values

Set

See Also

MuPAD Functions

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