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solvelib::preImage -- preimage of a set under a mapping

Introduction

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.

Call(s)

solvelib::preImage(a, x, S)

Parameters

a - arithmetic expression
x - identifier
S - set

Returns

set

Related Functions

solve

Details

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});
   
                                    1/2      1/2
                          {-3, 3, 13   , - 13   }
      

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));
                     ]1, 5^(1/2)[ union ]-5^(1/2), -1[

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