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Dom::ImageSet -- the domain of images of sets under mappings

Introduction

Dom::ImageSet is the domain of all sets of complex numbers that can be written as the set of all values taken on by some mapping, i.e., sets of the form {f(x1, ..., xn); xi ∈Si } for some function f and some sets S1, ..., Sn .

Domain

Dom::ImageSet()

Details

Introduction

Dom::ImageSet(f, x, S) represents the set of all values that can be obtained by substituting some element of S for x in the expression f.

Dom::ImageSet(f, [x1...], [S1...]) represents the set of all values that can be obtained by substituting, for each i, the identifier xi by some element of Si in the expression f.

Creating Elements

Dom::ImageSet(f, x, S)
Dom::ImageSet(f, [x1...], [S1...])

Parameters

f - arithmetical expression
x - identifier or indexed identifier
S - set of any type

Categories

Cat::Set

Details

Method changevar: change the name of a variable

Method setvar: set the name of the variable

Method homogpointwise: define an n-ary pointwise operator for image sets

Method isEmpty: tests whether a set is empty

Method substituteBySet: substitute an ImageSet for a variable

Method indets: free parameters of a set

Method expr: the defining mapping as an expression

Method variables: list of variables

Method nvars: number of variables

Method sets: list of sets

Method print: print image set

Example 1

We define S to be the set of all integer multiples of π.

>> S:=Dom::ImageSet(k*PI, k, Z_)
                           { X1*PI |  X1 in Z_ }

We may now apply the usual set-theoretic operations.

>> S intersect Dom::Interval(3..7) 
                                {PI, 2 PI}

Super-Domain

Dom::BaseDomain

Changes




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