# Documentation

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# `solvelib`::`VectorImageSet`

Domain of set of vectors that are images of sets under mappings

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## Syntax

### Domain Creation

`solvelib::VectorImageSet()`

### Element Creation

`solvelib::VectorImageSet(`v`, `x`, `S`)`
`Dom::ImageSet(`v`, `[x1, …]`, `[S1, …]`)`

## Description

### Domain Creation

`solvelib::VectorImageSet` is the domain of all sets of vectors of complex numbers that can be written as the set of all values taken on by some mapping, i.e., sets of the form for some complex-valued functions fj and some sets S1, …, Sn of complex numbers.

Sets of this type are used by `solve` to express solutions of systems of equations like .

### Element Creation

`solvelib::VectorImageSet(v, x, S)` represents the set of all vectors that can be obtained by substituting some element of `S` for `x` in the vector `v`.

`solvelib::VectorImageSet(v, [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 vector `v`.

## Superdomain

`Dom::ImageSet`

## Categories

`Cat::Set`

## Examples

### Example 1

We create a set of two-dimensional vectors:

`S:= Dom::ImageSet([k*PI, k*I*PI], k, Z_)`

Since this is a set of vectors, a `solvelib::VectorImageSet` is created automatically:

`type(S)`

Set-theoretic operations (union, intersection, set difference) may be applied to `S`:

`S intersect {[0, 0], [1, 1]}, S minus S`

`delete S:`

## Parameters

 `v` List or `matrix` `x` Identifier or indexed identifier `S` Set of any type