# Documentation

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# `solvelib`::`splitVectorSet`

Factor a set of vectors into a cartesian product

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## Syntax

```solvelib::splitVectorSet(`S`)
```

## Description

`solvelib::splitVectorSet(S)` returns a list S1, …, Sn of sets of complex numbers such that `S` is the cartesian product of the Si, or `FAIL` if such factorization could not be found.

The set `S` may be finite or infinite, of any type.

## Examples

### Example 1

We split a finite set of vectors into its factors:

`solvelib::splitVectorSet({[1, 2], [1, 3], [0, 2], [0, 3]})`

The following set cannot be written as a cartesian product:

`solvelib::splitVectorSet({[1, 2], [0, 2], [0, 3]})`

### Example 2

Infinite sets can also be handled:

`S:= Dom::ImageSet([k*PI, l*PI+2], [k, l], [Z_, Z_])`

`solvelib::splitVectorSet(S)`

`delete S:`

## Parameters

 `S` Set of vectors

## Return Values

List of type `DOM_LIST`, or `FAIL`

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