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# numlib::factorGaussInt

Factorization of Gaussian integers

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```numlib::factorGaussInt(n)
```

## Description

numlib::factorGaussInt(n) returns the factorization of the Gaussian integer n into Gaussian primes. Among associate primes, that one with smallest polar angle is chosen.

## Examples

### Example 1

In the Gaussian integers, 3 remains prime while 5 does not:

`numlib::factorGaussInt(3), numlib::factorGaussInt(5)`

### Example 2

The argument to numlib::factorGaussInt may be any Gaussian integer, that is, every complex number of the form a + b i where a and b are integers:

`numlib::factorGaussInt(2+2*I)`

## Parameters

 n An integer, or a complex number whose real and imaginary part are integers

## Return Values

numlib::factorGaussInt returns a list [u, p1, a1, ..., pk, ak] where u is a unit in the Gaussian integers, the pi are Gaussian primes and the ai are positive integers, such that .

## Algorithms

The function ifactor is used to factor the norm; this step takes most of the running time. Hence, the running time of the algorithm mainly depends on the size of the prime factors of the norm of n.