# Documentation

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# `numlib`::`phi`

Euler phi function

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## Syntax

```numlib::phi(`n`)
```

## Description

`numlib::phi(n)` calculates the Euler φ function of the argument `n`, i.e. the number of numbers smaller than |n| which are relatively prime to `n`. Cf. Example 1.

`numlib::phi` returns an error if the argument is a number but not an integer unequal to zero.

`numlib::phi` returns the function call with evaluated arguments if the argument is not a number. Cf. Example 2.

## Examples

### Example 1

`numlib::phi` works on integers unequal zero:

`numlib::phi(-7), numlib::phi(10)`

### Example 2

`numlib::phi` is returned as a function call with evaluated argument:

`x := a: numlib::phi(x)`

## Parameters

 `n` Integer not equal to zero

## Return Values

`numlib::phi` returns a positive integer, if the argument evaluates to an integer unequal zero. If the argument cannot be evaluate to a number, the function call with evaluated arguments is returned .

`n`