## `numlib::phi` -- Euler phi function, Euler totient function

#### Introduction

`numlib::phi(`n`)` calculates the Euler phi function of `n`.

#### Call(s)

`numlib::phi(n)`

#### Parameters

`n` | - | integer not equal to zero

#### Returns

`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 .

### Overloadable:

`n`

#### Related Functions

`numlib::invphi`

#### Details

- `numlib::phi(`n`)` calculates the Euler phi 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.

#### Example 1

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

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

                                       6, 4

#### Example 2

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

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

                                  numlib::phi(a)

#### Changes

- used to be called `phi`

Do you have questions or comments?
Copyright © SciFace Software GmbH & Co. KG 2000