# Documentation

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# `numlib`::`legendre`

Legendre symbol

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## Syntax

```numlib::legendre(`a`, `p`)
```

## Description

`numlib::legendre(a, p)` returns the Legendre symbol `(a | p)`.

`numlib::legendre` returns an error if one of its arguments evaluates to a number of wrong type.

`numlib::legendre` returns the function call with evaluated arguments if at least one of its arguments does not evaluate to a number.

## Examples

### Example 1

Computing the Legendre symbol `(132132 | 3231277)`:

`numlib::legendre(132132,3231227)`

### Example 2

Computing the Legendre symbol `(132131 | 3231277)`:

`numlib::legendre(132131,3231227)`

### Example 3

Computing the Legendre symbol `(-303 | 101)`:

`numlib::legendre(-303,101)`

## Parameters

 `a` An integer `p` An odd prime

## Return Values

`numlib::legendre(a,p)` returns `-1`, `0`, `1`, or the function call with evaluated arguments.

## Algorithms

If p is an odd prime and if a is an integer divisible by p then by definition the Legendre symbol `(a | p)` is zero.