## `numlib::legendre` -- Legendre symbol

#### Introduction

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

#### Call(s)

`numlib::legendre(a, p)`

#### Parameters

`a` | - | an integer
`p` | - | an odd prime

#### Returns

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

#### Related Functions

`numlib::jacobi`, `numlib::isquadres`

#### Details

- `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.

#### Example 1

Computing the Legendre symbol (132132 | 3231277):

    >> numlib::legendre(132132,3231227)

                                         1

#### Example 2

Computing the Legendre symbol (132131 | 3231277):

    >> numlib::legendre(132131,3231227)

                                        -1

#### Example 3

Computing the Legendre symbol (-303|101):

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

                                         0

#### Background

- 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.

#### Changes

- no changes

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