# Documentation

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# `numlib`::`jacobi`

Jacobi symbol

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## Syntax

```numlib::jacobi(`a`, `m`)
```

## Description

`numlib::jacobi(a,m)` returns the Jacobi symbol ```(a | m)```.

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

## Examples

### Example 1

Computing the Jacobi symbol `(222222 | 304679)`:

`numlib::jacobi(222222, 304679)`

### Example 2

Computing the Jacobi-Symbol `(222222 | 324889)`:

`numlib::jacobi(222222, 324899)`

### Example 3

Computing the Jacobi symbol `(222222 | 333333)`:

`numlib::jacobi(222222, 333333)`

## Parameters

 `a` An integer `m` An odd positive integer

## Return Values

`numlib::jacobi(a,m)` returns 0, 1, or -1, or the function call with evaluated arguments if one of the arguments is not a number.

## Algorithms

`numlib::jacobi` doesn't use `ifactor`.

If a is an integer and m is an odd integer not coprime to a then by definition the Jacobi Symbol `(a | m)` is zero.