Documentation

# `div`, `_div`

Integer part of a quotient

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## Syntax

```m div n
_div(`x`, `m`)
```

## Description

`x div m` represents the integer q satisfying x = qm + r with 0 ≤ r < |m|.

For positive `x` and `m`, `q` = ```x div m``` is the integer part of the quotient `x/m`, i.e., `q` = `trunc(x/m)`.

`x div m` is equivalent to the function call ```_div(x, m)```.

An integer is returned if both `x` and `m` evaluate to integers. A symbolic expression of type `"_div"` is returned if either `x` or `m` does not evaluate to a number. An error is raised if `x` or `m` evaluates to a number that is not an integer.

`div` does not operate on polynomials. Use `divide`.

## Examples

### Example 1

With the default setting for `mod`, the identity ```(x div m) * m + (x mod m) = x``` holds for integer numbers `x` and `m`:

`43 div 13 = trunc(43/13), 43 mod 13 = frac(43/13) * 13`
` `
`(43 div 13) * 13 + (43 mod 13) = 43`
` `

### Example 2

Symbolic expressions of type `"_div"` are returned, if either `x` or `m` does not evaluate to a number:

`43 div m, x div 13, x div m`
` `
`type(x div m)`
` `

If `x` or `m` are numbers, they must be integer numbers:

`1/2 div 2`
```Error: Invalid argument. [div] ```
`x div 2.0`
```Error: Invalid argument. [div] ```

## Parameters

 `x`, `m` Integers or symbolic arithmetical expressions; `m` must not be zero.

## Return Values

Integer or an arithmetical expression of type `"_div"`.

` m`, `x`