# quorem

Quotient and remainder

## Description

`[`

divides `Q`

,`R`

] =
quorem(`A`

,`B`

,`var`

)`A`

by
`B`

and returns the quotient
`Q`

and remainder
`R`

of the division, such that
`A = Q*B + R`

. This syntax
regards `A`

and
`B`

as polynomials in the
variable `var`

.

If `A`

and
`B`

are matrices,
`quorem`

performs elements-wise
division, using `var`

as a
variable. It returns the quotient
`Q`

and remainder
`R`

of the division, such that
`A = Q.*B + R`

.

`[`

uses the variable determined by
`Q`

,`R`

] =
quorem(`A`

,`B`

)`symvar(A,1)`

. If
`symvar(A,1)`

returns an empty
symbolic object `sym([])`

, then
`quorem`

uses the variable
determined by
`symvar(B,1)`

.

If both `symvar(A,1)`

and
`symvar(B,1)`

are empty, then
`A`

and `B`

must both be integers or matrices with integer
elements. In this case,
`quorem(A,B)`

returns symbolic
integers `Q`

and
`R`

, such that ```
A = Q*B
+ R
```

. If `A`

and
`B`

are matrices, then
`Q`

and `R`

are symbolic matrices with integer elements, such
that `A = Q.*B + R`

, and each
element of `R`

is smaller in
absolute value than the corresponding element of
`B`

.

## Examples

### Divide Multivariate Polynomials

Compute the quotient and
remainder of the division of these multivariate
polynomials with respect to the variable
`y`

:

syms x y p1 = x^3*y^4 - 2*x*y + 5*x + 1; p2 = x*y; [q, r] = quorem(p1, p2, y)

q = x^2*y^3 - 2 r = 5*x + 1

### Divide Univariate Polynomials

Compute the quotient and remainder of the division of these univariate polynomials:

syms x p = x^3 - 2*x + 5; [q, r] = quorem(x^5, p)

q = x^2 + 2 r = - 5*x^2 + 4*x - 10

### Divide Integers

Compute the quotient and remainder of the division of these integers:

[q, r] = quorem(sym(10)^5, sym(985))

q = 101 r = 515

## Input Arguments

## Output Arguments

## Version History

**Introduced before R2006a**