# quorem

Quotient and remainder

## Syntax

``````[Q,R] = quorem(A,B,var)``````
``````[Q,R] = quorem(A,B)``````

## Description

example

``````[Q,R] = quorem(A,B,var)``` divides `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`.```

example

``````[Q,R] = quorem(A,B)``` uses the variable determined by `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

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Dividend (numerator), specified as a symbolic integer, polynomial, or a vector or matrix of symbolic integers or polynomials.

Divisor (denominator), specified as a symbolic integer, polynomial, or a vector or matrix of symbolic integers or polynomials.

Polynomial variable, specified as a symbolic variable.

## Output Arguments

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Quotient of the division, returned as a symbolic integer, expression, or a vector or matrix of symbolic integers or expressions.

Remainder of the division, returned as a symbolic integer, expression, or a vector or matrix of symbolic integers or expressions.

## Version History

Introduced before R2006a