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# quorem

Quotient and remainder

## 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 are 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(10^5, sym(985))`
```q =
101

r =
515```

## Input Arguments

expand all

### A — Dividend (numerator)symbolic integer | polynomial | symbolic vector | symbolic matrix

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

### B — Divisor (denominator)symbolic integer | polynomial | symbolic vector | symbolic matrix

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

### var — Polynomial variablesymbolic variable

Polynomial variable, specified as a symbolic variable.

## Output Arguments

expand all

### Q — Quotient of the divisionsymbolic integer | symbolic expression | symbolic vector | symbolic matrix

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

### R — Remainder of the divisionsymbolic integer | symbolic expression | symbolic vector | symbolic matrix

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