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# mod

Symbolic modulus after division

## Description

example

mod(a,b) finds the modulus after division. To find the remainder, use rem.

If a is a polynomial expression, then mod(a,b) finds the modulus for each coefficient.

## Examples

### Divide Integers by Integers

Find the modulus after division in case both the dividend and divisor are integers.

Find the modulus after division for these numbers.

`[mod(sym(27), 4), mod(sym(27), -4), mod(sym(-27), 4), mod(sym(-27), -4)]`
```ans =
[ 3, -1, 1, -3]```

### Divide Rationals by Integers

Find the modulus after division in case the dividend is a rational number, and divisor is an integer.

Find the modulus after division for these numbers.

`[mod(sym(22/3), 5), mod(sym(1/2), 7), mod(sym(27/6), -11)]`
```ans =
[ 7/3, 1/2, -13/2]```

### Divide Polynomial Expressions by Integers

Find the modulus after division in case the dividend is a polynomial expression, and divisor is an integer. If the dividend is a polynomial expression, then mod finds the modulus for each coefficient.

Find the modulus after division for these polynomial expressions.

```syms x
mod(x^3 - 2*x + 999, 10)```
```ans =
x^3 + 8*x + 9```
`mod(8*x^3 + 9*x^2 + 10*x + 11, 7)`
```ans =
x^3 + 2*x^2 + 3*x + 4```

### Divide Elements of Matrices

For vectors and matrices, mod finds the modulus after division element-wise. Nonscalar arguments must be the same size.

Find the modulus after division for the elements of these two matrices.

```A = sym([27, 28; 29, 30]);
B = sym([2, 3; 4, 5]);
mod(A,B)```
```ans =
[ 1, 1]
[ 1, 0]```

Find the modulus after division for the elements of matrix A and the value 9. Here, mod expands 9 into the 2-by-2 matrix with all elements equal to 9.

`mod(A,9)`
```ans =
[ 0, 1]
[ 2, 3]```

## Input Arguments

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### a — Dividend (numerator)number | symbolic number | symbolic variable | polynomial expression | vector | matrix

Dividend (numerator), specified as a number, symbolic number, variable, polynomial expression, or a vector or matrix of numbers, symbolic numbers, variables, or polynomial expressions.

### b — Divisor (denominator)number | symbolic number | vector | matrix

Divisor (denominator), specified as a number, symbolic number, or a vector or matrix of numbers or symbolic numbers.

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### Modulus

The modulus of a and b is

$\mathrm{mod}\left(a,b\right)=a-b\ast \text{floor}\left(\frac{a}{b}\right),$

where floor rounds (a/b) towards negative infinity. For example, the modulus of -8 and -3 is -2, but the modulus of -8 and 3 is 1.

If b = 0, then mod(a,0) = 0.

### Tips

• Calling mod for numbers that are not symbolic objects invokes the MATLAB® mod function.

• All nonscalar arguments must be the same size. If one input arguments is nonscalar, then mod expands the scalar into a vector or matrix of the same size as the nonscalar argument, with all elements equal to the corresponding scalar.