# 1.0.0[−][src]Trait std::ops::Mul

```#[lang = "mul"]
pub trait Mul<RHS = Self> {
type Output;
#[must_use]
fn mul(self, rhs: RHS) -> Self::Output;
}```

The multiplication operator `*`.

Note that `RHS` is `Self` by default, but this is not mandatory.

# Examples

## `Mul`tipliable rational numbers

```use std::ops::Mul;

// By the fundamental theorem of arithmetic, rational numbers in lowest
// terms are unique. So, by keeping `Rational`s in reduced form, we can
// derive `Eq` and `PartialEq`.
#[derive(Debug, Eq, PartialEq)]
struct Rational {
nominator: usize,
denominator: usize,
}

impl Rational {
fn new(nominator: usize, denominator: usize) -> Self {
if denominator == 0 {
panic!("Zero is an invalid denominator!");
}

// Reduce to lowest terms by dividing by the greatest common
// divisor.
let gcd = gcd(nominator, denominator);
Rational {
nominator: nominator / gcd,
denominator: denominator / gcd,
}
}
}

impl Mul for Rational {
// The multiplication of rational numbers is a closed operation.
type Output = Self;

fn mul(self, rhs: Self) -> Self {
let nominator = self.nominator * rhs.nominator;
let denominator = self.denominator * rhs.denominator;
Rational::new(nominator, denominator)
}
}

// Euclid's two-thousand-year-old algorithm for finding the greatest common
// divisor.
fn gcd(x: usize, y: usize) -> usize {
let mut x = x;
let mut y = y;
while y != 0 {
let t = y;
y = x % y;
x = t;
}
x
}

assert_eq!(Rational::new(1, 2), Rational::new(2, 4));
assert_eq!(Rational::new(2, 3) * Rational::new(3, 4),
Rational::new(1, 2));Run```

## Multiplying vectors by scalars as in linear algebra

```use std::ops::Mul;

struct Scalar { value: usize }

#[derive(Debug, PartialEq)]
struct Vector { value: Vec<usize> }

impl Mul<Scalar> for Vector {
type Output = Vector;

fn mul(self, rhs: Scalar) -> Vector {
Vector { value: self.value.iter().map(|v| v * rhs.value).collect() }
}
}

let vector = Vector { value: vec![2, 4, 6] };
let scalar = Scalar { value: 3 };
assert_eq!(vector * scalar, Vector { value: vec![6, 12, 18] });Run```

## Associated Types

### `type Output`

The resulting type after applying the `*` operator.

## Required Methods

### ```#[must_use] fn mul(self, rhs: RHS) -> Self::Output```

Performs the `*` operation.