# Trait core::ops::Mul1.0.0 [−] [src]

```#[lang = "mul"]
pub trait Mul<RHS = Self> {
type Output;
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

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

Performs the `*` operation.

## Implementors

•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for Wrapping type Output = Wrapping;` [src]
•  `impl<'a> Mul> for &'a Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a> Mul<&'a Wrapping> for Wrapping type Output = as Mul>>::Output;` [src]
•  `impl<'a, 'b> Mul<&'a Wrapping> for &'b Wrapping type Output = as Mul>>::Output;` [src]
•  `impl Mul for usize type Output = usize;` [src]
•  `impl<'a> Mul for &'a usize type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a usize> for usize type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a usize> for &'b usize type Output = >::Output;` [src]
•  `impl Mul for u8 type Output = u8;` [src]
•  `impl<'a> Mul for &'a u8 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a u8> for u8 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a u8> for &'b u8 type Output = >::Output;` [src]
•  `impl Mul for u16 type Output = u16;` [src]
•  `impl<'a> Mul for &'a u16 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a u16> for u16 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a u16> for &'b u16 type Output = >::Output;` [src]
•  `impl Mul for u32 type Output = u32;` [src]
•  `impl<'a> Mul for &'a u32 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a u32> for u32 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a u32> for &'b u32 type Output = >::Output;` [src]
•  `impl Mul for u64 type Output = u64;` [src]
•  `impl<'a> Mul for &'a u64 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a u64> for u64 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a u64> for &'b u64 type Output = >::Output;` [src]
•  `impl Mul for u128 type Output = u128;` [src]
•  `impl<'a> Mul for &'a u128 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a u128> for u128 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a u128> for &'b u128 type Output = >::Output;` [src]
•  `impl Mul for isize type Output = isize;` [src]
•  `impl<'a> Mul for &'a isize type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a isize> for isize type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a isize> for &'b isize type Output = >::Output;` [src]
•  `impl Mul for i8 type Output = i8;` [src]
•  `impl<'a> Mul for &'a i8 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a i8> for i8 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a i8> for &'b i8 type Output = >::Output;` [src]
•  `impl Mul for i16 type Output = i16;` [src]
•  `impl<'a> Mul for &'a i16 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a i16> for i16 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a i16> for &'b i16 type Output = >::Output;` [src]
•  `impl Mul for i32 type Output = i32;` [src]
•  `impl<'a> Mul for &'a i32 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a i32> for i32 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a i32> for &'b i32 type Output = >::Output;` [src]
•  `impl Mul for i64 type Output = i64;` [src]
•  `impl<'a> Mul for &'a i64 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a i64> for i64 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a i64> for &'b i64 type Output = >::Output;` [src]
•  `impl Mul for i128 type Output = i128;` [src]
•  `impl<'a> Mul for &'a i128 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a i128> for i128 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a i128> for &'b i128 type Output = >::Output;` [src]
•  `impl Mul for f32 type Output = f32;` [src]
•  `impl<'a> Mul for &'a f32 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a f32> for f32 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a f32> for &'b f32 type Output = >::Output;` [src]
•  `impl Mul for f64 type Output = f64;` [src]
•  `impl<'a> Mul for &'a f64 type Output = >::Output;` [src]
•  `impl<'a> Mul<&'a f64> for f64 type Output = >::Output;` [src]
•  `impl<'a, 'b> Mul<&'a f64> for &'b f64 type Output = >::Output;` [src]
•  `impl Mul for Duration type Output = Duration;` [src]
•  `impl Mul for i8x2 type Output = Self;` [src]
•  `impl Mul for u8x2 type Output = Self;` [src]
•  `impl Mul for i16x2 type Output = Self;` [src]
•  `impl Mul for u16x2 type Output = Self;` [src]
•  `impl Mul for i8x4 type Output = Self;` [src]
•  `impl Mul for u8x4 type Output = Self;` [src]
•  `impl Mul for i8x8 type Output = Self;` [src]
•  `impl Mul for u8x8 type Output = Self;` [src]
•  `impl Mul for i16x4 type Output = Self;` [src]
•  `impl Mul for u16x4 type Output = Self;` [src]
•  `impl Mul for i32x2 type Output = Self;` [src]
•  `impl Mul for u32x2 type Output = Self;` [src]
•  `impl Mul for f32x2 type Output = Self;` [src]
•  `impl Mul for i8x16 type Output = Self;` [src]
•  `impl Mul for u8x16 type Output = Self;` [src]
•  `impl Mul for i16x8 type Output = Self;` [src]
•  `impl Mul for u16x8 type Output = Self;` [src]
•  `impl Mul for i32x4 type Output = Self;` [src]
•  `impl Mul for u32x4 type Output = Self;` [src]
•  `impl Mul for f32x4 type Output = Self;` [src]
•  `impl Mul for i64x2 type Output = Self;` [src]
•  `impl Mul for u64x2 type Output = Self;` [src]
•  `impl Mul for f64x2 type Output = Self;` [src]
•  `impl Mul for i8x32 type Output = Self;` [src]
•  `impl Mul for u8x32 type Output = Self;` [src]
•  `impl Mul for i16x16 type Output = Self;` [src]
•  `impl Mul for u16x16 type Output = Self;` [src]
•  `impl Mul for i32x8 type Output = Self;` [src]
•  `impl Mul for u32x8 type Output = Self;` [src]
•  `impl Mul for f32x8 type Output = Self;` [src]
•  `impl Mul for i64x4 type Output = Self;` [src]
•  `impl Mul for u64x4 type Output = Self;` [src]
•  `impl Mul for f64x4 type Output = Self;` [src]
•  `impl Mul for i8x64 type Output = Self;` [src]
•  `impl Mul for u8x64 type Output = Self;` [src]
•  `impl Mul for i16x32 type Output = Self;` [src]
•  `impl Mul for u16x32 type Output = Self;` [src]
•  `impl Mul for i32x16 type Output = Self;` [src]
•  `impl Mul for u32x16 type Output = Self;` [src]
•  `impl Mul for f32x16 type Output = Self;` [src]
•  `impl Mul for i64x8 type Output = Self;` [src]
•  `impl Mul for u64x8 type Output = Self;` [src]
•  `impl Mul for f64x8 type Output = Self;` [src]