Enum Natural 

pub enum Natural {
    Zero,
    Nonzero(Composite),
}

Natural number, either a Composite or Zero

m = prod p_k^{n_k} OR 0

Note this struct does NOT implement Divisible. That trait is meant for numbers that can be uniquely decomposed into Primes. This is not the case, since Natural can be zero.

Variants

Zero

The natural number 0

Nonzero(Composite)

A nonzero natural number

Implementations

impl Natural

pub fn gcd(&self, other: &Self) -> Self

Greatest common divisor

use adic::divisible::Natural;
let n1 = Natural::from(6);
let n2 = Natural::from(15);
assert_eq!(Natural::from(3), n1.gcd(&n2));

Panics

Panics if either self or other are zero

pub fn lcm(&self, other: &Self) -> Self

Least common multiple

use adic::divisible::Natural;
let n1 = Natural::from(6);
let n2 = Natural::from(15);
assert_eq!(Natural::from(30), n1.lcm(&n2));
assert_eq!(Natural::from(0), n1.lcm(&Natural::from(0)));

Trait Implementations

impl Add<&Natural> for Natural

type Output = Natural

The resulting type after applying the + operator.

fn add(self, rhs: &Natural) -> Self::Output

Performs the + operation.

impl Add<Natural> for &Natural

type Output = Natural

The resulting type after applying the + operator.

fn add(self, rhs: Natural) -> Self::Output

Performs the + operation.

impl Add for &Natural

type Output = Natural

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl Add for Natural

type Output = Natural

The resulting type after applying the + operator.

fn add(self, rhs: Natural) -> Self::Output

Performs the + operation.

impl AddAssign for Natural

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Natural

fn clone(&self) -> Natural

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Natural

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for Natural

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl From<BigUint> for Natural

fn from(u: BigUint) -> Self

Converts to this type from the input type.

impl From<Composite> for Natural

fn from(value: Composite) -> Self

Converts to this type from the input type.

impl From<Natural> for BigUint

fn from(n: Natural) -> Self

Converts to this type from the input type.

impl From<Natural> for u32

fn from(n: Natural) -> Self

Converts to this type from the input type.

impl From<Prime> for Natural

fn from(value: Prime) -> Self

Converts to this type from the input type.

impl From<PrimePower> for Natural

fn from(value: PrimePower) -> Self

Converts to this type from the input type.

impl From<u32> for Natural

fn from(u: u32) -> Self

Converts to this type from the input type.

impl Mul<&Natural> for Natural

type Output = Natural

The resulting type after applying the * operator.

fn mul(self, rhs: &Natural) -> Self::Output

Performs the * operation.

impl Mul<Natural> for &Natural

type Output = Natural

The resulting type after applying the * operator.

fn mul(self, rhs: Natural) -> Self::Output

Performs the * operation.

impl Mul for &Natural

type Output = Natural

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for Natural

type Output = Natural

The resulting type after applying the * operator.

fn mul(self, rhs: Natural) -> Self::Output

Performs the * operation.

impl MulAssign for Natural

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl One for Natural

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl PartialEq for Natural

fn eq(&self, other: &Natural) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Pow<u32> for Natural

type Output = Natural

The result after applying the operator.

fn pow(self, power: u32) -> Self::Output

Returns self to the power rhs.

impl Product for Natural

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl Rem<Composite> for Natural

type Output = BigUint

The resulting type after applying the % operator.

fn rem(self, rhs: Composite) -> Self::Output

Performs the % operation.

impl Sum for Natural

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Zero for Natural

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Eq for Natural

impl StructuralPartialEq for Natural