Struct GaussianInt

pub struct GaussianInt {
    pub re: i64,
    pub im: i64,
}

ガウス整数 $a + bi (a, b \in \mathbb{Z})$

Fields

re: i64

実部

im: i64

虚部

Implementations

impl GaussianInt

pub fn new(a: i64, b: i64) -> Self

ガウス整数$a + bi$を返す。

pub fn norm(self) -> u64

selfのノルム$N(\mathtt{self})$を返す。

ただし、$N(a + bi) = a^2 + b^2$

pub fn div_rem(self, b: Self) -> (Self, Self)

$\mathtt{self} = q \times \mathtt{b} + r (N(b) > N(r))$となる$q$と$r$を返す。

pub fn is_zero(self) -> bool

selfが$0 + 0i$ならばtrueを返す。

pub fn gcd(self, b: Self) -> Self

selfとbの最大公約数を返す。

Trait Implementations

impl Add for GaussianInt

type Output = GaussianInt

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign for GaussianInt

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for GaussianInt

fn clone(&self) -> GaussianInt

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for GaussianInt

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

Formats the value using the given formatter.

impl Default for GaussianInt

fn default() -> GaussianInt

Returns the “default value” for a type.

impl Div for GaussianInt

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

$\mathtt{self} = q \times \mathtt{b} + r (N(b) > N(r))$となる$q$を返す。

type Output = GaussianInt

The resulting type after applying the / operator.

impl DivAssign for GaussianInt

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl From<(i64, i64)> for GaussianInt

fn from(value: (i64, i64)) -> Self

Converts to this type from the input type.

impl From<GaussianInt> for (i64, i64)

fn from(value: GaussianInt) -> Self

Converts to this type from the input type.

impl Hash for GaussianInt

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for GaussianInt

type Output = GaussianInt

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign for GaussianInt

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for GaussianInt

type Output = GaussianInt

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for GaussianInt

fn eq(&self, other: &GaussianInt) -> 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 Rem for GaussianInt

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

$\mathtt{self} = q \times \mathtt{b} + r (N(b) > N(r))$となる$r$を返す。

type Output = GaussianInt

The resulting type after applying the % operator.

impl RemAssign for GaussianInt

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl Sub for GaussianInt

type Output = GaussianInt

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign for GaussianInt

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl Copy for GaussianInt

impl Eq for GaussianInt

impl StructuralPartialEq for GaussianInt