Struct Eisenstein 

pub struct Eisenstein {
    pub a: i64,
    pub b: i64,
}

An Eisenstein integer a + bω.

ω = e^(2πi/3) = (-1 + i√3)/2 is a primitive cube root of unity. Eisenstein integers form a hexagonal lattice in the complex plane.

Fields

a: i64

Coefficient of 1

b: i64

Coefficient of ω

Implementations

impl Eisenstein

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

Create a new Eisenstein integer.

pub fn to_cartesian(self) -> (f64, f64)

Convert to Cartesian (x, y) coordinates.

The conversion is:

x = a - b/2
y = (√3 / 2) · b

pub fn norm(self) -> f64

Euclidean norm of this Eisenstein integer (in the complex plane).

pub fn dist(self, other: Self) -> f64

Distance between two Eisenstein integers.

Trait Implementations

impl Clone for Eisenstein

fn clone(&self) -> Eisenstein

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Eisenstein

impl Debug for Eisenstein

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

Formats the value using the given formatter.

impl PartialEq for Eisenstein

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Eisenstein