Struct Vector8 

pub struct Vector8 { /* private fields */ }

8-dimensional vector with exact coordinates

Used for E₈ root system and Atlas coordinates. All coordinates are half-integers for exact arithmetic.

Examples

use atlas_embeddings::arithmetic::{Vector8, HalfInteger};

let v = Vector8::new([
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
    HalfInteger::new(1),   // 1/2
]);

// Norm squared: 8 * (1/2)² = 8 * 1/4 = 2
assert_eq!(v.norm_squared(), num_rational::Ratio::new(2, 1));

Implementations

impl Vector8

pub const fn new(coords: [HalfInteger; 8]) -> Self

Create a vector from 8 half-integer coordinates

pub fn zero() -> Self

Create a zero vector

pub const fn get(&self, index: usize) -> HalfInteger

Get coordinate at index

pub const fn coords(&self) -> &[HalfInteger; 8]

Get all coordinates as slice

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

Inner product (dot product) - exact rational result

⟨v, w⟩ = Σᵢ vᵢ·wᵢ

pub fn norm_squared(&self) -> Rational

Norm squared: ‖v‖² = ⟨v, v⟩

pub fn is_root(&self) -> bool

Check if this is a root (norm² = 2)

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

Vector addition

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

Vector subtraction

pub fn scale(&self, scalar: i64) -> Self

Scalar multiplication by integer

pub fn scale_rational(&self, scalar: Rational) -> Self

Scalar multiplication by rational

Multiplies each coordinate by a rational scalar (exact arithmetic)

pub fn negate(&self) -> Self

Negation

Trait Implementations

impl Add for Vector8

type Output = Vector8

The resulting type after applying the + operator.

fn add(self, other: Self) -> Self

Performs the + operation.

impl Clone for Vector8

fn clone(&self) -> Vector8

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Vector8

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

Formats the value using the given formatter.

impl Display for Vector8

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

Formats the value using the given formatter.

impl Hash for Vector8

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 Neg for Vector8

type Output = Vector8

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Vector8

fn eq(&self, other: &Vector8) -> 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 Sub for Vector8

type Output = Vector8

The resulting type after applying the - operator.

fn sub(self, other: Self) -> Self

Performs the - operation.

impl Copy for Vector8

impl Eq for Vector8

impl StructuralPartialEq for Vector8