Struct RationalMatrix 

pub struct RationalMatrix<const N: usize> { /* private fields */ }

Matrix with exact rational entries

Used to represent Weyl group elements as matrices. All operations use exact rational arithmetic (no floating point).

From certified Python implementation: ExactMatrix class

Implementations

impl<const N: usize> RationalMatrix<N>

pub const fn new(data: [[Rational; N]; N]) -> Self

Create matrix from 2D array

pub fn identity() -> Self

Create identity matrix

Examples

use atlas_embeddings::arithmetic::{RationalMatrix, Rational};

let id = RationalMatrix::<2>::identity();
assert_eq!(id.get(0, 0), Rational::new(1, 1));
assert_eq!(id.get(0, 1), Rational::new(0, 1));

pub fn reflection(root: &RationalVector<N>) -> Self

Create reflection matrix from root vector

Implements: R_α = I - 2(α ⊗ α)/⟨α,α⟩

This is the matrix representation of the reflection through the hyperplane perpendicular to α. Uses exact rational arithmetic.

From certified Python implementation: simple_reflection() method

Panics

Panics if root has norm² = 0

pub const fn get(&self, i: usize, j: usize) -> Rational

Get entry at (i, j)

pub const fn get_ref(&self, i: usize, j: usize) -> &Rational

Get reference to entry at (i, j)

pub const fn data(&self) -> &[[Rational; N]; N]

Get all data as reference

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

Matrix multiplication (exact rational arithmetic)

Computes C = A × B where all operations are exact. This is the composition operation for Weyl group elements.

pub fn trace(&self) -> Rational

Compute trace (sum of diagonal elements)

pub fn is_identity(&self) -> bool

Check if this is the identity matrix

Trait Implementations

impl<const N: usize> Clone for RationalMatrix<N>

fn clone(&self) -> RationalMatrix<N>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize> Debug for RationalMatrix<N>

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

Formats the value using the given formatter.

impl<const N: usize> Display for RationalMatrix<N>

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

Formats the value using the given formatter.

impl<const N: usize> Hash for RationalMatrix<N>

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<const N: usize> PartialEq for RationalMatrix<N>

fn eq(&self, other: &RationalMatrix<N>) -> 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<const N: usize> Eq for RationalMatrix<N>

impl<const N: usize> StructuralPartialEq for RationalMatrix<N>