Struct Multivector 

pub struct Multivector<const P: usize, const Q: usize, const R: usize, const N: usize> {
    pub coords: [f32; N],
}

Fixed-size stack-allocated Multivector in Clifford Algebra Cl(p, q, r).

• P, Q, R: Metric signature.
• N: Algebra dimension (2^(P + Q + R)).

Fields

coords: [f32; N]

Implementations

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Multivector<P, Q, R, N>

pub const fn zero() -> Self

Zero multivector.

pub fn from_scalar(alpha: f32) -> Self

Scalar multivector: alpha * 1.

pub fn from_vector(vec: &[f32]) -> Self

Creates a 1-vector from coordinate slice.

pub fn basis(i: usize) -> Self

Basis element e_i (1-indexed: e_1, e_2, …).

pub fn scalar(&self) -> f32

Scalar part _0.

pub fn grade_projection(&self, grade: usize) -> Self

Extracts the k-th grade projection _k.

pub fn reverse(&self) -> Self

Clifford Reverse: A~ = sum (-1)^{k(k-1)/2} _k.

pub fn grade_involution(&self) -> Self

Grade Involution: A^ = sum (-1)^k _k.

pub fn conjugation(&self) -> Self

Clifford Conjugation: \bar{A} = sum (-1)^{k(k+1)/2} _k.

pub fn geometric_product(&self, rhs: &Self) -> Self

Computes the Clifford Geometric Product: C = A * B.

pub fn wedge(&self, rhs: &Self) -> Self

Computes the Exterior Wedge Product: C = A ^ B.

pub fn left_contraction(&self, rhs: &Self) -> Self

Computes the Left Contraction: C = A _| B.

pub fn right_contraction(&self, rhs: &Self) -> Self

Computes the Right Contraction: C = A |_ B.

pub fn scalar_product(&self, rhs: &Self) -> f32

Scalar product <A, B> = <A B~>_0.

pub fn norm_sq(&self) -> f32

Squared magnitude: ||A||^2 = <A A~>_0.

pub fn norm(&self) -> f32

Magnitude / L2 norm.

pub fn normalize(&self) -> Self

Normalized multivector: A / ||A||.

pub fn sandwich(&self, x: &Self) -> Self

Versor sandwich product: X’ = V X V~.

pub fn pseudoscalar() -> Self

Returns the unit pseudoscalar I = e_1 ^ e_2 ^ … ^ e_n.

pub fn pseudoscalar_inverse() -> Option<Self>

Computes the pseudoscalar inverse I^{-1} for non-degenerate metrics (R == 0). Under signature (P, Q, 0): I^2 = (-1)^{n(n-1)/2 + Q}, so I^{-1} = I * (-1)^{n(n-1)/2 + Q}.

pub fn dual(&self) -> Option<Self>

Computes the Hodge Dual: A* = A I^{-1} (Macdonald Def 6.16, Hestenes Section 1.2).

pub fn undual(&self) -> Self

Computes the Undual (reverse duality): A I.

pub fn commutator(&self, rhs: &Self) -> Self

Computes the Lie Commutator Product: [A, B] = 1/2 (A B - B A) (Hestenes Eq 1.55). Anticommutative: [A, B] = -[B, A]. Satisfies the Jacobi identity.

pub fn anticommutator(&self, rhs: &Self) -> Self

Computes the Jordan Anticommutator (symmetric product): A ⊙ B = 1/2 (A B + B A).

pub fn regressive_product(&self, rhs: &Self) -> Option<Self>

Computes the Regressive (Meet) Product: A ∨ B = (A* ∧ B*).undual() In non-degenerate spaces, gives the geometric intersection of blade subspaces.

pub fn hestenes_inner_product(&self, rhs: &Self) -> Self

Computes the Hestenes Inner Product (Fat Dot): A • B = sum_{r>=1, s>=1} < _r s >{|r - s|}. As defined in Hestenes & Sobczyk (1984), Section 1.1, Eq. 1.8.

pub fn inverse(&self) -> Option<Self>

Computes the exact closed-form algebraic inverse A^{-1} for multivectors:

• For Cl(2, 0, 0): A^{-1} = \bar{A} / (A \bar{A})_0
• For Cl(3, 0, 0): A^{-1} = \bar{A} (A \bar{A})~ / det(A)
• General fallback for versors: A~ / ||A||^2 Returns None if multivector is singular (det(A) == 0).

Trait Implementations

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Add for Multivector<P, Q, R, N>

type Output = Multivector<P, Q, R, N>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> AddAssign for Multivector<P, Q, R, N>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Clone for Multivector<P, Q, R, N>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Copy for Multivector<P, Q, R, N>

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Debug for Multivector<P, Q, R, N>

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

Formats the value using the given formatter.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Default for Multivector<P, Q, R, N>

fn default() -> Self

Returns the “default value” for a type.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Mul for Multivector<P, Q, R, N>

type Output = Multivector<P, Q, R, N>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Mul<f32> for Multivector<P, Q, R, N>

type Output = Multivector<P, Q, R, N>

The resulting type after applying the * operator.

fn mul(self, scalar: f32) -> Self

Performs the * operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Neg for Multivector<P, Q, R, N>

type Output = Multivector<P, Q, R, N>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> PartialEq for Multivector<P, Q, R, N>

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

Equality operator ==.

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

Inequality operator !=.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> StructuralPartialEq for Multivector<P, Q, R, N>

impl<const P: usize, const Q: usize, const R: usize, const N: usize> Sub for Multivector<P, Q, R, N>

type Output = Multivector<P, Q, R, N>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<const P: usize, const Q: usize, const R: usize, const N: usize> SubAssign for Multivector<P, Q, R, N>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.