Type Alias RealMultiVector 

pub type RealMultiVector = CausalMultiVector<f64>;

Aliased Type

pub struct RealMultiVector { /* private fields */ }

Implementations

impl RealMultiVector

pub fn new_euclidean(data: Vec<f64>, dim: usize) -> Self

Cl(N, 0): Generic N-dimensional Euclidean algebra. All basis vectors square to +1.

impl RealMultiVector

pub fn new_complex_number(real: f64, imag: f64) -> Self

Cl(0, 1): Isomorphic to Complex Numbers C Basis: {1, e1} where e1^2 = -1 (acts as i)

pub fn new_split_complex(a: f64, b: f64) -> Self

Cl(1, 0): Isomorphic to Split-Complex (Hyperbolic) Numbers Basis: {1, e1} where e1^2 = +1 (acts as j)

pub fn new_quaternion(w: f64, x: f64, y: f64, z: f64) -> Self

Cl(0, 2): Isomorphic to Quaternions H Basis: {1, e1, e2, e12}. e1^2 = e2^2 = -1.

pub fn new_split_quaternion(a: f64, b: f64, c: f64, d: f64) -> Self

Cl(2, 0): Isomorphic to Split-Quaternions (Coquaternions) or M(2,R) Basis: {1, e1, e2, e12} where e1^2 = 1, e2^2 = 1.

This algebra is often used in representing 2D isometries.

impl RealMultiVector

pub fn new_aps_vector(data: Vec<f64>) -> Self

Cl(3, 0): Algebra of Physical Space (APS) / Pauli Algebra Used for non-relativistic quantum mechanics (Pauli Matrices).

pub fn new_spacetime_algebra_1_3(data: Vec<f64>) -> Self

Cl(1, 3): Space-Time Algebra (STA) / Dirac Algebra Physics Convention: Time-like vector is positive. Metric: (+ - - -) This is a specialized case of Metric::Generic { p: 1, q: 3, r: 0 }.

pub fn new_spacetime_algebra_3_1(data: Vec<f64>) -> Self

Cl(3, 1): Spacetime Algebra (STA) / Dirac Algebra Mathematics/GR Convention: Space-like vectors are positive. Metric: (- + + +) This is a specialized case of Metric::Generic { p: 3, q: 1, r: 0 }.

pub fn new_cga_vector(data: Vec<f64>) -> Self

Cl(4, 1): Conformal Geometric Algebra (CGA) Used for computer graphics and advanced robotics. 5 Dimensions. Metric (+ + + + -).

Basis: e1, e2, e3, e+ (e4), e- (e5). e5^2 = -1.