Struct Blade 

pub struct Blade { /* private fields */ }

A basis blade in a geometric algebra.

Blades are represented as bitmasks where bit i indicates the presence of basis vector eᵢ. This representation is always canonical since bits are inherently ordered.

Examples

use clifford_codegen::algebra::Blade;

// Scalar (grade 0)
let scalar = Blade::scalar();
assert_eq!(scalar.grade(), 0);
assert_eq!(scalar.index(), 0);

// Basis vector e₁
let e1 = Blade::basis(0);
assert_eq!(e1.grade(), 1);
assert_eq!(e1.index(), 1);

// Bivector e₁₂
let e12 = Blade::from_index(0b11);
assert_eq!(e12.grade(), 2);

Implementations

impl Blade

pub const fn from_index(index: usize) -> Self

Creates a blade from its bitmask index.

Example

use clifford_codegen::algebra::Blade;

let e12 = Blade::from_index(0b11);
assert_eq!(e12.index(), 3);

pub const fn scalar() -> Self

Creates the scalar blade (grade 0, index 0).

Example

use clifford_codegen::algebra::Blade;

let s = Blade::scalar();
assert_eq!(s.index(), 0);
assert_eq!(s.grade(), 0);

pub const fn basis(i: usize) -> Self

Creates a basis vector blade.

Blade::basis(i) creates blade eᵢ₊₁ (using 0-based indexing internally).

Example

use clifford_codegen::algebra::Blade;

let e1 = Blade::basis(0);
assert_eq!(e1.index(), 1);

let e2 = Blade::basis(1);
assert_eq!(e2.index(), 2);

let e3 = Blade::basis(2);
assert_eq!(e3.index(), 4);

pub const fn index(&self) -> usize

Returns the blade’s bitmask index.

Example

use clifford_codegen::algebra::Blade;

let e12 = Blade::from_index(3);
assert_eq!(e12.index(), 3);

pub const fn grade(&self) -> usize

Returns the grade (number of basis vectors in this blade).

The grade equals the number of 1-bits in the index.

Example

use clifford_codegen::algebra::Blade;

assert_eq!(Blade::scalar().grade(), 0);
assert_eq!(Blade::basis(0).grade(), 1);
assert_eq!(Blade::from_index(0b111).grade(), 3);

pub const fn contains(&self, i: usize) -> bool

Checks if this blade contains basis vector i.

Example

use clifford_codegen::algebra::Blade;

let e12 = Blade::from_index(0b11);
assert!(e12.contains(0)); // contains e1
assert!(e12.contains(1)); // contains e2
assert!(!e12.contains(2)); // does not contain e3

pub fn basis_vectors(&self) -> impl Iterator<Item = usize> + '_

Returns an iterator over the basis vector indices in this blade.

Indices are yielded in ascending order.

Example

use clifford_codegen::algebra::Blade;

let e135 = Blade::from_index(0b10101);
let indices: Vec<_> = e135.basis_vectors().collect();
assert_eq!(indices, vec![0, 2, 4]);

pub const fn len(&self) -> usize

Returns the number of basis vectors in this blade.

This is equivalent to self.grade().

pub const fn is_empty(&self) -> bool

Returns true if this is the scalar blade.

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

Computes the XOR of two blade indices.

This gives the result blade of the geometric product (before considering sign).

Example

use clifford_codegen::algebra::Blade;

let e1 = Blade::basis(0);
let e2 = Blade::basis(1);
let e12 = e1.xor(e2);
assert_eq!(e12.index(), 3);

pub const fn overlaps(&self, other: Self) -> bool

Returns true if this blade shares any basis vectors with another.

Example

use clifford_codegen::algebra::Blade;

let e12 = Blade::from_index(0b11);
let e23 = Blade::from_index(0b110);
let e45 = Blade::from_index(0b11000);

assert!(e12.overlaps(e23)); // share e2
assert!(!e12.overlaps(e45)); // disjoint

pub fn name(&self) -> String

Returns the blade name using standard notation.

Uses 1-based indexing for display: e1, e12, e123, etc.

Example

use clifford_codegen::algebra::Blade;

assert_eq!(Blade::scalar().name(), "1");
assert_eq!(Blade::basis(0).name(), "e1");
assert_eq!(Blade::from_index(0b11).name(), "e12");

Trait Implementations

impl Clone for Blade

fn clone(&self) -> Blade

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Blade

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

Formats the value using the given formatter.

impl Default for Blade

fn default() -> Self

Returns the “default value” for a type.

impl Display for Blade

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

Formats the value using the given formatter.

impl Hash for Blade

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 Ord for Blade

fn cmp(&self, other: &Blade) -> Ordering

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Blade

fn eq(&self, other: &Blade) -> 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 PartialOrd for Blade

fn partial_cmp(&self, other: &Blade) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Copy for Blade

impl Eq for Blade

impl StructuralPartialEq for Blade