Struct DividedPowerAlgebra 

pub struct DividedPowerAlgebra { /* private fields */ }

The divided power algebra Γ(V) on dim generators, the context object (mirroring CliffordAlgebra).

Implementations

impl DividedPowerAlgebra

pub fn new(dim: usize) -> Self

Constructs the divided-power algebra on dim generators.

pub fn dim(&self) -> usize

The number of generators of this divided power algebra.

pub fn zero<S: Scalar>(&self) -> DpVector<S>

The zero element.

pub fn scalar<S: Scalar>(&self, s: S) -> DpVector<S>

The scalar s as an element of Γ (the empty-degree term).

pub fn one<S: Scalar>(&self) -> DpVector<S>

The identity 1 = γ^{[0]}.

pub fn divided_power<S: Scalar>(&self, i: usize, k: u128) -> DpVector<S>

The divided power γ_i^{[k]}.

pub fn gamma1<S: Scalar>(&self, i: usize) -> DpVector<S>

The generator γ_i = γ_i^{[1]} (primitive).

pub fn monomial<S: Scalar>(&self, alpha: &[u128], coeff: S) -> DpVector<S>

The monomial coeff · γ^{[α]} from a multidegree (padded / checked).

pub fn add<S: Scalar>(&self, x: &DpVector<S>, y: &DpVector<S>) -> DpVector<S>

Adds two divided-power vectors.

pub fn scalar_mul<S: Scalar>(&self, s: &S, x: &DpVector<S>) -> DpVector<S>

Multiplies a divided-power vector by a scalar.

pub fn mul<S: Scalar>(&self, x: &DpVector<S>, y: &DpVector<S>) -> DpVector<S>

The binomial product γ^{[α]} · γ^{[β]} = Π_i \binom{α_i+β_i}{α_i} γ^{[α+β]}.

Each factor \binom{α_i+β_i}{α_i} is embedded char-faithfully: in characteristic p > 0 this applies Lucas’ theorem so the embedding is O(log_p(α_i+β_i)) regardless of the magnitude of the binomial coefficient — no O(binom) loop.

pub fn coproduct<S: Scalar>(&self, x: &DpVector<S>) -> BTreeMap<DpTensorKey, S>

The deconcatenation coproduct Δγ^{[α]} = Σ_{β+γ=α} γ^{[β]} ⊗ γ^{[γ]} (sign-free — the symmetric mirror of the exterior unshuffle). Returned as a map (β, γ) → coeff over Γ ⊗ Γ.

pub fn counit<S: Scalar>(&self, x: &DpVector<S>) -> S

The counit ε: Γ → S — projection to the empty-degree (scalar) part.

pub fn antipode<S: Scalar>(&self, x: &DpVector<S>) -> DpVector<S>

The antipode S(γ^{[α]}) = (−1)^{|α|} γ^{[α]} — the grade involution by total degree (sign through the scalar’s own neg, so char 2 ⇒ identity).

Trait Implementations

impl Clone for DividedPowerAlgebra

fn clone(&self) -> DividedPowerAlgebra

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DividedPowerAlgebra

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

Formats the value using the given formatter.

impl Eq for DividedPowerAlgebra

impl PartialEq for DividedPowerAlgebra

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for DividedPowerAlgebra