Struct TowerBasis

pub struct TowerBasis<F: Field> { /* private fields */ }

Represents the $\mathcal{T}{\iota}$-basis of $\mathcal{T}{\iota+k}$

Recall that $\mathcal{T}_{\iota}$ is defined as

• Let \mathbb{F} := \mathbb{F}2[X_0, \ldots, X{\iota-1}]
• Let \mathcal{J} := (X_0^2 + X_0 + 1, \ldots, X_{\iota-1}^2 + X_{\iota-1}X_{\iota-2} + 1)
• $\mathcal{T}_{\iota} := \mathbb{F} / J $

and $\mathcal{T}_{\iota}$ has the following $\mathbb{F}_2$-basis:

• $1, X_0, X_1, X_0X_1, X_2, \ldots, X_0 X_1 \ldots X_{\iota-1}$

Thus, $\mathcal{T}{\iota+k}$ has a $\mathcal{T}{\iota}$-basis of size $2^k$:

• $1, X_{\iota}, X_{\iota+1}, X_{\iota}X_{\iota+1}, X_{\iota+2}, \ldots, X_{\iota} X_{\iota+1} \ldots X_{\iota+k-1}$

Implementations

impl<F: TowerField> TowerBasis<F>

pub fn new(k: usize, iota: usize) -> Result<Self, Error>

pub fn multilinear_extension<P: PackedField<Scalar = F>>( &self, ) -> Result<MultilinearExtension<P>, Error>

Trait Implementations

impl<F: Clone + Field> Clone for TowerBasis<F>

fn clone(&self) -> TowerBasis<F>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F: Debug + Field> Debug for TowerBasis<F>

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

Formats the value using the given formatter.

impl<F> MultivariatePoly<F> for TowerBasis<F>

where F: TowerField,

fn n_vars(&self) -> usize

The number of variables.

fn degree(&self) -> usize

Total degree of the polynomial.

fn evaluate(&self, query: &[F]) -> Result<F, Error>

Evaluate the polynomial at a point in the extension field.

fn binary_tower_level(&self) -> usize

Returns the maximum binary tower level of all constants in the arithmetic expression.

impl<F: Copy + Field> Copy for TowerBasis<F>