Struct EqIndPartialEval

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

Represents $\text{eq}(X, r)$, the partial evaluation of the equality indicator polynomial at a point $r$.

The $2 \mu$-variate multilinear polynomial $\text{eq}(X, Y)$ is defined as the multilinear extension of the map

$$ (x, y) \mapsto \begin{cases} 1 &\text{if } x = y \\ 0 &\text{if } x \ne y \end{cases}. $$

The polynomial can be efficiency computed with the following explicit formulation:

$$ \text{eq}(X, Y) = \prod_{i=0}^{\mu - 1} \left(X_i Y_i + (1 - X_i)(1 - Y_i)\right). $$

Implementations

impl<F: Field> EqIndPartialEval<F>

pub fn new(r: impl Into<Vec<F>>) -> Self

pub fn n_vars(&self) -> usize

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

Trait Implementations

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

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

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

Formats the value using the given formatter.

impl<F: TowerField, P: PackedField<Scalar = F>> MultivariatePoly<P> for EqIndPartialEval<F>

fn n_vars(&self) -> usize

The number of variables.

fn degree(&self) -> usize

Total degree of the polynomial.

fn evaluate(&self, query: &[P]) -> Result<P, 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.

fn erased_serialize( &self, write_buf: &mut dyn BufMut, mode: SerializationMode, ) -> Result<(), SerializationError>

Serialize a type erased MultivariatePoly. Since not every MultivariatePoly implements serialization, this defaults to returning an error.