# Trait ark_poly::evaluations::multivariate::multilinear::MultilinearExtension[−][src]

```pub trait MultilinearExtension<F: Field>: Sized + Clone + Debug + Hash + PartialEq + Eq + Add + Neg + Zero + CanonicalSerialize + CanonicalDeserialize + for<'a> AddAssign<&'a Self> + for<'a> AddAssign<(F, &'a Self)> + for<'a> SubAssign<&'a Self> + Index<usize> {
fn num_vars(&self) -> usize;
fn evaluate(&self, point: &[F]) -> Option<F>;
fn rand<R: Rng>(num_vars: usize, rng: &mut R) -> Self;
fn relabel(&self, a: usize, b: usize, k: usize) -> Self;
fn fix_variables(&self, partial_point: &[F]) -> Self;
fn to_evaluations(&self) -> Vec<F>;
}```
Expand description

This trait describes an interface for the multilinear extension of an array. The latter is a multilinear polynomial represented in terms of its evaluations over the domain {0,1}^`num_vars` (i.e. the Boolean hypercube).

Index represents a point, which is a vector in {0,1}^`num_vars` in little endian form. For example, `0b1011` represents `P(1,1,0,1)`

## Required methods

Returns the number of variables in `self`

Evaluates `self` at the given the vector `point` in slice. If the number of variables does not match, return `None`.

Outputs an `l`-variate multilinear extension where value of evaluations are sampled uniformly at random.

Relabel the point by swapping `k` scalars from positions `a..a+k` to positions `b..b+k`, and from position `b..b+k` to position `a..a+k` in vector.

This function turns `P(x_1,...,x_a,...,x_{a+k - 1},...,x_b,...,x_{b+k - 1},...,x_n)` to `P(x_1,...,x_b,...,x_{b+k - 1},...,x_a,...,x_{a+k - 1},...,x_n)`

Reduce the number of variables of `self` by fixing the `partial_point.len()` variables at `partial_point`.

Returns a list of evaluations over the domain, which is the boolean hypercube.

## Implementors

Outputs an `l`-variate multilinear extension where value of evaluations are sampled uniformly at random. The number of nonzero entries is `sqrt(2^num_vars)` and indices of those nonzero entries are distributed uniformly at random.