Struct Polynomial 

pub struct Polynomial<const N: usize, E: FieldScalar> { /* private fields */ }

Univariate negacyclic polynomial ring (modulus X^N + 1). Accelerated with number theoretic transforms and lazy moves between coefficient and eval representation.

Implementations

impl<const N: usize, E: FieldScalar> Polynomial<N, E>

pub fn to_eval_form(&mut self)

pub fn to_coef_form(&mut self)

pub fn into_eval_form(self) -> Self

pub fn into_coef_form(self) -> Self

pub fn evaluate(&self, x: E) -> E

Evaluate the polynomial at a point.

pub fn batch_mul(self, rhs: Vector<Self>) -> Vector<Self>

Multiply a single polynomial by a vector of polynomials.

pub fn split_root(root: E) -> Result<Self>

Retrieve the product of monomial factors split by the provided root of unity.

pub fn coefs_slice_mut(&mut self) -> &mut [E; N]

pub fn coefs(&self) -> impl Iterator<Item = E> + ExactSizeIterator + Clone

Get an iterator over all coefficients.

TODO: coefs_nonzero ?

pub fn coefs_mut(&mut self) -> impl Iterator<Item = &mut E> + ExactSizeIterator

Get a mutable iterator over all coefficients.

pub fn norm_l2(&self) -> f64

The l2 norm of the polynomial. Represents the magnitude.

The distance of each coefficient from zero is squared and then summed. The square root of the sum is returned.

sqrt(x[0]^2 + x[1]^2 + x[2]^2 ...)

pub fn sample_gaussian<R: Rng>(sigma: f64, rng: &mut R) -> Self

Sample a polynomial with coefficients in a gaussian distribution with standard deviation sigma.

Internally uses a statically cached distribution table for each stddev initialized on first call.

Trait Implementations

impl<const N: usize, E: FieldScalar> Add for Polynomial<N, E>

type Output = Polynomial<N, E>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl<const N: usize, E: FieldScalar> AddAssign for Polynomial<N, E>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<const N: usize, E: Clone + FieldScalar> Clone for Polynomial<N, E>

fn clone(&self) -> Polynomial<N, E>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: usize, E: Debug + FieldScalar> Debug for Polynomial<N, E>

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

Formats the value using the given formatter.

impl<const N: usize, E: FieldScalar> Default for Polynomial<N, E>

fn default() -> Self

Returns the “default value” for a type.

impl<const N: usize, E: FieldScalar> Display for Polynomial<N, E>

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

Formats the value using the given formatter.

impl<const N: usize, E: FieldScalar> From<&Vector<E>> for Polynomial<N, E>

fn from(coefs: &Vector<E>) -> Self

Converts to this type from the input type.

impl<const N: usize, E: FieldScalar> From<[E; N]> for Polynomial<N, E>

fn from(coefs: [E; N]) -> Self

Converts to this type from the input type.

impl<const N: usize, E: FieldScalar> From<E> for Polynomial<N, E>

fn from(coef: E) -> Self

Converts to this type from the input type.

impl<const N: usize, E: FieldScalar> From<u128> for Polynomial<N, E>

fn from(value: u128) -> Self

Converts to this type from the input type.

impl<const N: usize, E: FieldScalar> Into<u128> for Polynomial<N, E>

fn into(self) -> u128

Converts this type into the (usually inferred) input type.

impl<const N: usize, E: FieldScalar> Mul<E> for Polynomial<N, E>

type Output = Polynomial<N, E>

The resulting type after applying the * operator.

fn mul(self, rhs: E) -> Self::Output

Performs the * operation.

impl<const N: usize, E: FieldScalar> Mul for Polynomial<N, E>

type Output = Polynomial<N, E>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl<const N: usize, E: FieldScalar> MulAssign<E> for Polynomial<N, E>

fn mul_assign(&mut self, rhs: E)

Performs the *= operation.

impl<const N: usize, E: FieldScalar> MulAssign for Polynomial<N, E>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<const N: usize, E: PartialEq + FieldScalar> PartialEq for Polynomial<N, E>

fn eq(&self, other: &Polynomial<N, E>) -> 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<const N: usize, E: FieldScalar> Product for Polynomial<N, E>

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<const N: usize, E: FieldScalar> RingElement for Polynomial<N, E>

fn sample_uniform<R: Rng>(rng: &mut R) -> Self

Uniform randomly sample an element from the ring provided an RNG source.

const CARDINALITY: u128

fn as_le_bytes(&self) -> Vec<u8>

const Q: u128 = Self::CARDINALITY

fn is_zero(&self) -> bool

Is the element the additive identity?

fn one() -> Self

Multiplicative identity.

fn negone() -> Self

Multiplicatively flips a value in centered representation. Additive inverse of the multiplicative identity. (Negative one)

fn zero() -> Self

Additive identity.

impl<const N: usize, E: FieldScalar> Sub for Polynomial<N, E>

type Output = Polynomial<N, E>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl<const N: usize, E: FieldScalar> SubAssign for Polynomial<N, E>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<const N: usize, E: FieldScalar> Sum for Polynomial<N, E>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<const N: usize, E: Copy + FieldScalar> Copy for Polynomial<N, E>

impl<const N: usize, E: FieldScalar> StructuralPartialEq for Polynomial<N, E>