Type Alias QM31 

pub type QM31 = BinomialExtensionField<Complex<Mersenne31>, 2>;

The degree-4 extension of Mersenne31: Mersenne31[i][u] with i² = -1 and u² = 2 + i.

Aliased Type

pub struct QM31 { /* private fields */ }

Trait Implementations

impl Add<Mersenne31> for QM31

type Output = ExtField<ExtField<Mersenne31, 2, Binomial<Mersenne31>>, 2, Binomial<ExtField<Mersenne31, 2, Binomial<Mersenne31>>>>

The resulting type after applying the + operator.

fn add(self, rhs: Mersenne31) -> Self

Performs the + operation.

impl AddAssign<Mersenne31> for QM31

fn add_assign(&mut self, rhs: Mersenne31)

Performs the += operation.

impl Algebra<Mersenne31> for QM31

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl BasedVectorSpace<Mersenne31> for QM31

const DIMENSION: usize = 4

The dimension of the vector space, i.e. the number of elements in its basis.

fn as_basis_coefficients_slice(&self) -> &[Mersenne31]

Fixes a basis for the algebra A and uses this to map an element of A to a slice of DIMENSION F elements.

fn from_basis_coefficients_fn<Fn: FnMut(usize) -> Mersenne31>(f: Fn) -> Self

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A. Similar to core:array::from_fn, the DIMENSION F elements are given by Fn(0), ..., Fn(DIMENSION - 1) called in that order.

fn from_basis_coefficients_iter<I: ExactSizeIterator<Item = Mersenne31>>( iter: I, ) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn flatten_to_base(vec: Vec<Self>) -> Vec<Mersenne31>

Convert from a vector of Self to a vector of F by flattening the basis coefficients.

fn reconstitute_from_base(vec: Vec<Mersenne31>) -> Vec<Self>

Convert from a vector of F to a vector of Self by combining the basis coefficients.

fn from_basis_coefficients_slice(slice: &[F]) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn ith_basis_element(i: usize) -> Option<Self>

Given a basis for the Algebra A, return the i’th basis element.

impl ExtensionField<Mersenne31> for QM31

type ExtensionPacking = PackedQM31

fn is_in_basefield(&self) -> bool

Determine if the given element lies in the base field.

fn as_base(&self) -> Option<Mersenne31>

If the element lies in the base field project it down. Otherwise return None.

fn from_ext_basis_coefficients(coeffs: &[Self]) -> Option<Self>

Reassemble an element of Self from D = DIMENSION coefficients in Self via Σⱼ basisⱼ · coeffsⱼ. Returns None if coeffs.len() != Self::DIMENSION.

impl From<Mersenne31> for QM31

fn from(x: Mersenne31) -> Self

Converts to this type from the input type.

impl Mul<Mersenne31> for QM31

type Output = ExtField<ExtField<Mersenne31, 2, Binomial<Mersenne31>>, 2, Binomial<ExtField<Mersenne31, 2, Binomial<Mersenne31>>>>

The resulting type after applying the * operator.

fn mul(self, rhs: Mersenne31) -> Self

Performs the * operation.

impl MulAssign<Mersenne31> for QM31

fn mul_assign(&mut self, rhs: Mersenne31)

Performs the *= operation.

impl Sub<Mersenne31> for QM31

type Output = ExtField<ExtField<Mersenne31, 2, Binomial<Mersenne31>>, 2, Binomial<ExtField<Mersenne31, 2, Binomial<Mersenne31>>>>

The resulting type after applying the - operator.

fn sub(self, rhs: Mersenne31) -> Self

Performs the - operation.

impl SubAssign<Mersenne31> for QM31

fn sub_assign(&mut self, rhs: Mersenne31)

Performs the -= operation.