Trait BinomiallyExtendable 

pub trait BinomiallyExtendable<const D: usize>: Field + BinomiallyExtendableAlgebra<Self, D> {
    const W: Self;
    const DTH_ROOT: Self;
    const EXT_GENERATOR: [Self; D];
}

Trait for fields that support binomial extension of the form F[X]/(X^D - W).

A type implementing this trait can define a degree-D extension field using an irreducible binomial polynomial X^D - W, where W is a nonzero constant in the base field.

This is used to construct extension fields with efficient arithmetic.

Required Associated Constants

const W: Self

The constant coefficient W in the binomial X^D - W.

const DTH_ROOT: Self

A D-th root of unity derived from W.

This is W^((n - 1)/D), where n is the order of the field. Valid only when n = kD + 1 for some k.

const EXT_GENERATOR: [Self; D]

A generator for the extension field, expressed as a degree-D polynomial.

This is an array of size D, where each entry is a base field element.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementations on Foreign Types

impl BinomiallyExtendable<2> for Goldilocks

const W: Goldilocks

const DTH_ROOT: Goldilocks

const EXT_GENERATOR: [Goldilocks; 2]

impl BinomiallyExtendable<5> for Goldilocks

const W: Goldilocks

const DTH_ROOT: Goldilocks

const EXT_GENERATOR: [Goldilocks; 5]

impl<const WIDTH: usize, FP> BinomiallyExtendable<WIDTH> for MontyField31<FP>

where FP: BinomialExtensionData<WIDTH> + FieldParameters,

const W: MontyField31<FP> = FP::W

const DTH_ROOT: MontyField31<FP> = FP::DTH_ROOT

const EXT_GENERATOR: [MontyField31<FP>; WIDTH] = FP::EXT_GENERATOR

Implementors

impl BinomiallyExtendable<2> for Felt

const W: Felt

const DTH_ROOT: Felt

const EXT_GENERATOR: [Felt; 2]

impl BinomiallyExtendable<5> for Felt

const W: Felt

const DTH_ROOT: Felt

const EXT_GENERATOR: [Felt; 5]

impl<F> BinomiallyExtendable<2> for F

where F: ComplexExtendable,

const W: F = F::NEG_ONE

const DTH_ROOT: F = F::NEG_ONE

const EXT_GENERATOR: [F; 2]

impl<F, const D: usize> BinomiallyExtendable<D> for BinomialExtensionField<F, 2>

where F: HasComplexBinomialExtension<D>,

const W: BinomialExtensionField<F, 2>

const DTH_ROOT: BinomialExtensionField<F, 2>

const EXT_GENERATOR: [BinomialExtensionField<F, 2>; D] = F::EXT_GENERATOR