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", so this trait is not object safe.

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