Trait IsField 

pub trait IsField: Debug + Clone {
    type BaseType: Clone + Debug + Unpin + ByteConversion + Default;

    // Required methods
    fn add(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType;
    fn mul(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType;
    fn sub(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType;
    fn neg(a: &Self::BaseType) -> Self::BaseType;
    fn inv(a: &Self::BaseType) -> Result<Self::BaseType, FieldError>;
    fn div(
        a: &Self::BaseType,
        b: &Self::BaseType,
    ) -> Result<Self::BaseType, FieldError>;
    fn eq(a: &Self::BaseType, b: &Self::BaseType) -> bool;
    fn one() -> Self::BaseType;
    fn from_u64(x: u64) -> Self::BaseType;
    fn from_base_type(x: Self::BaseType) -> Self::BaseType;

    // Provided methods
    fn double(a: &Self::BaseType) -> Self::BaseType { ... }
    fn square(a: &Self::BaseType) -> Self::BaseType { ... }
    fn pow<T>(a: &Self::BaseType, exponent: T) -> Self::BaseType
       where T: IsUnsignedInteger { ... }
    fn zero() -> Self::BaseType { ... }
}

Trait to add field behaviour to a struct.

Required Associated Types

type BaseType: Clone + Debug + Unpin + ByteConversion + Default

The underlying base type for representing elements from the field.

Required Methods

fn add(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the sum of a and b.

fn mul(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the multiplication of a and b.

fn sub(a: &Self::BaseType, b: &Self::BaseType) -> Self::BaseType

Returns the subtraction of a and b.

fn neg(a: &Self::BaseType) -> Self::BaseType

Returns the additive inverse of a.

fn inv(a: &Self::BaseType) -> Result<Self::BaseType, FieldError>

Returns the multiplicative inverse of a.

fn div( a: &Self::BaseType, b: &Self::BaseType, ) -> Result<Self::BaseType, FieldError>

Returns the division of a and b.

fn eq(a: &Self::BaseType, b: &Self::BaseType) -> bool

Returns a boolean indicating whether a and b are equal or not.

fn one() -> Self::BaseType

Returns the multiplicative neutral element.

fn from_u64(x: u64) -> Self::BaseType

Returns the element x * 1 where 1 is the multiplicative neutral element.

fn from_base_type(x: Self::BaseType) -> Self::BaseType

Takes as input an element of BaseType and returns the internal representation of that element in the field.

Provided Methods

fn double(a: &Self::BaseType) -> Self::BaseType

Returns the double of a.

fn square(a: &Self::BaseType) -> Self::BaseType

Returns the multiplication of a and a.

fn pow<T>(a: &Self::BaseType, exponent: T) -> Self::BaseType

where T: IsUnsignedInteger,

Returns the power of a to the T, a^T Uses the square and multiply algorithm, which takes O(log2(T)) steps This is a non-constant time implementation!

fn zero() -> Self::BaseType

Returns the additive neutral 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.

Implementors

impl IsField for lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_377::field_extension::Degree2ExtensionField

type BaseType = [FieldElement<MontgomeryBackendPrimeField<BLS12377FieldModulus, 6>>; 2]

impl IsField for lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::field_extension::Degree2ExtensionField

type BaseType = [FieldElement<MontgomeryBackendPrimeField<BLS12381FieldModulus, 6>>; 2]

impl IsField for lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::Degree2ExtensionField

type BaseType = [FieldElement<MontgomeryBackendPrimeField<BN254FieldModulus, 4>>; 2]

impl IsField for Degree4BabyBearExtensionField

type BaseType = [FieldElement<MontgomeryBackendPrimeField<MontgomeryConfigBabybear31PrimeField, 1>>; 4]

impl IsField for Degree4BabyBearU32ExtensionField

We implement directly the degree four extension for performance reasons, instead of using the default quadratic extension provided by the library

type BaseType = [FieldElement<U32MontgomeryBackendPrimeField<2013265921>>; 4]

impl IsField for lambdaworks_math::field::fields::mersenne31::extensions::Degree2ExtensionField

type BaseType = [FieldElement<Mersenne31Field>; 2]

impl IsField for Degree4ExtensionField

type BaseType = [FieldElement<Degree2ExtensionField>; 2]

impl IsField for Mersenne31Field

type BaseType = u32

impl IsField for P448GoldilocksPrimeField

type BaseType = U56x8

impl IsField for Goldilocks64Field

type BaseType = u64

impl<F, Q> IsField for CubicExtensionField<F, Q>

where F: IsField, Q: Clone + Debug + HasCubicNonResidue<F>,

type BaseType = [FieldElement<F>; 3]

impl<F, Q> IsField for QuadraticExtensionField<F, Q>

where F: IsField, Q: Clone + Debug + HasQuadraticNonResidue<F>,

type BaseType = [FieldElement<F>; 2]

impl<M, const NUM_LIMBS: usize> IsField for MontgomeryBackendPrimeField<M, NUM_LIMBS>

where M: IsModulus<UnsignedInteger<NUM_LIMBS>> + Clone + Debug,

type BaseType = UnsignedInteger<NUM_LIMBS>

impl<const MODULUS: u32> IsField for U32MontgomeryBackendPrimeField<MODULUS>

type BaseType = u32

impl<const MODULUS: u32> IsField for U32Field<MODULUS>

type BaseType = u32

impl<const MODULUS: u64> IsField for U64PrimeField<MODULUS>

type BaseType = u64

impl<const MODULUS: u64> IsField for U64Field<MODULUS>

type BaseType = u64