Struct lambdaworks_math::field::extensions::quadratic::QuadraticExtensionField

pub struct QuadraticExtensionField<T> { /* private fields */ }

A general quadratic extension field over F with quadratic non residue Q::residue()

Trait Implementations

impl<T: Clone> Clone for QuadraticExtensionField<T>

fn clone(&self) -> QuadraticExtensionField<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for QuadraticExtensionField<T>

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

Formats the value using the given formatter.

impl<Q> IsField for QuadraticExtensionField<Q>where Q: Clone + Debug + HasQuadraticNonResidue,

fn add( a: &[FieldElement<Q::BaseField>; 2], b: &[FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Returns the component wise addition of a and b

fn mul( a: &[FieldElement<Q::BaseField>; 2], b: &[FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Returns the multiplication of a and b using the following equation: (a0 + a1 * t) * (b0 + b1 * t) = a0 * b0 + a1 * b1 * Q::residue() + (a0 * b1 + a1 * b0) * t where t.pow(2) equals Q::residue().

fn sub( a: &[FieldElement<Q::BaseField>; 2], b: &[FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Returns the component wise subtraction of a and b

fn neg(a: &[FieldElement<Q::BaseField>; 2]) -> [FieldElement<Q::BaseField>; 2]

Returns the component wise negation of a

fn inv( a: &[FieldElement<Q::BaseField>; 2] ) -> Result<[FieldElement<Q::BaseField>; 2], FieldError>

Returns the multiplicative inverse of a This uses the equality (a0 + a1 * t) * (a0 - a1 * t) = a0.pow(2) - a1.pow(2) * Q::residue()

fn div( a: &[FieldElement<Q::BaseField>; 2], b: &[FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Returns the division of a and b

fn eq( a: &[FieldElement<Q::BaseField>; 2], b: &[FieldElement<Q::BaseField>; 2] ) -> bool

Returns a boolean indicating whether a and b are equal component wise.

fn zero() -> [FieldElement<Q::BaseField>; 2]

Returns the additive neutral element of the field extension.

fn one() -> [FieldElement<Q::BaseField>; 2]

Returns the multiplicative neutral element of the field extension.

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

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

fn from_base_type( x: [FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Takes as input an element of BaseType and returns the internal representation of that element in the field. Note: for this case this is simply the identity, because the components already have correct representations.

type BaseType = [FieldElement<<Q as HasQuadraticNonResidue>::BaseField>; 2]

The underlying base type for representing elements from the field.

fn square( a: &[FieldElement<Q::BaseField>; 2] ) -> [FieldElement<Q::BaseField>; 2]

Returns the multiplication of a and a.

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

impl<T: PartialEq> PartialEq for QuadraticExtensionField<T>

fn eq(&self, other: &QuadraticExtensionField<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: Eq> Eq for QuadraticExtensionField<T>

impl<T> StructuralEq for QuadraticExtensionField<T>

impl<T> StructuralPartialEq for QuadraticExtensionField<T>