Trait Field 

pub trait Field:
    Sized
    + Eq
    + Copy
    + Clone
    + Default
    + Send
    + Sync
    + Debug
    + Display
    + Hash
    + 'static
    + Neg<Output = Self>
    + Add<Output = Self>
    + Sub<Output = Self>
    + Mul<Output = Self>
    + for<'a> Add<&'a Self, Output = Self>
    + for<'a> Sub<&'a Self, Output = Self>
    + for<'a> Mul<&'a Self, Output = Self>
    + Sum
    + Product
    + for<'a> Sum<&'a Self>
    + for<'a> Product<&'a Self>
    + AddAssign
    + SubAssign
    + MulAssign
    + for<'a> AddAssign<&'a Self>
    + for<'a> SubAssign<&'a Self>
    + for<'a> MulAssign<&'a Self>
    + Square
    + InvertOrZero
    + Random
    + Zeroable
    + SerializeBytes
    + DeserializeBytes {
    const ZERO: Self;
    const ONE: Self;
    const CHARACTERISTIC: usize;
    const ORDER_EXPONENT: usize;
    const MULTIPLICATIVE_GENERATOR: Self;

    // Required method
    fn double(&self) -> Self;

    // Provided methods
    fn is_zero(&self) -> bool { ... }
    fn invert(&self) -> Option<Self> { ... }
    fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self { ... }
}

An element of a finite field.

A finite field (also called a Galois field) has order p^k where p is the CHARACTERISTIC and k is the ORDER_EXPONENT.

Required Associated Constants

const ZERO: Self

The zero element of the field, the additive identity.

const ONE: Self

The one element of the field, the multiplicative identity.

const CHARACTERISTIC: usize

The characteristic p of the field. The field order is p^k where k is ORDER_EXPONENT.

const ORDER_EXPONENT: usize

The exponent k such that the field order equals CHARACTERISTIC^k.

const MULTIPLICATIVE_GENERATOR: Self

Fixed generator of the multiplicative group.

Required Methods

fn double(&self) -> Self

Doubles this element.

Provided Methods

fn is_zero(&self) -> bool

Returns true iff this element is zero.

fn invert(&self) -> Option<Self>

Computes the multiplicative inverse of this element, failing if the element is zero.

fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self

Exponentiates self by exp, where exp is a little-endian order integer exponent.

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 Field for AESTowerField8b

const ZERO: Self

const ONE: Self

const CHARACTERISTIC: usize = 2

const ORDER_EXPONENT: usize = <u8 as crate::underlier::UnderlierType>::BITS

const MULTIPLICATIVE_GENERATOR: AESTowerField8b

impl Field for BinaryField1b

const ZERO: Self

const ONE: Self

const CHARACTERISTIC: usize = 2

const ORDER_EXPONENT: usize = <U1 as crate::underlier::UnderlierType>::BITS

const MULTIPLICATIVE_GENERATOR: BinaryField1b

impl Field for BinaryField128bGhash

const ZERO: Self

const ONE: Self

const CHARACTERISTIC: usize = 2

const ORDER_EXPONENT: usize = <u128 as crate::underlier::UnderlierType>::BITS

const MULTIPLICATIVE_GENERATOR: BinaryField128bGhash