Struct lambdaworks_math::field::element::FieldElement

pub struct FieldElement<F: IsField> { /* private fields */ }

A field element with operations algorithms defined in F

Implementations

impl FieldElement<FqField>

pub fn new_base(a_hex: &str) -> Self

impl FieldElement<BLS12377PrimeField>

pub fn new_base(a_hex: &str) -> Self

impl FieldElement<BLS12381PrimeField>

pub fn new_base(a_hex: &str) -> Self

impl FieldElement<Degree2ExtensionField>

pub fn new_base(a_hex: &str) -> Self

pub fn conjugate(&self) -> Self

impl FieldElement<Degree6ExtensionField>

pub fn new_base(a_hex: &str) -> Self

impl FieldElement<Degree12ExtensionField>

pub fn new_base(a_hex: &str) -> Self

pub fn from_coefficients(coefficients: &[&str; 12]) -> Self

impl<F: IsField> FieldElement<F>

pub fn inplace_batch_inverse(numbers: &mut [Self]) -> Result<(), FieldError>

impl<F> FieldElement<F>

where F::BaseType: Clone, F: IsField,

pub fn from_raw(value: &F::BaseType) -> Self

pub const fn const_from_raw(value: F::BaseType) -> Self

impl<F> FieldElement<F>

where F: IsField,

FieldElement general implementation Most of this is delegated to the trait F that implements the field operations.

pub fn new(value: F::BaseType) -> Self

Creates a field element from value

pub fn value(&self) -> &F::BaseType

Returns the underlying value

pub fn inv(&self) -> Result<Self, FieldError>

Returns the multiplicative inverse of self

pub fn square(&self) -> Self

Returns the square of self

pub fn pow<T>(&self, exponent: T) -> Self

where T: IsUnsignedInteger,

Returns self raised to the power of exponent

pub fn one() -> Self

Returns the multiplicative neutral element of the field.

pub fn zero() -> Self

Returns the additive neutral element of the field.

impl<F: IsPrimeField> FieldElement<F>

pub fn representative(&self) -> F::RepresentativeType

pub fn sqrt(&self) -> Option<(Self, Self)>

pub fn legendre_symbol(&self) -> LegendreSymbol

pub fn from_hex(hex_string: &str) -> Result<Self, CreationError>

Creates a FieldElement from a hexstring. It can contain 0x or not. Returns an CreationError::InvalidHexStringif the value is not a hexstring. Returns a CreationError::EmptyString if the input string is empty.

impl<M, const NUM_LIMBS: usize> FieldElement<MontgomeryBackendPrimeField<M, NUM_LIMBS>>

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

pub const fn from_hex_unchecked(hex: &str) -> Self

Creates a FieldElement from a hexstring. It can contain 0x or not.

Panics

Panics if value is not a hexstring

impl<Q> FieldElement<QuadraticExtensionField<Q>>

where Q: Clone + Debug + HasQuadraticNonResidue,

pub fn conjugate(&self) -> Self

impl FieldElement<Babybear31PrimeField>

pub fn to_bytes_le(&self) -> [u8; 8]

pub fn to_bytes_be(&self) -> [u8; 8]

impl FieldElement<Stark252PrimeField>

pub fn to_bytes_le(&self) -> [u8; 32]

No std version of to_bytes_le from ByteConversion trait This follows the convention used by Starkware and Lambdaclass Cairo VM It’s the same as ByteConversion to_bytes_le.

pub fn to_bits_le(&self) -> [bool; 256]

This follows the convention used by starknet-rs

pub fn to_bytes_be(&self) -> [u8; 32]

No std version of to_bytes_be from ByteConversion trait This follows the convention used by Starkware and Lambdaclass Cairo VM It’s the same as ByteConversion to_bytes_be.

impl FieldElement<U64GoldilocksPrimeField>

pub fn to_bytes_le(&self) -> [u8; 8]

pub fn to_bytes_be(&self) -> [u8; 8]

impl FieldElement<Mersenne31MontgomeryPrimeField>

pub fn to_bytes_le(&self) -> [u8; 8]

pub fn to_bytes_be(&self) -> [u8; 8]

impl FieldElement<Mersenne31Field>

pub fn to_bytes_le(&self) -> Vec<u8>

pub fn to_bytes_be(&self) -> Vec<u8>

Trait Implementations

impl<F> Add<&FieldElement<F>> for &FieldElement<F>

where F: IsField,

Addition operator overloading for field elements

type Output = FieldElement<F>

The resulting type after applying the + operator.

fn add(self, rhs: &FieldElement<F>) -> Self::Output

Performs the + operation.

impl<F: IsField> Add<&FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F> Add<&FieldElement<F>> for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the + operator.

fn add(self, rhs: &FieldElement<F>) -> Self::Output

Performs the + operation.

impl<F: IsField> Add<&FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F: IsField> Add<&Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: &Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F: IsField> Add<&Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: &Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F> Add<FieldElement<F>> for &FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the + operator.

fn add(self, rhs: FieldElement<F>) -> Self::Output

Performs the + operation.

impl<F: IsField> Add<FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F: IsField> Add<FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F: IsField> Add<Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F: IsField> Add<Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the + operator.

fn add(self, other: Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the + operation.

impl<F> Add for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the + operator.

fn add(self, rhs: FieldElement<F>) -> Self::Output

Performs the + operation.

impl<F> AddAssign for FieldElement<F>

where F: IsField,

AddAssign operator overloading for field elements

fn add_assign(&mut self, rhs: FieldElement<F>)

Performs the += operation.

impl ByteConversion for FieldElement<Degree2ExtensionField>

fn to_bytes_be(&self) -> Vec<u8>

Returns the byte representation of the element in big-endian order.}

fn to_bytes_le(&self) -> Vec<u8>

Returns the byte representation of the element in little-endian order.

fn from_bytes_be(bytes: &[u8]) -> Result<Self, ByteConversionError>

where Self: Sized,

Returns the element from its byte representation in big-endian order.

fn from_bytes_le(bytes: &[u8]) -> Result<Self, ByteConversionError>

where Self: Sized,

Returns the element from its byte representation in little-endian order.

impl<M, const NUM_LIMBS: usize> ByteConversion for FieldElement<MontgomeryBackendPrimeField<M, NUM_LIMBS>>

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

fn to_bytes_be(&self) -> Vec<u8>

Returns the byte representation of the element in big-endian order.}

fn to_bytes_le(&self) -> Vec<u8>

Returns the byte representation of the element in little-endian order.

fn from_bytes_be(bytes: &[u8]) -> Result<Self, ByteConversionError>

Returns the element from its byte representation in big-endian order.

fn from_bytes_le(bytes: &[u8]) -> Result<Self, ByteConversionError>

Returns the element from its byte representation in little-endian order.

impl<F: Clone + IsField> Clone for FieldElement<F>

where F::BaseType: Clone,

fn clone(&self) -> FieldElement<F>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F: Debug + IsField> Debug for FieldElement<F>

where F::BaseType: Debug,

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

Formats the value using the given formatter.

impl<F> Default for FieldElement<F>

where F: IsField,

fn default() -> Self

Returns the “default value” for a type.

impl<const MODULUS: u64> Deserializable for FieldElement<U64PrimeField<MODULUS>>

fn deserialize(bytes: &[u8]) -> Result<Self, DeserializationError>

where Self: Sized,

impl Display for FieldElement<Goldilocks64Field>

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

Formats the value using the given formatter.

impl Display for FieldElement<Mersenne31Field>

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

Formats the value using the given formatter.

impl<M, const NUM_LIMBS: usize> Display for FieldElement<MontgomeryBackendPrimeField<M, NUM_LIMBS>>

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

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

Formats the value using the given formatter.

impl<F> Div<&FieldElement<F>> for &FieldElement<F>

where F: IsField,

Division operator overloading for field elements*/

type Output = FieldElement<F>

The resulting type after applying the / operator.

fn div(self, rhs: &FieldElement<F>) -> Self::Output

Performs the / operation.

impl<F> Div<&FieldElement<F>> for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the / operator.

fn div(self, rhs: &FieldElement<F>) -> Self::Output

Performs the / operation.

impl<F> Div<FieldElement<F>> for &FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the / operator.

fn div(self, rhs: FieldElement<F>) -> Self::Output

Performs the / operation.

impl<F> Div for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the / operator.

fn div(self, rhs: FieldElement<F>) -> Self::Output

Performs the / operation.

impl<F> From<&<F as IsField>::BaseType> for FieldElement<F>

where F::BaseType: Clone, F: IsField,

From overloading for field elements

fn from(value: &F::BaseType) -> Self

Converts to this type from the input type.

impl<F> From<u64> for FieldElement<F>

where F: IsField,

From overloading for U64

fn from(value: u64) -> Self

Converts to this type from the input type.

impl<F: Hash + IsField> Hash for FieldElement<F>

where F::BaseType: Hash,

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<F> Mul<&FieldElement<F>> for &FieldElement<F>

where F: IsField,

Multiplication operator overloading for field elements*/

type Output = FieldElement<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &FieldElement<F>) -> Self::Output

Performs the * operation.

impl<F: IsField> Mul<&FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul(self, multiplicand: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F> Mul<&FieldElement<F>> for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &FieldElement<F>) -> Self::Output

Performs the * operation.

impl<F: IsField> Mul<&FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul(self, multiplicand: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F: IsField> Mul<&Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul( self, multiplicand: &Polynomial<FieldElement<F>> ) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F: IsField> Mul<&Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul( self, multiplicand: &Polynomial<FieldElement<F>> ) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F> Mul<FieldElement<F>> for &FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the * operator.

fn mul(self, rhs: FieldElement<F>) -> Self::Output

Performs the * operation.

impl<F: IsField> Mul<FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul(self, multiplicand: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F: IsField> Mul<FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul(self, multiplicand: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F: IsField> Mul<Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul( self, multiplicand: Polynomial<FieldElement<F>> ) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F: IsField> Mul<Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the * operator.

fn mul( self, multiplicand: Polynomial<FieldElement<F>> ) -> Polynomial<FieldElement<F>>

Performs the * operation.

impl<F> Mul for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the * operator.

fn mul(self, rhs: FieldElement<F>) -> Self::Output

Performs the * operation.

impl<F> Neg for &FieldElement<F>

where F: IsField,

Negation operator overloading for field elements*/

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<F> Neg for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Ord for FieldElement<Mersenne31MontgomeryPrimeField>

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized + PartialOrd,

Restrict a value to a certain interval.

impl Ord for FieldElement<Stark252PrimeField>

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized + PartialOrd,

Restrict a value to a certain interval.

impl Ord for FieldElement<U64GoldilocksPrimeField>

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized + PartialOrd,

Restrict a value to a certain interval.

impl<F> PartialEq for FieldElement<F>

where F: IsField,

Equality operator overloading for field elements

fn eq(&self, other: &FieldElement<F>) -> 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 PartialOrd for FieldElement<Mersenne31MontgomeryPrimeField>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialOrd for FieldElement<Stark252PrimeField>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl PartialOrd for FieldElement<U64GoldilocksPrimeField>

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<M, const NUM_LIMBS: usize> Serializable for FieldElement<MontgomeryBackendPrimeField<M, NUM_LIMBS>>

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

fn serialize(&self) -> Vec<u8>

Default serialize without args

impl<const MODULUS: u64> Serializable for FieldElement<U64PrimeField<MODULUS>>

fn serialize(&self) -> Vec<u8>

Default serialize without args

impl<F> Sub<&FieldElement<F>> for &FieldElement<F>

where F: IsField,

Subtraction operator overloading for field elements*/

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn sub(self, rhs: &FieldElement<F>) -> Self::Output

Performs the - operation.

impl<F: IsField> Sub<&FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F> Sub<&FieldElement<F>> for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn sub(self, rhs: &FieldElement<F>) -> Self::Output

Performs the - operation.

impl<F: IsField> Sub<&FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: &FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F: IsField> Sub<&Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: &Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F: IsField> Sub<&Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: &Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F> Sub<FieldElement<F>> for &FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn sub(self, rhs: FieldElement<F>) -> Self::Output

Performs the - operation.

impl<F: IsField> Sub<FieldElement<F>> for &Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F: IsField> Sub<FieldElement<F>> for Polynomial<FieldElement<F>>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: FieldElement<F>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F: IsField> Sub<Polynomial<FieldElement<F>>> for &FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F: IsField> Sub<Polynomial<FieldElement<F>>> for FieldElement<F>

type Output = Polynomial<FieldElement<F>>

The resulting type after applying the - operator.

fn sub(self, other: Polynomial<FieldElement<F>>) -> Polynomial<FieldElement<F>>

Performs the - operation.

impl<F> Sub for FieldElement<F>

where F: IsField,

type Output = FieldElement<F>

The resulting type after applying the - operator.

fn sub(self, rhs: FieldElement<F>) -> Self::Output

Performs the - operation.

impl<F> Sum for FieldElement<F>

where F: IsField,

Sum operator for field elements

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<F: Copy + IsField> Copy for FieldElement<F>

where F::BaseType: Copy,

impl<F> Eq for FieldElement<F>

where F: IsField,