Struct ExtField 

pub struct ExtField<F, const D: usize, Shape, A = F> { /* private fields */ }

Unified extension-field representation.

An ExtField<F, D, Shape, A> represents an element of a degree-D extension of the base field F, with the reducing polynomial determined by Shape. The A parameter is the algebra over F storing each coefficient — usually F itself for scalar elements, or F::Packing for SIMD-packed elements.

The three public-facing extension types — BinomialExtensionField, CubicTrinomialExtensionField, QuinticTrinomialExtensionField — are type aliases over this struct with their respective Shapes.

Implementations

impl<F: Copy, const D: usize> ExtField<F, D, Binomial<F>>

pub const fn new_array<const N: usize>(input: [[F; D]; N]) -> [Self; N]

Convert a [[F; D]; N] array to an array of extension field elements.

Const version of input.map(BinomialExtensionField::new).

Panics

Panics if N == 0.

impl<R: PrimeCharacteristicRing> ExtField<R, 2, Binomial<R>>

Convenience methods for complex extensions

pub const fn new_complex(real: R, imag: R) -> Self

pub const fn new_real(real: R) -> Self

pub const fn new_imag(imag: R) -> Self

pub fn real(&self) -> R

pub fn imag(&self) -> R

pub fn conjugate(&self) -> Self

pub fn norm(&self) -> R

pub fn to_array(&self) -> [R; 2]

pub fn rotate<Ext: Algebra<R>>(&self, rhs: &Complex<Ext>) -> Complex<Ext>

impl<F: Copy> ExtField<F, 3, CubicTrinomial>

pub const fn new_array<const N: usize>(input: [[F; 3]; N]) -> [Self; N]

Convert a [[F; D]; N] array to an array of extension field elements.

Const version of input.map(CubicTrinomialExtensionField::new).

Panics

Panics if N == 0.

impl<F: Copy> ExtField<F, 5, QuinticTrinomial>

pub const fn new_array<const N: usize>(input: [[F; 5]; N]) -> [Self; N]

Convert a [[F; 5]; N] array to an array of extension field elements.

Panics

Panics if N == 0.

impl<F, const D: usize, Shape, A> ExtField<F, D, Shape, A>

pub const fn new(value: [A; D]) -> Self

Create an extension field element from an array of base/algebra elements.

Any array is accepted. No reduction is required since each entry is already a valid element of the algebra over F.

Panics

Panics (at compile time) if D <= 1. A degree-0 or degree-1 “extension” is degenerate — use F directly instead.

Trait Implementations

impl<F, PF> Add<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 3, CubicTrinomial>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F, PF> Add<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 5, QuinticTrinomial>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<F, PF, const D: usize> Add<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, D, Binomial<F>>

The resulting type after applying the + operator.

fn add(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the + operation.

impl<F, PF> AddAssign<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

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

Performs the += operation.

impl<F, PF> AddAssign<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

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

Performs the += operation.

impl<F, PF, const D: usize> AddAssign<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

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

Performs the += operation.

impl<F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>> Algebra<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl<F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>> Algebra<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl<F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>, const D: usize> Algebra<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

fn mixed_dot_product<const N: usize>(a: &[Self; N], f: &[F; N]) -> Self

where F: Dup,

Dot product between algebra elements and base field scalars.

const BATCHED_LC_CHUNK: usize = 8

Optimal chunk size for batched_linear_combination.

fn batched_linear_combination(values: &[Self], coeffs: &[F]) -> Self

where F: Dup,

Runtime-length linear combination: Σ values[i] * coeffs[i].

impl<F, A: Algebra<F>, const D: usize, Shape: ExtensionShape + Clone> BasedVectorSpace<A> for ExtField<F, D, Shape, A>

where F: Field + ExtensionAlgebra<F, D, Shape>,

const DIMENSION: usize = D

The dimension of the vector space, i.e. the number of elements in its basis.

fn as_basis_coefficients_slice(&self) -> &[A]

Fixes a basis for the algebra A and uses this to map an element of A to a slice of DIMENSION F elements.

fn from_basis_coefficients_fn<Fn: FnMut(usize) -> A>(f: Fn) -> Self

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A. Similar to core:array::from_fn, the DIMENSION F elements are given by Fn(0), ..., Fn(DIMENSION - 1) called in that order.

fn from_basis_coefficients_iter<I: ExactSizeIterator<Item = A>>( iter: I, ) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn flatten_to_base(vec: Vec<Self>) -> Vec<A>

Convert from a vector of Self to a vector of F by flattening the basis coefficients.

fn reconstitute_from_base(vec: Vec<A>) -> Vec<Self>

Convert from a vector of F to a vector of Self by combining the basis coefficients.

fn from_basis_coefficients_slice(slice: &[F]) -> Option<Self>

Fixes a basis for the algebra A and uses this to map DIMENSION F elements to an element of A.

fn ith_basis_element(i: usize) -> Option<Self>

Given a basis for the Algebra A, return the i’th basis element.

impl<F: Clone, const D: usize, Shape: Clone, A: Clone> Clone for ExtField<F, D, Shape, A>

fn clone(&self) -> ExtField<F, D, Shape, A>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Copy, const D: usize, Shape: Copy, A: Copy> Copy for ExtField<F, D, Shape, A>

impl<F: Debug, const D: usize, Shape: Debug, A: Debug> Debug for ExtField<F, D, Shape, A>

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

Formats the value using the given formatter.

impl<F: Field, A: Algebra<F>, const D: usize, Shape: ExtensionShape> Default for ExtField<F, D, Shape, A>

fn default() -> Self

Returns the “default value” for a type.

impl<'de, F, const D: usize, Shape, A> Deserialize<'de> for ExtField<F, D, Shape, A>

where A: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F, const D: usize, Shape: ExtensionShape> Distribution<ExtField<F, D, Shape>> for StandardUniform

where F: Field + ExtensionAlgebra<F, D, Shape>, Self: Distribution<F>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> ExtField<F, D, Shape>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl<F, PF> Div<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 3, CubicTrinomial>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<F, PF> Div<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 5, QuinticTrinomial>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<F, PF, const D: usize> Div<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, D, Binomial<F>>

The resulting type after applying the / operator.

fn div(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the / operation.

impl<F, PF> DivAssign<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

fn div_assign(&mut self, rhs: CubicTrinomialExtensionField<F>)

Performs the /= operation.

impl<F, PF> DivAssign<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

fn div_assign(&mut self, rhs: QuinticTrinomialExtensionField<F>)

Performs the /= operation.

impl<F, PF, const D: usize> DivAssign<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn div_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the /= operation.

impl<F: Eq, const D: usize, Shape: Eq, A: Eq> Eq for ExtField<F, D, Shape, A>

impl<F, const D: usize> ExtensionAlgebra<ExtField<F, 2, Binomial<F>>, D, Binomial<ExtField<F, 2, Binomial<F>>>> for Complex<F>

where F: HasComplexBinomialExtension<D>,

fn ext_mul(a: &[Self; D], b: &[Self; D], res: &mut [Self; D])

Multiplication in the algebra extension ring.

fn ext_square(a: &[Self; D], res: &mut [Self; D])

Squaring in the algebra extension ring.

fn ext_add(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Coefficient-wise addition.

fn ext_sub(a: &[Self; D], b: &[Self; D]) -> [Self; D]

Coefficient-wise subtraction.

fn ext_base_mul(lhs: [Self; D], rhs: Self) -> [Self; D]

Multiply an extension element by a base-field scalar.

impl<F: Field, A: Algebra<F>, const D: usize, Shape: ExtensionShape> From<A> for ExtField<F, D, Shape, A>

fn from(x: A) -> Self

Converts to this type from the input type.

impl<F: Field, PF: PackedField<Scalar = F>> From<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

fn from(x: CubicTrinomialExtensionField<F>) -> Self

Converts to this type from the input type.

impl<F: Field, PF: PackedField<Scalar = F>> From<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

fn from(x: QuinticTrinomialExtensionField<F>) -> Self

Converts to this type from the input type.

impl<F: Field, PF: PackedField<Scalar = F>, const D: usize> From<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

fn from(x: BinomialExtensionField<F, D>) -> Self

Converts to this type from the input type.

impl<F, A, const D: usize, Shape: ExtensionShape> From<[A; D]> for ExtField<F, D, Shape, A>

fn from(x: [A; D]) -> Self

Converts to this type from the input type.

impl<F: Hash, const D: usize, Shape: Hash, A: Hash> Hash for ExtField<F, D, Shape, A>

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, PF> Mul<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 3, CubicTrinomial>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<F, PF> Mul<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 5, QuinticTrinomial>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<F, PF, const D: usize> Mul<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, D, Binomial<F>>

The resulting type after applying the * operator.

fn mul(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the * operation.

impl<F, PF> MulAssign<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

fn mul_assign(&mut self, rhs: CubicTrinomialExtensionField<F>)

Performs the *= operation.

impl<F, PF> MulAssign<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

fn mul_assign(&mut self, rhs: QuinticTrinomialExtensionField<F>)

Performs the *= operation.

impl<F, PF, const D: usize> MulAssign<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn mul_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the *= operation.

impl<F: Ord, const D: usize, Shape: Ord, A: Ord> Ord for ExtField<F, D, Shape, A>

fn cmp(&self, other: &ExtField<F, D, Shape, A>) -> 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,

Restrict a value to a certain interval.

impl<F, const D: usize, Shape> Packable for ExtField<F, D, Shape>

where F: Field + ExtensionAlgebra<F, D, Shape>, Shape: ExtensionShape + Copy + Eq + Hash + Send + Sync,

impl<F: CubicTrinomialExtendable> PackedFieldExtension<F, ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, F::Packing>

fn from_ext_fn(f: impl Fn(usize) -> CubicTrinomialExtensionField<F>) -> Self

Construct a packed extension by applying f to each lane.

fn packed_ext_powers(base: CubicTrinomialExtensionField<F>) -> Powers<Self>

Similar to packed_powers, construct an iterator which returns powers of base packed into PackedFieldExtension elements.

fn from_ext_slice(slice: &[ExtField]) -> Self

Pack a length-WIDTH slice of extension field elements into one packed extension.

fn pack_ext_columns<const N: usize>(rows: &[[ExtField; N]]) -> [Self; N]

Pack N columns from W rows of extension field elements into N packed extensions.

fn pack_ext_columns_fn<const N: usize>( row_fn: impl Fn(usize) -> [ExtField; N], ) -> [Self; N]

Pack N columns using a closure that produces each row.

fn extract(&self, lane: usize) -> ExtField

Extract the extension field element at the given SIMD lane.

fn to_ext_slice(&self, out: &mut [ExtField])

Write all W lanes into the given slice.

fn unpack_ext_into<const N: usize>( packed: &[Self; N], rows: &mut [[ExtField; N]], )

Unpack N packed extensions into W rows of N extension elements.

fn unpack_ext_iter<const N: usize>( packed: [Self; N], ) -> impl Iterator<Item = [ExtField; N]>

Iterator equivalent of PackedFieldExtension::unpack_ext_into.

fn to_ext_iter( iter: impl IntoIterator<Item = Self>, ) -> impl Iterator<Item = ExtField>

Convert an iterator of packed extension field elements to an iterator of extension field elements (flat — one ExtField per lane per packed value).

fn packed_ext_powers_capped( base: ExtField, unpacked_len: usize, ) -> impl Iterator<Item = Self>

Similar to packed_ext_powers but only returns unpacked_len powers of base.

impl<F: QuinticTrinomialExtendable> PackedFieldExtension<F, ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, F::Packing>

fn from_ext_fn(f: impl Fn(usize) -> QuinticTrinomialExtensionField<F>) -> Self

Construct a packed extension by applying f to each lane.

fn packed_ext_powers(base: QuinticTrinomialExtensionField<F>) -> Powers<Self>

Similar to packed_powers, construct an iterator which returns powers of base packed into PackedFieldExtension elements.

fn from_ext_slice(slice: &[ExtField]) -> Self

Pack a length-WIDTH slice of extension field elements into one packed extension.

fn pack_ext_columns<const N: usize>(rows: &[[ExtField; N]]) -> [Self; N]

Pack N columns from W rows of extension field elements into N packed extensions.

fn pack_ext_columns_fn<const N: usize>( row_fn: impl Fn(usize) -> [ExtField; N], ) -> [Self; N]

Pack N columns using a closure that produces each row.

fn extract(&self, lane: usize) -> ExtField

Extract the extension field element at the given SIMD lane.

fn to_ext_slice(&self, out: &mut [ExtField])

Write all W lanes into the given slice.

fn unpack_ext_into<const N: usize>( packed: &[Self; N], rows: &mut [[ExtField; N]], )

Unpack N packed extensions into W rows of N extension elements.

fn unpack_ext_iter<const N: usize>( packed: [Self; N], ) -> impl Iterator<Item = [ExtField; N]>

Iterator equivalent of PackedFieldExtension::unpack_ext_into.

fn to_ext_iter( iter: impl IntoIterator<Item = Self>, ) -> impl Iterator<Item = ExtField>

Convert an iterator of packed extension field elements to an iterator of extension field elements (flat — one ExtField per lane per packed value).

fn packed_ext_powers_capped( base: ExtField, unpacked_len: usize, ) -> impl Iterator<Item = Self>

Similar to packed_ext_powers but only returns unpacked_len powers of base.

impl<F, const D: usize> PackedFieldExtension<F, ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, F::Packing, D>

where F: BinomiallyExtendable<D>,

fn from_ext_fn(f: impl Fn(usize) -> BinomialExtensionField<F, D>) -> Self

Construct a packed extension by applying f to each lane.

fn packed_ext_powers(base: BinomialExtensionField<F, D>) -> Powers<Self>

Similar to packed_powers, construct an iterator which returns powers of base packed into PackedFieldExtension elements.

fn from_ext_slice(slice: &[ExtField]) -> Self

Pack a length-WIDTH slice of extension field elements into one packed extension.

fn pack_ext_columns<const N: usize>(rows: &[[ExtField; N]]) -> [Self; N]

Pack N columns from W rows of extension field elements into N packed extensions.

fn pack_ext_columns_fn<const N: usize>( row_fn: impl Fn(usize) -> [ExtField; N], ) -> [Self; N]

Pack N columns using a closure that produces each row.

fn extract(&self, lane: usize) -> ExtField

Extract the extension field element at the given SIMD lane.

fn to_ext_slice(&self, out: &mut [ExtField])

Write all W lanes into the given slice.

fn unpack_ext_into<const N: usize>( packed: &[Self; N], rows: &mut [[ExtField; N]], )

Unpack N packed extensions into W rows of N extension elements.

fn unpack_ext_iter<const N: usize>( packed: [Self; N], ) -> impl Iterator<Item = [ExtField; N]>

Iterator equivalent of PackedFieldExtension::unpack_ext_into.

fn to_ext_iter( iter: impl IntoIterator<Item = Self>, ) -> impl Iterator<Item = ExtField>

Convert an iterator of packed extension field elements to an iterator of extension field elements (flat — one ExtField per lane per packed value).

fn packed_ext_powers_capped( base: ExtField, unpacked_len: usize, ) -> impl Iterator<Item = Self>

Similar to packed_ext_powers but only returns unpacked_len powers of base.

impl<F: PartialEq, const D: usize, Shape: PartialEq, A: PartialEq> PartialEq for ExtField<F, D, Shape, A>

fn eq(&self, other: &ExtField<F, D, Shape, A>) -> bool

Tests for self and other values to be equal, and is used by ==.

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

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

impl<F: PartialOrd, const D: usize, Shape: PartialOrd, A: PartialOrd> PartialOrd for ExtField<F, D, Shape, A>

fn partial_cmp(&self, other: &ExtField<F, D, Shape, A>) -> Option<Ordering>

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

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

Tests less than (for self and other) and is used by the < operator.

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

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

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

Tests greater than (for self and other) and is used by the > operator.

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

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

impl<F, PF> Product<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

fn product<I: Iterator<Item = CubicTrinomialExtensionField<F>>>(iter: I) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<F, PF> Product<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

fn product<I: Iterator<Item = QuinticTrinomialExtensionField<F>>>( iter: I, ) -> Self

Takes an iterator and generates Self from the elements by multiplying the items.

impl<F, const D: usize, Shape, A> Serialize for ExtField<F, D, Shape, A>

where A: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F: PartialEq, const D: usize, Shape: PartialEq, A: PartialEq> StructuralPartialEq for ExtField<F, D, Shape, A>

impl<F, PF> Sub<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 3, CubicTrinomial>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F, PF> Sub<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, 5, QuinticTrinomial>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<F, PF, const D: usize> Sub<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

type Output = PackedExtField<F, PF, D, Binomial<F>>

The resulting type after applying the - operator.

fn sub(self, rhs: BinomialExtensionField<F, D>) -> Self

Performs the - operation.

impl<F, PF> SubAssign<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

fn sub_assign(&mut self, rhs: CubicTrinomialExtensionField<F>)

Performs the -= operation.

impl<F, PF> SubAssign<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

fn sub_assign(&mut self, rhs: QuinticTrinomialExtensionField<F>)

Performs the -= operation.

impl<F, PF, const D: usize> SubAssign<ExtField<F, D, Binomial<F>>> for PackedBinomialExtensionField<F, PF, D>

where F: BinomiallyExtendable<D>, PF: PackedField<Scalar = F>,

fn sub_assign(&mut self, rhs: BinomialExtensionField<F, D>)

Performs the -= operation.

impl<F, PF> Sum<ExtField<F, 3, CubicTrinomial>> for PackedCubicTrinomialExtensionField<F, PF>

where F: CubicTrinomialExtendable, PF: PackedField<Scalar = F>,

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

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<F, PF> Sum<ExtField<F, 5, QuinticTrinomial>> for PackedQuinticTrinomialExtensionField<F, PF>

where F: QuinticTrinomialExtendable, PF: PackedField<Scalar = F>,

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

Takes an iterator and generates Self from the elements by “summing up” the items.