Struct ark_ff::fields::models::quadratic_extension::QuadExtField [−][src]
An element of a quadratic extension field F_p[X]/(X^2 - P::NONRESIDUE) is
represented as c0 + c1 * X, for c0, c1 in P::BaseField
.
Fields
c0: P::BaseField
c1: P::BaseField
Implementations
impl<P: Fp2Parameters> QuadExtField<Fp2ParamsWrapper<P>>
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pub fn mul_assign_by_fp(&mut self, other: &P::Fp)
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impl<P: Fp4Parameters> QuadExtField<Fp4ParamsWrapper<P>>
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pub fn mul_by_fp(&mut self, element: &<P::Fp2Params as Fp2Parameters>::Fp)
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pub fn mul_by_fp2(&mut self, element: &Fp2<P::Fp2Params>)
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impl<P: Fp6Parameters> QuadExtField<Fp6ParamsWrapper<P>>
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pub fn mul_by_034(
&mut self,
c0: &<P::Fp3Params as Fp3Parameters>::Fp,
c3: &<P::Fp3Params as Fp3Parameters>::Fp,
c4: &<P::Fp3Params as Fp3Parameters>::Fp
)
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&mut self,
c0: &<P::Fp3Params as Fp3Parameters>::Fp,
c3: &<P::Fp3Params as Fp3Parameters>::Fp,
c4: &<P::Fp3Params as Fp3Parameters>::Fp
)
pub fn mul_by_014(
&mut self,
c0: &<P::Fp3Params as Fp3Parameters>::Fp,
c1: &<P::Fp3Params as Fp3Parameters>::Fp,
c4: &<P::Fp3Params as Fp3Parameters>::Fp
)
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&mut self,
c0: &<P::Fp3Params as Fp3Parameters>::Fp,
c1: &<P::Fp3Params as Fp3Parameters>::Fp,
c4: &<P::Fp3Params as Fp3Parameters>::Fp
)
impl<P: Fp12Parameters> QuadExtField<Fp12ParamsWrapper<P>>
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pub fn mul_by_fp(
&mut self,
element: &<<P::Fp6Params as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp
)
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&mut self,
element: &<<P::Fp6Params as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp
)
pub fn mul_by_034(
&mut self,
c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c3: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)
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&mut self,
c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c3: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)
pub fn mul_by_014(
&mut self,
c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c1: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)
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&mut self,
c0: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c1: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>,
c4: &Fp2<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>
)
pub fn cyclotomic_square_in_place(&mut self)
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pub fn cyclotomic_square(&self) -> Self
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impl<P: QuadExtParameters> QuadExtField<P>
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pub fn new(c0: P::BaseField, c1: P::BaseField) -> Self
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pub fn conjugate(&mut self)
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This is only to be used when the element is known to be in the cyclotomic subgroup.
pub fn cyclotomic_exp(&self, exponent: impl AsRef<[u64]>) -> Self
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This is only to be used when the element is known to be in the cyclotomic subgroup.
pub fn norm(&self) -> P::BaseField
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Norm of QuadExtField over P::BaseField
:Norm(a) = a * a.conjugate()
.
This simplifies to: Norm(a) = a.x^2 - P::NON_RESIDUE * a.y^2
.
This is alternatively expressed as Norm(a) = a^(1 + p)
.
pub fn mul_assign_by_basefield(&mut self, element: &P::BaseField)
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Trait Implementations
impl<'a, P: QuadExtParameters> Add<&'a QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the +
operator.
fn add(self, other: &Self) -> Self
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impl<'a, P: QuadExtParameters> Add<&'a mut QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the +
operator.
fn add(self, other: &'a mut Self) -> Self
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impl<P: QuadExtParameters> Add<QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the +
operator.
fn add(self, other: Self) -> Self
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impl<'a, P: QuadExtParameters> AddAssign<&'a QuadExtField<P>> for QuadExtField<P>
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fn add_assign(&mut self, other: &Self)
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impl<'a, P: QuadExtParameters> AddAssign<&'a mut QuadExtField<P>> for QuadExtField<P>
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fn add_assign(&mut self, other: &'a mut Self)
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impl<P: QuadExtParameters> AddAssign<QuadExtField<P>> for QuadExtField<P>
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fn add_assign(&mut self, other: Self)
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impl<P: QuadExtParameters> CanonicalDeserialize for QuadExtField<P>
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fn deserialize<R: Read>(reader: R) -> Result<Self, SerializationError>
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pub fn deserialize_uncompressed<R>(
reader: R
) -> Result<Self, SerializationError> where
R: Read,
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reader: R
) -> Result<Self, SerializationError> where
R: Read,
pub fn deserialize_unchecked<R>(reader: R) -> Result<Self, SerializationError> where
R: Read,
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R: Read,
impl<P: QuadExtParameters> CanonicalDeserializeWithFlags for QuadExtField<P>
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fn deserialize_with_flags<R: Read, F: Flags>(
reader: R
) -> Result<(Self, F), SerializationError>
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reader: R
) -> Result<(Self, F), SerializationError>
impl<P: QuadExtParameters> CanonicalSerialize for QuadExtField<P>
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fn serialize<W: Write>(&self, writer: W) -> Result<(), SerializationError>
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fn serialized_size(&self) -> usize
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pub fn serialize_uncompressed<W>(
&self,
writer: W
) -> Result<(), SerializationError> where
W: Write,
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&self,
writer: W
) -> Result<(), SerializationError> where
W: Write,
pub fn serialize_unchecked<W>(
&self,
writer: W
) -> Result<(), SerializationError> where
W: Write,
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&self,
writer: W
) -> Result<(), SerializationError> where
W: Write,
pub fn uncompressed_size(&self) -> usize
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impl<P: QuadExtParameters> CanonicalSerializeWithFlags for QuadExtField<P>
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fn serialize_with_flags<W: Write, F: Flags>(
&self,
writer: W,
flags: F
) -> Result<(), SerializationError>
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&self,
writer: W,
flags: F
) -> Result<(), SerializationError>
fn serialized_size_with_flags<F: Flags>(&self) -> usize
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impl<P: QuadExtParameters> Clone for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
fn clone(&self) -> Self
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pub fn clone_from(&mut self, source: &Self)
1.0.0[src]
impl<P: QuadExtParameters> Copy for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
impl<P: QuadExtParameters> Debug for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
impl<P: QuadExtParameters> Default for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
impl<P: QuadExtParameters> Display for QuadExtField<P>
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impl<'a, P: QuadExtParameters> Div<&'a QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the /
operator.
fn div(self, other: &Self) -> Self
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impl<'a, P: QuadExtParameters> Div<&'a mut QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the /
operator.
fn div(self, other: &'a mut Self) -> Self
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impl<P: QuadExtParameters> Div<QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the /
operator.
fn div(self, other: Self) -> Self
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impl<'a, P: QuadExtParameters> DivAssign<&'a QuadExtField<P>> for QuadExtField<P>
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fn div_assign(&mut self, other: &Self)
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impl<'a, P: QuadExtParameters> DivAssign<&'a mut QuadExtField<P>> for QuadExtField<P>
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fn div_assign(&mut self, other: &'a mut Self)
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impl<P: QuadExtParameters> DivAssign<QuadExtField<P>> for QuadExtField<P>
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fn div_assign(&mut self, other: Self)
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impl<P: QuadExtParameters> Eq for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
impl<P: QuadExtParameters> Field for QuadExtField<P>
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type BasePrimeField = P::BasePrimeField
fn extension_degree() -> u64
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fn from_base_prime_field_elems(elems: &[Self::BasePrimeField]) -> Option<Self>
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fn double(&self) -> Self
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fn double_in_place(&mut self) -> &mut Self
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fn square(&self) -> Self
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fn from_random_bytes_with_flags<F: Flags>(bytes: &[u8]) -> Option<(Self, F)>
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fn from_random_bytes(bytes: &[u8]) -> Option<Self>
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fn square_in_place(&mut self) -> &mut Self
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fn inverse(&self) -> Option<Self>
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fn inverse_in_place(&mut self) -> Option<&mut Self>
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fn frobenius_map(&mut self, power: usize)
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fn characteristic<'a>() -> &'a [u64]
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#[must_use]fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self
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fn pow_with_table<S: AsRef<[u64]>>(powers_of_2: &[Self], exp: S) -> Option<Self>
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impl<P: QuadExtParameters> From<bool> for QuadExtField<P>
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impl<P: QuadExtParameters> From<u128> for QuadExtField<P>
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impl<P: QuadExtParameters> From<u16> for QuadExtField<P>
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impl<P: QuadExtParameters> From<u32> for QuadExtField<P>
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impl<P: QuadExtParameters> From<u64> for QuadExtField<P>
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impl<P: QuadExtParameters> From<u8> for QuadExtField<P>
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impl<P: QuadExtParameters> FromBytes for QuadExtField<P>
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impl<P: QuadExtParameters> Hash for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
fn hash<__HP>(&self, __state: &mut __HP) where
__HP: Hasher,
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__HP: Hasher,
pub fn hash_slice<H>(data: &[Self], state: &mut H) where
H: Hasher,
1.3.0[src]
H: Hasher,
impl<'a, P: QuadExtParameters> Mul<&'a QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the *
operator.
fn mul(self, other: &Self) -> Self
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impl<'a, P: QuadExtParameters> Mul<&'a mut QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the *
operator.
fn mul(self, other: &'a mut Self) -> Self
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impl<P: QuadExtParameters> Mul<QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the *
operator.
fn mul(self, other: Self) -> Self
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impl<'a, P: QuadExtParameters> MulAssign<&'a QuadExtField<P>> for QuadExtField<P>
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fn mul_assign(&mut self, other: &Self)
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impl<'a, P: QuadExtParameters> MulAssign<&'a mut QuadExtField<P>> for QuadExtField<P>
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fn mul_assign(&mut self, other: &'a mut Self)
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impl<P: QuadExtParameters> MulAssign<QuadExtField<P>> for QuadExtField<P>
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fn mul_assign(&mut self, other: Self)
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impl<P: QuadExtParameters> Neg for QuadExtField<P>
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type Output = Self
The resulting type after applying the -
operator.
#[must_use]fn neg(self) -> Self
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impl<P: QuadExtParameters> One for QuadExtField<P>
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impl<P: QuadExtParameters> Ord for QuadExtField<P>
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QuadExtField
elements are ordered lexicographically.
fn cmp(&self, other: &Self) -> Ordering
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#[must_use]pub fn max(self, other: Self) -> Self
1.21.0[src]
#[must_use]pub fn min(self, other: Self) -> Self
1.21.0[src]
#[must_use]pub fn clamp(self, min: Self, max: Self) -> Self
1.50.0[src]
impl<P: QuadExtParameters> PartialEq<QuadExtField<P>> for QuadExtField<P> where
P: QuadExtParameters,
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P: QuadExtParameters,
impl<P: QuadExtParameters> PartialOrd<QuadExtField<P>> for QuadExtField<P>
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fn partial_cmp(&self, other: &Self) -> Option<Ordering>
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#[must_use]pub fn lt(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn le(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn gt(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn ge(&self, other: &Rhs) -> bool
1.0.0[src]
impl<'a, P: QuadExtParameters> Product<&'a QuadExtField<P>> for QuadExtField<P>
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impl<P: QuadExtParameters> Product<QuadExtField<P>> for QuadExtField<P>
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impl<'a, P: QuadExtParameters> SquareRootField for QuadExtField<P> where
P::BaseField: SquareRootField,
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P::BaseField: SquareRootField,
fn legendre(&self) -> LegendreSymbol
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fn sqrt(&self) -> Option<Self>
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fn sqrt_in_place(&mut self) -> Option<&mut Self>
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impl<'a, P: QuadExtParameters> Sub<&'a QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the -
operator.
fn sub(self, other: &Self) -> Self
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impl<'a, P: QuadExtParameters> Sub<&'a mut QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the -
operator.
fn sub(self, other: &'a mut Self) -> Self
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impl<P: QuadExtParameters> Sub<QuadExtField<P>> for QuadExtField<P>
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type Output = Self
The resulting type after applying the -
operator.
fn sub(self, other: Self) -> Self
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impl<'a, P: QuadExtParameters> SubAssign<&'a QuadExtField<P>> for QuadExtField<P>
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fn sub_assign(&mut self, other: &Self)
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impl<'a, P: QuadExtParameters> SubAssign<&'a mut QuadExtField<P>> for QuadExtField<P>
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fn sub_assign(&mut self, other: &'a mut Self)
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impl<P: QuadExtParameters> SubAssign<QuadExtField<P>> for QuadExtField<P>
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fn sub_assign(&mut self, other: Self)
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impl<'a, P: QuadExtParameters> Sum<&'a QuadExtField<P>> for QuadExtField<P>
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impl<P: QuadExtParameters> Sum<QuadExtField<P>> for QuadExtField<P>
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impl<P: QuadExtParameters> ToBytes for QuadExtField<P>
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impl<P: QuadExtParameters> ToConstraintField<<P as QuadExtParameters>::BasePrimeField> for QuadExtField<P> where
P::BaseField: ToConstraintField<P::BasePrimeField>,
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P::BaseField: ToConstraintField<P::BasePrimeField>,
fn to_field_elements(&self) -> Option<Vec<P::BasePrimeField>>
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impl<P: QuadExtParameters> Zero for QuadExtField<P>
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impl<P: QuadExtParameters> Zeroize for QuadExtField<P>
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Auto Trait Implementations
impl<P> Send for QuadExtField<P>
impl<P> Sync for QuadExtField<P>
impl<P> Unpin for QuadExtField<P> where
P: Unpin,
<P as QuadExtParameters>::BaseField: Unpin,
P: Unpin,
<P as QuadExtParameters>::BaseField: Unpin,
Blanket Implementations
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
pub fn borrow_mut(&mut self) -> &mut T
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impl<T> From<T> for T
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
pub fn to_owned(&self) -> T
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pub fn clone_into(&self, target: &mut T)
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impl<T> ToString for T where
T: Display + ?Sized,
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T: Display + ?Sized,
impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
pub fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
The type returned in the event of a conversion error.
pub fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<T> UniformRand for T where
Standard: Distribution<T>,
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Standard: Distribution<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
V: MultiLane<T>,