GaloisAutomorphism

Struct GaloisAutomorphism 

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pub struct GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,
{ /* private fields */ }
Available on crate feature unstable-enable only.
Expand description

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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impl<K, Impl, I> GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

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pub fn new(field: K, image_of_canonical_gen: El<K>) -> Self

Creates a new Galois automorphism, mapping the canonical generator of field to the given element.

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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pub fn compose_gal(self, first: &Self) -> Self

Returns the galois automorphism x -> self(first(x))

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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pub fn pow(self, k: usize) -> Self

Returns the galois automorphism x -> self(...(self(x))...), where self is applied k times.

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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pub fn is_identity(&self) -> bool

Returns true if this is the identity map.

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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pub fn invert(self) -> Self

Returns the inverse of this automorphism

§Availability

This API is marked as unstable and is only available when the unstable-enable crate feature is enabled. This comes with no stability guarantees, and could be changed or removed at any time.

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impl<K, Impl, I> Clone for GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>> + Clone, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

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fn clone(&self) -> Self

Returns a duplicate of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<K, Impl, I> Debug for GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

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

Formats the value using the given formatter. Read more
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impl<K, Impl, I> Hash for GaloisAutomorphism<K, Impl, I>

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

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl<K, Impl, I> Homomorphism<NumberFieldBase<Impl, I>, NumberFieldBase<Impl, I>> for GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

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type DomainStore = K

The type of the RingStore used by this object to store the domain ring.
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type CodomainStore = K

The type of the RingStore used by this object to store the codomain ring.
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fn codomain<'a>(&'a self) -> &'a Self::CodomainStore

Returns a reference to the codomain ring.
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fn domain<'a>(&'a self) -> &'a Self::DomainStore

Returns a reference to the domain ring.
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fn map_ref( &self, x: &<NumberFieldBase<Impl, I> as RingBase>::Element, ) -> <NumberFieldBase<Impl, I> as RingBase>::Element

Applies this homomorphism to the given element from the domain ring, resulting in an element in the codomain ring.
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fn map( &self, x: <NumberFieldBase<Impl, I> as RingBase>::Element, ) -> <NumberFieldBase<Impl, I> as RingBase>::Element

Applies this homomorphism to the given element from the domain ring, resulting in an element in the codomain ring.
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fn mul_assign_map(&self, lhs: &mut Codomain::Element, rhs: Domain::Element)

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn mul_assign_ref_map(&self, lhs: &mut Codomain::Element, rhs: &Domain::Element)

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn mul_map( &self, lhs: Codomain::Element, rhs: Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn fma_map( &self, lhs: &Codomain::Element, rhs: &Domain::Element, summand: Codomain::Element, ) -> Codomain::Element

Fused-multiply-add. This computes lhs * rhs + summand, where rhs is mapped into the ring via this homomorphism. Read more
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fn mul_ref_fst_map( &self, lhs: &Codomain::Element, rhs: Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn mul_ref_snd_map( &self, lhs: Codomain::Element, rhs: &Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn mul_ref_map( &self, lhs: &Codomain::Element, rhs: &Domain::Element, ) -> Codomain::Element

Multiplies the given element in the codomain ring with an element obtained by applying this homomorphism to a given element from the domain ring. Read more
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fn compose<F, PrevDomain: ?Sized + RingBase>( self, prev: F, ) -> ComposedHom<PrevDomain, Domain, Codomain, F, Self>
where Self: Sized, F: Homomorphism<PrevDomain, Domain>,

Constructs the homomorphism x -> self.map(prev.map(x)).
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fn mul_assign_ref_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, Domain>>( &self, lhs: &mut Codomain::Element, rhs: &First::Element, hom: H, )

Multiplies the given element in the codomain ring with an element obtained by applying this and another homomorphism to a given element from another ring. Read more
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fn mul_assign_map_through_hom<First: ?Sized + RingBase, H: Homomorphism<First, Domain>>( &self, lhs: &mut Codomain::Element, rhs: First::Element, hom: H, )

Multiplies the given element in the codomain ring with an element obtained by applying this and another homomorphism to a given element from another ring. Read more
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impl<K, Impl, I> PartialEq for GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

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fn eq(&self, other: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<K, Impl, I> Eq for GaloisAutomorphism<K, Impl, I>
where K: RingStore<Type = NumberFieldBase<Impl, I>>, Impl: RingStore, Impl::Type: Field + FreeAlgebra, <Impl::Type as RingExtension>::BaseRing: RingStore<Type = RationalFieldBase<I>>, I: RingStore, I::Type: IntegerRing,

Auto Trait Implementations§

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impl<K, Impl, I> Freeze for GaloisAutomorphism<K, Impl, I>
where <<Impl as RingStore>::Type as RingExtension>::BaseRing: Sized, K: Freeze,

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impl<K, Impl, I> RefUnwindSafe for GaloisAutomorphism<K, Impl, I>

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impl<K, Impl, I> Send for GaloisAutomorphism<K, Impl, I>
where <<Impl as RingStore>::Type as RingExtension>::BaseRing: Sized, K: Send, <<Impl as RingStore>::Type as RingBase>::Element: Send,

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impl<K, Impl, I> Sync for GaloisAutomorphism<K, Impl, I>
where <<Impl as RingStore>::Type as RingExtension>::BaseRing: Sized, K: Sync, <<Impl as RingStore>::Type as RingBase>::Element: Sync,

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impl<K, Impl, I> Unpin for GaloisAutomorphism<K, Impl, I>
where <<Impl as RingStore>::Type as RingExtension>::BaseRing: Sized, K: Unpin, <<Impl as RingStore>::Type as RingBase>::Element: Unpin,

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impl<K, Impl, I> UnwindSafe for GaloisAutomorphism<K, Impl, I>
where <<Impl as RingStore>::Type as RingExtension>::BaseRing: Sized, K: UnwindSafe, <<Impl as RingStore>::Type as RingBase>::Element: UnwindSafe,

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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where T: ?Sized,

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fn borrow(&self) -> &T

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fn borrow_mut(&mut self) -> &mut T

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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<T> Pointable for T

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const ALIGN: usize

The alignment of pointer.
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type Init = T

The type for initializers.
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unsafe fn init(init: <T as Pointable>::Init) -> usize

Initializes a with the given initializer. Read more
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unsafe fn deref<'a>(ptr: usize) -> &'a T

Dereferences the given pointer. Read more
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unsafe fn deref_mut<'a>(ptr: usize) -> &'a mut T

Mutably dereferences the given pointer. Read more
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unsafe fn drop(ptr: usize)

Drops the object pointed to by the given pointer. Read more
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where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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Uses borrowed data to replace owned data, usually by cloning. Read more
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where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
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type Error = <U as TryFrom<T>>::Error

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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.