PrincipalIntegerMap

algebraeon_rings::structure

Struct PrincipalIntegerMap 

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pub struct PrincipalIntegerMap<Ring: RingSignature, RingB: BorrowedStructure<Ring>> { /* private fields */ }
Expand description

The unique ring homomorphism Z -> R of the integers into any ring R

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impl<Ring: RingSignature, RingB: BorrowedStructure<Ring>> PrincipalIntegerMap<Ring, RingB>

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pub fn new(ring: RingB) -> Self

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impl<Ring: Clone + RingSignature, RingB: Clone + BorrowedStructure<Ring>> Clone for PrincipalIntegerMap<Ring, RingB>

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fn clone(&self) -> PrincipalIntegerMap<Ring, RingB>

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<Ring: Debug + RingSignature, RingB: Debug + BorrowedStructure<Ring>> Debug for PrincipalIntegerMap<Ring, RingB>

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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<B: BorrowedStructure<RationalCanonicalStructure>> FieldOfFractionsInclusion<IntegerCanonicalStructure, RationalCanonicalStructure> for PrincipalIntegerMap<RationalCanonicalStructure, B>

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fn numerator_and_denominator(&self, a: &Rational) -> (Integer, Integer)

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fn numerator(&self, a: &Field::Set) -> Ring::Set

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fn denominator(&self, a: &Field::Set) -> Ring::Set

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impl<Ring: RingSignature, RingB: BorrowedStructure<Ring>> Function<IntegerCanonicalStructure, Ring> for PrincipalIntegerMap<Ring, RingB>

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fn image(&self, x: &Integer) -> <Ring as SetSignature>::Set

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impl<Ring: CharZeroRingSignature, RingB: BorrowedStructure<Ring>> InjectiveFunction<IntegerCanonicalStructure, Ring> for PrincipalIntegerMap<Ring, RingB>

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fn try_preimage(&self, x: &<Ring as SetSignature>::Set) -> Option<Integer>

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impl<B: BorrowedStructure<ComplexAlgebraicCanonicalStructure>> IntegralDomainExtensionAllPolynomialRoots<IntegerCanonicalStructure, ComplexAlgebraicCanonicalStructure> for PrincipalIntegerMap<ComplexAlgebraicCanonicalStructure, B>

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fn all_roots(&self, polynomial: &Polynomial<Integer>) -> Vec<ComplexAlgebraic>

Return all roots of the polynomial in B with duplicate elements according to multiplicity
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impl<B: BorrowedStructure<PAdicAlgebraicStructure>> IntegralDomainExtensionAllPolynomialRoots<IntegerCanonicalStructure, PAdicAlgebraicStructure> for PrincipalIntegerMap<PAdicAlgebraicStructure, B>

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fn all_roots(&self, polynomial: &Polynomial<Integer>) -> Vec<PAdicAlgebraic>

Return all roots of the polynomial in B with duplicate elements according to multiplicity
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impl<B: BorrowedStructure<RealAlgebraicCanonicalStructure>> IntegralDomainExtensionAllPolynomialRoots<IntegerCanonicalStructure, RealAlgebraicCanonicalStructure> for PrincipalIntegerMap<RealAlgebraicCanonicalStructure, B>

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fn all_roots(&self, polynomial: &Polynomial<Integer>) -> Vec<RealAlgebraic>

Return all roots of the polynomial in B with duplicate elements according to multiplicity
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impl<Ring: RingSignature, RingB: BorrowedStructure<Ring>> Morphism<IntegerCanonicalStructure, Ring> for PrincipalIntegerMap<Ring, RingB>

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fn domain(&self) -> &IntegerCanonicalStructure

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fn range(&self) -> &Ring

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impl<Ring: PartialEq + RingSignature, RingB: PartialEq + BorrowedStructure<Ring>> PartialEq for PrincipalIntegerMap<Ring, RingB>

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fn eq(&self, other: &PrincipalIntegerMap<Ring, RingB>) -> 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<Ring: RingSignature, RingB: BorrowedStructure<Ring>> RingHomomorphism<IntegerCanonicalStructure, Ring> for PrincipalIntegerMap<Ring, RingB>

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fn range_module_structure<'h>( &'h self, ) -> RingHomomorphismRangeModuleStructure<'h, Domain, Range, Self>

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fn into_range_module_structure( self, ) -> RingHomomorphismRangeModuleStructure<'static, Domain, Range, Self>

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impl<Ring: Eq + RingSignature, RingB: Eq + BorrowedStructure<Ring>> Eq for PrincipalIntegerMap<Ring, RingB>

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impl<Ring: RingSignature, RingB: BorrowedStructure<Ring>> StructuralPartialEq for PrincipalIntegerMap<Ring, RingB>

Auto Trait Implementations§

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impl<Ring, RingB> Freeze for PrincipalIntegerMap<Ring, RingB>
where RingB: Freeze,

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impl<Ring, RingB> RefUnwindSafe for PrincipalIntegerMap<Ring, RingB>
where RingB: RefUnwindSafe, Ring: RefUnwindSafe,

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impl<Ring, RingB> Send for PrincipalIntegerMap<Ring, RingB>

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impl<Ring, RingB> Sync for PrincipalIntegerMap<Ring, RingB>

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impl<Ring, RingB> Unpin for PrincipalIntegerMap<Ring, RingB>
where RingB: Unpin, Ring: Unpin,

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impl<Ring, RingB> UnwindSafe for PrincipalIntegerMap<Ring, RingB>
where RingB: UnwindSafe, Ring: UnwindSafe,

Blanket Implementations§

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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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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more
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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<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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fn equivalent(&self, key: &K) -> bool

Checks if this value is equivalent to the given key. Read more
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impl<Q, K> Equivalent<K> for Q
where Q: Eq + ?Sized, K: Borrow<Q> + ?Sized,

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fn equivalent(&self, key: &K) -> bool

Compare self to key and return true if they are equal.
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impl<T, U> ExactFrom<T> for U
where U: TryFrom<T>,

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fn exact_from(value: T) -> U

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impl<T, U> ExactInto<U> for T
where U: ExactFrom<T>,

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fn exact_into(self) -> U

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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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impl<T> IntoEither for T

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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, U> OverflowingInto<U> for T
where U: OverflowingFrom<T>,

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fn overflowing_into(self) -> (U, bool)

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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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impl<T, U> RoundingInto<U> for T
where U: RoundingFrom<T>,

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fn rounding_into(self, rm: RoundingMode) -> (U, Ordering)

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<T, U> SaturatingInto<U> for T
where U: SaturatingFrom<T>,

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fn saturating_into(self) -> U

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impl<T> ToDebugString for T
where T: Debug,

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fn to_debug_string(&self) -> String

Returns the String produced by Ts Debug implementation.

§Examples
use malachite_base::strings::ToDebugString;

assert_eq!([1, 2, 3].to_debug_string(), "[1, 2, 3]");
assert_eq!(
    [vec![2, 3], vec![], vec![4]].to_debug_string(),
    "[[2, 3], [], [4]]"
);
assert_eq!(Some(5).to_debug_string(), "Some(5)");
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T, U> TryFrom<U> for T
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
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

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

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T, U> WrappingInto<U> for T
where U: WrappingFrom<T>,

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fn wrapping_into(self) -> U

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impl<Domain, Range, M, BM> BorrowedMorphism<Domain, Range, M> for BM
where Domain: Signature, Range: Signature, M: Morphism<Domain, Range>, BM: Borrow<M> + Clone + Debug + Send + Sync,

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impl<S, BS> BorrowedSet<S> for BS
where BS: Borrow<S> + Clone + Debug + Send + Sync,

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impl<S, BS> BorrowedStructure<S> for BS
where S: Signature, BS: Borrow<S> + Clone + Debug + Eq + Send + Sync,

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impl<X, T> Endomorphism<X> for T
where X: Signature, T: Morphism<X, X>,