PermutationCanonicalStructure

algebraeon_groups::examples::symmetric

Struct PermutationCanonicalStructure 

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pub struct PermutationCanonicalStructure<const N: usize> {}

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impl<const N: usize> AssociativeCompositionSignature for PermutationCanonicalStructure<N>

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fn compose_nonempty_list( &self, elems: Vec<impl Borrow<Self::Set>>, ) -> Option<Self::Set>

Returns None if the list is empty.
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impl<const N: usize> Clone for PermutationCanonicalStructure<N>

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fn clone(&self) -> PermutationCanonicalStructure<N>

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<const N: usize> CompositionSignature for PermutationCanonicalStructure<N>

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fn compose(&self, a: &Self::Set, b: &Self::Set) -> Self::Set

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fn compose_mut(&self, a: &mut Self::Set, b: &Self::Set)

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impl<const N: usize> Debug for PermutationCanonicalStructure<N>

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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<const N: usize> GroupSignature for PermutationCanonicalStructure<N>

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fn inverse(&self, a: &Self::Set) -> Self::Set

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fn int_pow(&self, a: &Self::Set, n: &Integer) -> Self::Set

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fn generated_finite_subgroup_table( &self, generators: Vec<Self::Set>, ) -> (FiniteGroupMultiplicationTable, Vec<Self::Set>, HashMap<Self::Set, usize>)
where Self::Set: Hash + Eq,

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fn generated_finite_subgroup( &self, gens: Vec<Self::Set>, ) -> FiniteSubgroup<Self::Set>
where Self::Set: Hash + Eq,

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impl<const N: usize> IdentitySignature for PermutationCanonicalStructure<N>

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fn identity(&self) -> Self::Set

Returns the identity element e.
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impl<const N: usize> LeftCancellativeCompositionSignature for PermutationCanonicalStructure<N>

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fn try_left_difference(&self, a: &Self::Set, b: &Self::Set) -> Option<Self::Set>

Try to find x such that a = compose(b, x).
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impl<const N: usize> MonoidSignature for PermutationCanonicalStructure<N>

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fn compose_list(&self, elems: Vec<impl Borrow<Self::Set>>) -> Self::Set

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fn nat_pow(&self, a: &Self::Set, n: &Natural) -> Self::Set

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impl<const N: usize> PartialEq for PermutationCanonicalStructure<N>

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fn eq(&self, other: &PermutationCanonicalStructure<N>) -> 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<const N: usize> RightCancellativeCompositionSignature for PermutationCanonicalStructure<N>

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fn try_right_difference( &self, a: &Self::Set, b: &Self::Set, ) -> Option<Self::Set>

Try to find x such that a = compose(x, b).
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impl<const N: usize> SetSignature for PermutationCanonicalStructure<N>

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type Set = Permutation<N>

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fn is_element(&self, _x: &Self::Set) -> Result<(), String>

Some instances of Self::Set may not be valid to represent elements of this set. Return true if x is a valid element and false if not.
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impl<const N: usize> TryInverseSignature for PermutationCanonicalStructure<N>

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fn try_inverse(&self, a: &Self::Set) -> Option<Self::Set>

Return x such that compose(x, a) = compose(a, x) = e or None if no such x exists. Read more
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impl<const N: usize> TryLeftInverseSignature for PermutationCanonicalStructure<N>

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fn try_left_inverse(&self, a: &Self::Set) -> Option<Self::Set>

Return x such that compose(x, a) = e or None if no such x exists.
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impl<const N: usize> TryRightInverseSignature for PermutationCanonicalStructure<N>

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fn try_right_inverse(&self, a: &Self::Set) -> Option<Self::Set>

Return x such that compose(a, x) = e or None if no such x exists.
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impl<const N: usize> Eq for PermutationCanonicalStructure<N>

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impl<const N: usize> Signature for PermutationCanonicalStructure<N>

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impl<const N: usize> StructuralPartialEq for PermutationCanonicalStructure<N>

Auto Trait 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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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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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,