Struct qsym2::permutation::Permutation

pub struct Permutation<T: PermutationRank> { /* private fields */ }

Structure to manage permutation actions of a finite set.

Implementations

impl<T: PermutationRank> Permutation<T>

pub fn from_image(image: Vec<T>) -> Result<Self, Error>

Constructs a permutation from the image of its action on an ordered sequence of integers, $0, 1, \ldots$.

Arguments

• image - The image of the permutation when acting on an ordered sequence of integers, $0, 1, \ldots$.

Returns

The corresponding permutation.

Panics

Panics if image contains repeated elements.

pub fn from_cycles(cycles: &[Vec<T>]) -> Result<Self, Error>

Constructs a permutation from its disjoint cycles.

Arguments

• cycles - The disjoint cycles defining the permutation.

Returns

The corresponding permutation.

Panics

Panics if the cycles in cycles contain repeated elements.

pub fn from_lehmer(lehmer: Vec<T>) -> Result<Self, Error>

where <T as TryFrom<usize>>::Error: Debug, Range<T>: Iterator, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>,

Constructs a permutation from its Lehmer encoding.

See here for additional information.

pub fn from_lehmer_index(index: usize, rank: T) -> Result<Self, Error>

where <T as TryFrom<usize>>::Error: Debug, Range<T>: Iterator, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>,

Constructs a permutation from the integer index obtained from a Lehmer encoding.

See here and Korf, R. E. Linear-time disk-based implicit graph search. J. ACM 55, 1–40 (2008). for additional information.

Arguments

• index - An integer index.
• rank - A rank for the permutation to be constructed.

Returns

Returns the corresponding permutation.

Errors

If index is not valid for a permutation of rank rank.

pub fn rank(&self) -> T

The rank of the permutation.

pub fn image(&self) -> &Vec<T>

If the permutation is to act on an ordered sequence of integers, $0, 1, \ldots$, then this gives the result of the action.

pub fn cycles(&self) -> Vec<Vec<T>>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

Obtains the cycle representation of the permutation.

pub fn cycle_pattern(&self) -> Vec<T>

where <T as TryFrom<usize>>::Error: Debug, Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

Returns the pattern of the cycle representation of the permutation.

pub fn is_identity(&self) -> bool

where <T as TryFrom<usize>>::Error: Debug,

Returns true if this permutation is the identity permutation for this rank.

pub fn lehmer( &self, count_ones_opt: Option<&HashMap<BitVec<T, Lsb0>, T>>, ) -> Vec<T>

where <T as TryFrom<usize>>::Error: Debug,

Returns the Lehmer encoding of the permutation.

Arguments

• count_ones_opt - An optional hashmap containing the number of ones in each of the possible bit vectors of length Self::rank.

Returns

The Lehmer encoding of this permutation. See here for additional information.

pub fn lehmer_index( &self, count_ones_opt: Option<&HashMap<BitVec<T, Lsb0>, T>>, ) -> usize

where <T as TryFrom<usize>>::Error: Debug,

Returns the integer corresponding to the Lehmer encoding of this permutation.

See here and Korf, R. E. Linear-time disk-based implicit graph search. J. ACM 55, 1–40 (2008). for additional information.

Arguments

• count_ones_opt - An optional hashmap containing the number of ones in each of the possible bit vectors of length Self::rank.

Returns

Returns the integer corresponding to the Lehmer encoding of this permutation.

Trait Implementations

impl<T: Clone + PermutationRank> Clone for Permutation<T>

fn clone(&self) -> Permutation<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug + PermutationRank> Debug for Permutation<T>

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

Formats the value using the given formatter.

impl<'de, T> Deserialize<'de> for Permutation<T>

where T: Deserialize<'de> + PermutationRank,

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T: PermutationRank + Display> Display for Permutation<T>

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

Formats the value using the given formatter.

impl<T: PermutationRank + Display> FiniteOrder for Permutation<T>

where u32: From<T>, Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

fn order(&self) -> Self::Int

Calculates the order of this permutation. This is the lowest common multiplier of the lengths of the disjoint cycles constituting this permutation.

type Int = u32

The integer type for the order of the element.

impl<T: Hash + PermutationRank> Hash for Permutation<T>

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<T: PermutationRank> Inv for &Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: PermutationRank> Inv for Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: PermutationRank> Mul<&Permutation<T>> for &Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Permutation<T>) -> Self::Output

Performs the * operation.

impl<T: PermutationRank> Mul<&Permutation<T>> for Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Permutation<T>) -> Self::Output

Performs the * operation.

impl<T: PermutationRank> Mul<Permutation<T>> for &Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Permutation<T>) -> Self::Output

Performs the * operation.

impl<T: PermutationRank> Mul for Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Permutation<T>) -> Self::Output

Performs the * operation.

impl<T: PartialEq + PermutationRank> PartialEq for Permutation<T>

fn eq(&self, other: &Permutation<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

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

impl<T: PermutationRank> Pow<i32> for &Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The result after applying the operator.

fn pow(self, rhs: i32) -> Self::Output

Returns self to the power rhs.

impl<T: PermutationRank> Pow<i32> for Permutation<T>

where Range<T>: Iterator + DoubleEndedIterator, Vec<T>: FromIterator<<Range<T> as Iterator>::Item>, VecDeque<T>: FromIterator<<Range<T> as Iterator>::Item>, <T as TryFrom<usize>>::Error: Debug, IndexSet<T>: FromIterator<<Range<T> as Iterator>::Item>,

type Output = Permutation<T>

The result after applying the operator.

fn pow(self, rhs: i32) -> Self::Output

Returns self to the power rhs.

impl<T> Serialize for Permutation<T>

where T: Serialize + PermutationRank,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<T: Eq + PermutationRank> Eq for Permutation<T>

impl<T: PermutationRank> StructuralPartialEq for Permutation<T>