Struct PermutationGroup 

pub struct PermutationGroup { /* private fields */ }

Dedicated structure for managing permutation groups efficiently. Only permutation groups of ranks up to 20 are supported, as higher-rank permutation groups have too large orders not representable with usize which is u64 on most modern machines.

Implementations

impl PermutationGroup

pub fn builder() -> PermutationGroupBuilder

Trait Implementations

impl CharacterProperties for PermutationGroup

type RowSymbol = PermutationIrrepSymbol

Type of the row-labelling symbols in the associated character table.

type CharTab = RepCharacterTable<PermutationIrrepSymbol, PermutationClassSymbol<u8>>

Type of the associated character table whose row-labelling symbol type is constrained to be the same as Self::RowSymbol.

fn character_table(&self) -> &Self::CharTab

Returns a shared reference to the character table of this group.

fn unitary_represented(&self) -> bool

Returns a boolean indicating if this character table contains irreducible representations of a unitary-represented group.

impl ClassProperties for PermutationGroup

fn compute_class_structure(&mut self) -> Result<(), Error>

Computes the class structure of this permutation group based on cycle patterns.

fn class_size(&self, cc_idx: usize) -> Option<usize>

Computes the class size given a class index.

The closed form for a conjugacy class of a particular cycle pattern is given here.

type ClassSymbol = PermutationClassSymbol<u8>

The type of class symbols.

fn get_cc_index(&self, cc_idx: usize) -> Option<&HashSet<usize>>

Given a class index, returns an optional shared reference to the set containing the indices of all elements in that class.

fn filter_cc_symbols<P: FnMut(&Self::ClassSymbol) -> bool>( &self, predicate: P, ) -> Vec<Self::ClassSymbol>

Given a predicate, returns conjugacy class symbols satisfying it.

fn get_cc_of_element_index(&self, e_idx: usize) -> Option<usize>

Given an element index, returns an optional index of the conjugacy class to which the element belongs.

fn get_cc_transversal(&self, cc_idx: usize) -> Option<Self::GroupElement>

Given a class index, returns an optional representative element of that conjugacy class.

fn get_index_of_cc_symbol(&self, cc_sym: &Self::ClassSymbol) -> Option<usize>

Given a conjugacy class symbol, returns the index of the corresponding conjugacy class.

fn get_cc_symbol_of_index(&self, cc_idx: usize) -> Option<Self::ClassSymbol>

Given a class index, returns its conjugacy class symbol, if any.

fn set_class_symbols(&mut self, cc_symbols: &[Self::ClassSymbol])

Sets the conjugacy class symbols for this group.

fn get_inverse_cc(&self, cc_idx: usize) -> Option<usize>

Given a class index, returns an index for its inverse.

fn class_number(&self) -> usize

Returns the number of conjugacy classes in the group.

fn class_matrix( &self, ctb_opt: Option<&Array2<usize>>, r: usize, ) -> Array2<usize>

The class matrix $\mathbf{N}_r$ for the conjugacy classes in the group.

impl Clone for PermutationGroup

fn clone(&self) -> PermutationGroup

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl GroupProperties for PermutationGroup

type GroupElement = Permutation<u8>

The type of the elements in the group.

type ElementCollection = PermutationIterator<u8>

fn name(&self) -> String

Returns the name of the group.

fn finite_subgroup_name(&self) -> Option<&String>

Returns the finite subgroup name of this group, if any.

fn get_index(&self, index: usize) -> Option<Self::GroupElement>

Given an index, returns the element associated with it, or None if the index is out of range.

fn get_index_of(&self, g: &Self::GroupElement) -> Option<usize>

Given an element, returns its index in the group, or None if the element does not exist in the group.

fn contains(&self, g: &Self::GroupElement) -> bool

Checks if an element is a member of the group.

fn elements(&self) -> &Self::ElementCollection

Returns an iterable collection of the elements in the group.

fn is_abelian(&self) -> bool

Checks if this group is abelian.

fn order(&self) -> usize

Returns the order of the group.

fn cayley_table(&self) -> Option<&Array2<usize>>

Returns the Cayley table of the group, if any.

impl IrrepCharTabConstruction for PermutationGroup

fn set_irrep_character_table(&mut self, chartab: Self::CharTab)

Sets the irrep character table internally.

fn construct_irrep_character_table(&mut self)

Constructs the irrep character table for this group using the Burnside–Dixon algorithm with Schneider optimisation.

impl PermutationGroupProperties for PermutationGroup

fn from_rank(rank: u8) -> Result<Self, Error>

Constructs a permutation group $Sym(n)$ from a given rank $n$ (i.e. the number of elements in the set to be permuted).

fn canonicalise_character_table(&mut self)

Reorders and relabels the rows and columns of the constructed character table using permutation-specific rules and conventions.

fn set_class_symbols_from_cycle_patterns(&mut self)

Sets class symbols from cycle patterns.