Cayley graphs

This page contains information about the member functions of the FroidurePinBase class related to left and right Cayley graphs.

inline element_index_type libsemigroups::FroidurePinBase::left(element_index_type i, letter_type j)

Returns the index of the product of a generator and an element.

Returns the index of the product of the generator with index j with the element in position i.

See also

right.

Complexity

At worst \(O(|S|n)\) where \(S\) is the semigroup represented by this, and \(n\) is the return value of FroidurePin::number_of_generators.

Parameters

• i – the index of the element

• j – the index of the generator

Throws

• LibsemigroupsException – if i is greater than or equal to size().

• LibsemigroupsException – if j is greater than or equal to FroidurePin::number_of_generators().

Returns

A value of type element_index_type.

inline cayley_graph_type const &libsemigroups::FroidurePinBase::left_cayley_graph()

Returns a const reference to the left Cayley graph.

Complexity

At worst \(O(|S|n)\) where \(S\) is the semigroup represented by this, and \(n\) is the return value of FroidurePin::number_of_generators.

Parameters

None.

Throws

(None) – This function guarantees not to throw a LibsemigroupsException.

Returns

A const reference to cayley_graph_type.

inline element_index_type libsemigroups::FroidurePinBase::right(element_index_type i, letter_type j)

Returns the index of the product of an element and a generator.

Returns the index of the product of the element in position i with the generator with index j.

See also

left.

Complexity

At worst \(O(|S|n)\) where \(S\) is the semigroup represented by this, and \(n\) is the return value of FroidurePin::number_of_generators.

Parameters

• i – the index of the element

• j – the index of the generator

Throws

• LibsemigroupsException – if i is greater than or equal to size().

• LibsemigroupsException – if j is greater than or equal to FroidurePin::number_of_generators().

Returns

A value of type element_index_type.

inline cayley_graph_type const &libsemigroups::FroidurePinBase::right_cayley_graph()

Returns a const reference to the right Cayley graph.

Complexity

At worst \(O(|S|n)\) where \(S\) is the semigroup represented by this, and \(n\) is the return value of FroidurePin::number_of_generators.

Parameters

None.

Throws

(None) – This function guarantees not to throw a LibsemigroupsException.

Returns

A const reference to cayley_graph_type.