The Congruence class

Defined in cong-class.hpp.

On this page we describe the functionality relating to the class template Congruence in libsemigroups. This class can be used for computing a congruence over a semigroup or monoid by running every applicable algorithm from libsemigroups (and some variants of the same algorithm) in parallel. This class is provided for convenience, at present it is not very customisable, and lacks some of the fine grained control offered by the classes implementing individual algorithms, such as Kambites, KnuthBendix, and ToddCoxeter.

Template Parameters

Word	the type of the words used in the presentation and generating_pairs.

See also

Common congruence helpers for information about helper functions for the Congruence class template.

Example

Presentation<word_type> p;
p.alphabet(2)
presentation::add_rule(p, {0, 1}, {});
Congruence cong(congruence_kind::twosided, p);
is_obviously_infinite(cong);  // true
congruence_common::add_generating_pair(cong, {0, 0, 0}, {});
cong.number_of_classes(); // 3

Topics
	Member Types
	Public member types.
	Constructors + initializers
	Construct or re-initialize a Congruence instance (public member function).
	Settings
	Settings that control the behaviour of a Congruence instance.
	Common member functions
	Documentation of common member functions of Congruence, Kambites, KnuthBendix, and ToddCoxeter.
	Accessors
	Member functions that can be used to access the state of a Congruence instance.

Functions
template<typename Word>
	Congruence (Congruence< Word > &&) -> Congruence< Word >
	Deduction guide.
template<typename Word>
	Congruence (Congruence< Word > const &) -> Congruence< Word >
	Deduction guide.
template<typename Word>
	Congruence (congruence_kind, Presentation< Word > &&) -> Congruence< Word >
	Deduction guide.
template<typename Word>
	Congruence (congruence_kind, Presentation< Word > const &) -> Congruence< Word >
	Deduction guide.

Function Documentation

Congruence() [1/4]

template<typename Word>

Congruence

(

Congruence< Word > &&

)

-> Congruence< Word >

Defined in cong-class.hpp.

Deduction guide to construct a Congruence<Word> from a Congruence<Word>.

Congruence() [2/4]

template<typename Word>

Congruence

(

Congruence< Word > const &

)

-> Congruence< Word >

Defined in cong-class.hpp.

Deduction guide to construct a Congruence<Word> from a Congruence<Word>.

Congruence() [3/4]

template<typename Word>

Congruence	(	congruence_kind	,
		Presentation< Word > &&	) -> Congruence< Word >

Defined in cong-class.hpp.

Deduction guide to construct a Congruence<Word> from a congruence_kind and Presentation<Word> rvalue reference.

Congruence() [4/4]

template<typename Word>

Congruence	(	congruence_kind	,
		Presentation< Word > const &	) -> Congruence< Word >

Defined in cong-class.hpp.

Deduction guide to construct a Congruence<Word> from a congruence_kind and Presentation<Word> const reference.