Add generating pairs

This page contains the documentation of the functions add_generating_pair and add_generating_pair_no_checks which can be invoked with a variety of different argument types.

Functions
template<typename Thing>
void	add_generating_pair (Thing &thing, char const *u, char const *v)
	Helper for adding a generating pair of words (string literals).
template<typename Thing, typename Int>
void	add_generating_pair (Thing &thing, std::initializer_list< Int > const &u, std::initializer_list< Int > const &v)
	Helper for adding a generating pair of words (std::initializer_list).
template<typename Thing>
void	add_generating_pair (Thing &thing, std::string_view u, std::string_view v)
	Helper for adding a generating pair of words (std::string_view).
template<typename Thing>
void	add_generating_pair (Thing &thing, typename Thing::native_word_type const &u, typename Thing::native_word_type const &v)
	Helper for adding a generating pair of words.
template<typename Thing>
void	add_generating_pair_no_checks (Thing &thing, char const *u, char const *v)
	Helper for adding a generating pair of words (string literals).
template<typename Thing, typename Int>
void	add_generating_pair_no_checks (Thing &thing, std::initializer_list< Int > const &u, std::initializer_list< Int > const &v)
	Helper for adding a generating pair of words (std::initializer_list).
template<typename Thing>
void	add_generating_pair_no_checks (Thing &thing, std::string_view u, std::string_view v)
	Helper for adding a generating pair of words (std::string_view).
template<typename Thing>
void	add_generating_pair_no_checks (Thing &thing, typename Thing::native_word_type const &u, typename Thing::native_word_type const &v)
	Helper for adding a generating pair of words.

Function Documentation

add_generating_pair() [1/4]

template<typename Thing>

void add_generating_pair	(	Thing &	thing,
		char const *	u,
		char const *	v )

Defined in cong-common-helpers.hpp.

See add_generating_pairs for details.

add_generating_pair() [2/4]

template<typename Thing, typename Int>

void add_generating_pair	(	Thing &	thing,
		std::initializer_list< Int > const &	u,
		std::initializer_list< Int > const &	v )

Defined in cong-common-helpers.hpp.

Template Parameters

Int	must satisfy std::integral_type_v<Int>.

See add_generating_pairs for details.

add_generating_pair() [3/4]

template<typename Thing>

void add_generating_pair	(	Thing &	thing,
		std::string_view	u,
		std::string_view	v )

Defined in cong-common-helpers.hpp.

See add_generating_pairs for details.

add_generating_pair() [4/4]

template<typename Thing>

void add_generating_pair	(	Thing &	thing,
		typename Thing::native_word_type const &	u,
		typename Thing::native_word_type const &	v )

Defined in cong-common-helpers.hpp.

This function can be used to add a generating pair to thing using objects themselves rather than iterators.

Template Parameters

Thing

the type of the first parameter must be one of Kambites, KnuthBendix, ToddCoxeter, or Congruence.

Parameters

thing	the object to add generating pairs to.
u	the left hand side of the pair to add.
v	the right hand side of the pair to add.

Exceptions

LibsemigroupsException

if any of the values pointed at by the iterators is out of range, i.e. they do not belong to presentation().alphabet() and Presentation::validate_word throws.

add_generating_pair_no_checks() [1/4]

template<typename Thing>

void add_generating_pair_no_checks	(	Thing &	thing,
		char const *	u,
		char const *	v )

Defined in cong-common-helpers.hpp.

See add_generating_pair_no_checks for details.

add_generating_pair_no_checks() [2/4]

template<typename Thing, typename Int>

void add_generating_pair_no_checks	(	Thing &	thing,
		std::initializer_list< Int > const &	u,
		std::initializer_list< Int > const &	v )

Defined in cong-common-helpers.hpp.

Template Parameters

Int	must satisfy std::integral_type_v<Int>.

See add_generating_pair_no_checks for details.

add_generating_pair_no_checks() [3/4]

template<typename Thing>

void add_generating_pair_no_checks	(	Thing &	thing,
		std::string_view	u,
		std::string_view	v )

Defined in cong-common-helpers.hpp.

See add_generating_pair_no_checks for details.

add_generating_pair_no_checks() [4/4]

template<typename Thing>

void add_generating_pair_no_checks	(	Thing &	thing,
		typename Thing::native_word_type const &	u,
		typename Thing::native_word_type const &	v )

Defined in cong-common-helpers.hpp.

This function can be used to add a generating pair to thing using objects themselves rather than iterators.

Template Parameters

Thing

the type of the first parameter must be one of Kambites, KnuthBendix, ToddCoxeter, or Congruence.

Parameters

thing	the object to add generating pairs to.
u	the left hand side of the pair to add.
v	the right hand side of the pair to add.

Warning

This function does not check that the arguments are valid. In particular, it is assumed that every value pointed at by the iterators belongs to presentation().alphabet().