This file contains documentation related to semigroup and monoid presentations in libsemigroups.

There are two classes and two namespaces with functionality related to presentations:

For documentation on how to create presentations from other libsemigroups objects, see the documentation for the to<Presentation> functions here.

Namespaces
namespace	libsemigroups::presentation
	Namespace for Presentation helper functions.

namespace	libsemigroups::presentation::examples
	Namespace for presentations of some finitely presented semigroups.

Classes
class	InversePresentation< Word >
	For an implementation of inverse presentations for semigroups or monoids. More...

class	Presentation< Word >
	For an implementation of presentations for semigroups or monoids. More...

Functions
template<typename Word>
bool	operator!= (InversePresentation< Word > const &lhop, InversePresentation< Word > const &rhop)
	Compare for inequality.

template<typename Word>
bool	operator!= (Presentation< Word > const &lhop, Presentation< Word > const &rhop)
	Compare for inequality.

template<typename Word>
bool	operator== (InversePresentation< Word > const &lhop, InversePresentation< Word > const &rhop)
	Compare for equality.

template<typename Word>
bool	operator== (Presentation< Word > const &lhop, Presentation< Word > const &rhop)
	Compare for equality.

template<typename Word>
	Presentation (Presentation< Word > &&) -> Presentation< Word >
	Deduction guide.

template<typename Word>
	Presentation (Presentation< Word > const &) -> Presentation< Word >
	Deduction guide.

template<typename Word>
std::string	to_human_readable_repr (InversePresentation< Word > const &p)
	Return a human readable representation of an InversePresentation.

template<typename Word>
std::string	to_human_readable_repr (Presentation< Word > const &p)
	Return a human readable representation of a presentation.

Variables
template<typename T>
static constexpr bool	IsInversePresentation = detail::IsInversePresentationHelper<T>::value
	Helper variable template.

template<typename T>
static constexpr bool	IsPresentation = detail::IsPresentationHelper<T>::value
	Helper variable template.

Function Documentation

◆ operator!=() [1/2]

template<typename Word>

bool operator!=	(	InversePresentation< Word > const &	lhop,
		InversePresentation< Word > const &	rhop )

Returns true if lhop does not equal rhop by comparing the the alphabets and the rules.

Template Parameters

Word	the type of the words in the inverse presentations.

Parameters

lhop	an inverse presentation that is to be compared.
rhop	an inverse presentation that is to be compared.

Returns: A value of type bool.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in the sum of the alphabet sizes and numbers of rules.

◆ operator!=() [2/2]

template<typename Word>

bool operator!=	(	Presentation< Word > const &	lhop,
		Presentation< Word > const &	rhop )

Returns true if lhop does not equal rhop by comparing the the alphabets and the rules.

Template Parameters

Word	the type of the words in the presentations.

Parameters

lhop	a presentation that is to be compared.
rhop	a presentation that is to be compared.

Returns: A value of type bool.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in the sum of the alphabet sizes and numbers of rules.

◆ operator==() [1/2]

template<typename Word>

bool operator==	(	InversePresentation< Word > const &	lhop,
		InversePresentation< Word > const &	rhop )

Returns true if lhop equals rhop by comparing the the alphabets and the rules.

Template Parameters

Word	the type of the words in the inverse presentations.

Parameters

lhop	an inverse presentation that is to be compared.
rhop	an inverse presentation that is to be compared.

Returns: A value of type bool.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in the sum of the alphabet sizes and numbers of rules.

◆ operator==() [2/2]

template<typename Word>

bool operator==	(	Presentation< Word > const &	lhop,
		Presentation< Word > const &	rhop )

Returns true if lhop equals rhop by comparing the the alphabets and the rules.

Template Parameters

Word	the type of the words in the presentations.

Parameters

lhop	a presentation that is to be compared.
rhop	a presentation that is to be compared.

Returns: A value of type bool.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Complexity: At worst linear in the sum of the alphabet sizes and numbers of rules.

◆ Presentation() [1/2]

template<typename Word>

Presentation ( Presentation< Word > && ) -> Presentation< Word >

Defined in presentation.hpp

Deduction guide to construct a Presentation<Word> from a Presentation<Word>&&.

◆ Presentation() [2/2]

template<typename Word>

Presentation ( Presentation< Word > const & ) -> Presentation< Word >

Defined in presentation.hpp

Deduction guide to construct a Presentation<Word> from a Presentation<Word> const&.

◆ to_human_readable_repr() [1/2]

template<typename Word>

std::string to_human_readable_repr ( InversePresentation< Word > const & p )

Return a human readable representation of an InversePresentation.

Template Parameters

Word	the type of the words in the InversePresentation.

Parameters

p	the InversePresentation.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

◆ to_human_readable_repr() [2/2]

template<typename Word>

std::string to_human_readable_repr ( Presentation< Word > const & p )

Return a human readable representation of a presentation.

Template Parameters

Word	the type of the words in the presentation.

Parameters

p	the presentation.

Exceptions: This function guarantees not to throw a LibsemigroupsException.

Variable Documentation

◆ IsInversePresentation

template<typename T>

bool IsInversePresentation = detail::IsInversePresentationHelper<T>::value

staticconstexpr

Helper variable template.

The value of this variable is true if the template parameter T is InversePresentation.

Template Parameters

T a type.

◆ IsPresentation

template<typename T>

bool IsPresentation = detail::IsPresentationHelper<T>::value

staticconstexpr

Helper variable template.

The value of this variable is true if the template parameter T is InversePresentation.

Template Parameters

T a type.

Namespaces

Classes

Functions

Variables

Function Documentation

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ Presentation() [1/2]

◆ Presentation() [2/2]

◆ to_human_readable_repr() [1/2]

◆ to_human_readable_repr() [2/2]

Variable Documentation

◆ IsInversePresentation

◆ IsPresentation