to<Presentation>

This file contains documentation for creating semigroup and monoid presentations in libsemigroups from other types of objects.

See also

The `to` function for an overview of possible conversions between libsemigroups types.

Functions
template<typename Result, typename Word>
auto	to (Congrence< Word > &c) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >
	Make a presentation from a Congruence.
template<typename Result>
auto	to (FroidurePinBase &fp) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a FroidurePin object.
template<typename Result, typename Word>
auto	to (Kambtes< Word > &k) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >
	Make a presentation from a Kambites.
template<template< typename... > typename Thing, typename Word, typename Rewriter typename ReductionOrder>
auto	to (KnutBendix< Word, Rewriter, ReductionOrder > &kb) -> std::enable_if_t< std::is_same_v< Thing< Word >, Presentation< Word > >, Presentation< Word > >
	Make a presentation from a KnuthBendix object.
template<typename Result, typename WordIn, typename Rewriter, typename ReductionOrder>
auto	to (KnuthBendix< WordIn, Rewriter, ReductionOrder > &kb) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a KnuthBendix object.
template<typename Result, typename Word>
auto	to (Presentation< Word > const &p) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >
	Make a presentation from a different type of presentation.
template<typename Result, typename Word, typename Func>
auto	to (Presentation< Word > const &p, Func &&f) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a different type of presentation.
template<typename Result, typename PresentationType>
auto	to (Stephen< PresentationType > &s) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >
	Make a presentation from a Stephen object.
template<typename Result, typename Word>
auto	to (ToddCoxter< Word > &tc) -> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >
	Make a presentation from a ToddCoxeter object.

Function Documentation

to() [1/9]

template<typename Result, typename Word>

auto to

(

Congrence< Word > &

c

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >

Defined in to-presentation.hpp

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(c);

There are two versions of this function:

1. When typename Result::word_type and Word are not the same, this function calls to<Presentation<typename Result::word_type> on c.presentation() to return a presentation equivalent to the object used to construct or initialise the Congruence object (if any) but of a different type (for example, can be used to convert from std::string to word_type).
2. If the word representations are the same, the function returns a reference to the presentation used to construct or initialise the Congruence object (if any) via c.presentation().

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
Word	the type of the words in the input Congruence.

Parameters

c	the Congruence object from which to obtain the rules.

Returns

A value of type Presentation<Word>.

to() [2/9]

template<typename Result>

auto to

(

FroidurePinBase &

fp

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(fp);

This function constructs and returns a Presentation object using the rules of a FroidurePin object, accessed via FroidurePin::cbegin_rules and FroidurePin::cend_rules.

No enumeration of the argument fp is performed, so it might be the case that the resulting presentation does not define the same semigroup as fp. To ensure that the resulting presentation defines the same semigroup as fp, run FroidurePin::run (or any other function that fully enumerates fp) prior to calling this function.

Template Parameters

Result

the return type, also used for SFINAE, should be Presentation<Word> for some type Word.

Parameters

fp	the FroidurePin object from which to obtain the rules.

Returns

An object of type Presentation<Word>.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

to() [3/9]

template<typename Result, typename Word>

auto to

(

Kambtes< Word > &

k

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >

Defined in to-presentation.hpp

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(k);

There are two versions of this function:

1. When typename Result::word_type and Word are not the same, this function calls to<Presentation<typename Result::word_type> on k.presentation() to return a presentation equivalent to the object used to construct or initialise the Kambites object (if any) but of a different type (for example, this function can be used to convert from std::string to word_type).
2. If the word representations are the same, the function returns a reference to the presentation used to construct or initialise the Kambites object (if any) via k.presentation().

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
Word	the type of the words in the input Kambites.

Parameters

k	the Kambites object from which to obtain the rules.

Returns

A value of type Presentation<Word>.

to() [4/9]

template<template< typename... > typename Thing, typename Word, typename Rewriter typename ReductionOrder>

auto to

(

KnutBendix< Word, Rewriter, ReductionOrder > &

kb

)

-> std::enable_if_t< std::is_same_v< Thing< Word >, Presentation< Word > >, Presentation< Word > >

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<Presentation>(kb);

This function constructs and returns a Presentation object using the currently active rules of kb.

No enumeration of the argument kb is performed, so it might be the case that the resulting presentation does not define the same semigroup/monoid as kb. To ensure that the resulting presentation defines the same semigroup as kb, run run (or any other function that fully enumerates kb) prior to calling this function.

Template Parameters

Thing	used for SFINAE, must be Presentation.
Word	the type of the rules in the presentation of the KnuthBendix object kb.
Rewriter	the second template parameter for KnuthBendix.
ReductionOrder	the third template parameter for KnuthBendix.

Parameters

kb	the KnuthBendix object from which to obtain the rules.

Returns

An object of type Presentation<Word>.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

to() [5/9]

template<typename Result, typename WordIn, typename Rewriter, typename ReductionOrder>

auto to

(

KnuthBendix< WordIn, Rewriter, ReductionOrder > &

kb

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result >, Result >

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<WordOut>>(kb);

This function constructs and returns a Presentation<WordOut> object using the currently active rules of kb.

No enumeration of the argument kb is performed, so it might be the case that the resulting presentation does not define the same semigroup/monoid as kb. To ensure that the resulting presentation defines the same semigroup as kb, run run (or any other function that fully enumerates kb) prior to calling this function.

Template Parameters

Result	the return type, also used for SFINAE. Must be Presentation<WordOut> for some type WordOut.
WordIn	the type of the rules in the presentation of the KnuthBendix object kb.
Rewriter	the second template parameter for KnuthBendix.
ReductionOrder	the third template parameter for KnuthBendix.

Parameters

kb	the KnuthBendix object from which to obtain the rules.

Returns

An object of type Presentation<WordOut>.

Exceptions

This function guarantees not to throw a LibsemigroupsException.

Note

If the word type of the desired presentation is the same as that kb, then the simpler to<Presentation>(kb) may be used instead.

to() [6/9]

template<typename Result, typename Word>

auto to ( Presentation< Word > const & p ) -> std::enable_if_t< std::is_same_v<Presentation<typename Result::word_type>, Result> && !std::is_same_v<typename Result::word_type, Word>, Result>

noexcept

Make an inverse presentation from a presentation.

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(p, func);

There are 2 versions of this function:

1. When typename Result::word_type and Word are not the same, this function returns a presentation equivalent to the input presentation but of a different type (for example, can be used to convert from std::string to word_type).
2. When typename Result::word_type and Word are the same, this function just returns its argument p (as a reference), and is included solely for the purpose of simplifying certain client code, where presentations must be converted from one type to another sometimes, but not other times.

If the alphabet of of p is \(\{a_0, a_1, \dots a_{n-1}\}\), then the conversion from Presentation<WordInput>::letter_type to Presentation<WordOutput>::letter_type is \(a_i \mapsto\) human_readable_letter<WordOutput>(size_t i).

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
Word	the type of the words in the input presentation.

Parameters

p	the input presentation.

Returns

A value of type Result.

Exceptions

LibsemigroupsException

if typename Result::word_type and Word are not the same and p.throw_if_bad_alphabet_or_rules() throws. If typename Result::word_type and Word are the same, then this function is noexcept.

Note

This function will be moved from the header to-presentation.hpp to presentation.hpp in v4 of libsemigroups.

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<InversePresentation>(p);

This function returns an inverse presentation with rules equivalent to those of the input presentation, but over a normalised alphabet. If the alphabet of p is \(\{a_0, a_1, \dots, a_{n-1}\}\), then the alphabet of the returned inverse presentation will be \(\{0, 1, \dots, n-1, n, \dots, 2n-1\}\), where the inverse of letter \(i\) is the letter \(i + n\, (\text{mod }2n)\).

Template Parameters

Thing	used for SFINAE, must be InversePresentation.
Word	the type of the words in the input presentation.

Parameters

p	the input presentation.

Returns

A value of type InversePresentation<Word>.

Exceptions

LibsemigroupsException

if p.throw_if_bad_alphabet_or_rules() throws.

Note

This function will be moved from the header to-presentation.hpp to presentation.hpp in v4 of libsemigroups.

to() [7/9]

template<typename Result, typename Word, typename Func>

auto to	(	Presentation< Word > const &	p,
		Func &&	f ) -> std::enable_if_t< std::is_same_v<Presentation<typename Result::word_type>, Result>, Result>

Defined in to-presentation.hpp.

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(p, func);

This function returns a presentation equivalent to the input presentation but of a different type (for example, can be used to convert from std::string to word_type). The second parameter specifies how to map the letters of one presentation to the other.

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
Word	the type of the words in the input presentation.
Func	the type of a function for transforming letters.

Parameters

p	the input presentation.
f	a function mapping Presentation<Word>::letter_type to Result::letter_type.

Returns

A value of type Result.

Exceptions

LibsemigroupsException

if p.throw_if_bad_alphabet_or_rules() throws.

Note

Func must be a function type that is invocable with values of Presentation<Word>::letter_type. If this is not true, then template substitution will fail.

This function will be moved from the header to-presentation.hpp to presentation.hpp in v4 of libsemigroups.

to() [8/9]

template<typename Result, typename PresentationType>

auto to

(

Stephen< PresentationType > &

s

)

-> std::enable_if_t< std::is_same_v<Presentation<typename Result::word_type>, Result>, Result>

Defined in to-presentation.hpp

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<std::string>>(s);

This function calls to<Presentation<typename Result::word_type> on s.presentation() to return a presentation equivalent to the object used to construct or initialise the Stephen object (if any) but of a different type (for example, can be used to convert from word_type to std::string).

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
PresentationType	the type of the presentation in the input Stephen.

Parameters

s	the Stephen object from which to obtain the rules.

Returns

A value of type Presentation<typename Result::word_type>.

to() [9/9]

template<typename Result, typename Word>

auto to

(

ToddCoxter< Word > &

tc

)

-> std::enable_if_t< std::is_same_v< Presentation< typename Result::word_type >, Result > &&!std::is_same_v< typename Result::word_type, Word >, Result >

Defined in to-presentation.hpp

Despite the hideous signature, this function should be invoked as follows:

to<Presentation<Word>>(tc);

There are two versions of this function:

1. When typename Result::word_type and Word are not the same, this function calls to<Presentation<typename Result::word_type> on tc.presentation() to return a presentation equivalent to the object used to construct or initialise the ToddCoxeter object (if any) but of a different type (for example, can be used to convert from std::string to word_type).
2. If the word representations are the same, the function returns a reference to the presentation used to construct or initialise the ToddCoxeter object (if any) via tc.presentation().

Template Parameters

Result	the return type, also used for SFINAE, should be Presentation<T> for some type T.
Word	the type of the words in the input ToddCoxeter.

Parameters

tc	the ToddCoxeter object from which to obtain the rules.

Returns

A value of type Presentation<Word>.