The Presentation class

Presentations for semigroups and monoids.

This class can be used to construction presentations for semigroups or monoids and is intended to be used as the input to other algorithms in libsemigroups_pybind11. The idea is to provide a shallow wrapper around a collection of words of type Word. We refer to this list of words as the rules of the presentation. The Presentation class also provides some checks that the rules really define a presentation, (i.e. it’s consistent with its alphabet), and some related functionality is available in the module libsemigroups_pybind11.presentation.

Types

In what follows, we use the following pseudo-types:

Letter for str | int

Word for str | list[int]

Recall that, once a presentation has been constructed, the type of its letters and words are fixed.

Contents

`Presentation`	Presentations for semigroups and monoids.
`Presentation.add_generator`(…)	Overloaded function.
`Presentation.alphabet`(…)	Overloaded function.
`Presentation.alphabet_from_rules`(…)	Set the alphabet to be the letters in the rules.
`Presentation.contains_empty_word`(…)	Overloaded function.
`Presentation.copy`(…)	Copy a `Presentation` object.
`Presentation.in_alphabet`(…)	Check if a letter belongs to the alphabet or not.
`Presentation.index`(…)	Return the index of a letter in the alphabet.
`Presentation.init`(…)	Remove the alphabet and all rules.
`Presentation.letter`(…)	Get a letter in the alphabet by index.
`Presentation.remove_generator`(…)	Remove the letter x as a generator.
`Presentation.rules`	Data member holding the rules of the presentation.
`Presentation.throw_if_alphabet_has_duplicates`(…)	Check if the alphabet is valid.
`Presentation.throw_if_bad_alphabet_or_rules`(…)	Check if the alphabet and rules are valid.
`Presentation.throw_if_bad_rules`(…)	Check if every rule consists of letters belonging to the alphabet.
`Presentation.throw_if_letter_not_in_alphabet`(…)	Overloaded function.

Full API

class Presentation

__init__(*args, **kwargs)

Overloaded function.

__init__(self: Presentation, word: type) → None

Default constructor.

This function default constructs an uninitialised Presentation instance.

Keyword Arguments:

word (type) – the type of words to use. Must be either str or list[int].

__init__(self: Presentation, alphabet: str | list[int]) → None

Construct a presentation from an alphabet.

This function constructs a Presentation instance with the alphabet specified by alphabet.

Parameters:: alphabet (str | list[int]) – the alphabet of the presentation.
Raises:: LibsemigroupsError – if there are duplicate letters in alphabet.

add_generator(*args, **kwargs)

Overloaded function.

add_generator(self: Presentation) → Letter

Add a generator.

Add the first letter not in the alphabet as a generator, and return this letter.

Returns:: the letter added to the alphabet.
Return type:: Letter

add_generator(self: Presentation, x: Letter) → Presentation

Add the letter x as a generator.

Parameters:: x (Letter) – the letter to add as a generator.
Returns:: self.
Return type:: Presentation
Raises:: LibsemigroupsError – if x is in alphabet().

alphabet(*args, **kwargs)

Overloaded function.

alphabet(self: Presentation) → Word

Return the alphabet of the presentation.

Returns:: The alphabet of the presentation.
Return type:: Word
Complexity:: Constant.

alphabet(self: Presentation, n: int) → Presentation

Set the alphabet by size.

Sets the alphabet to the the first \(n\) values with type Letter. For str-types, we assume the order of letters to be a-zA-Z0-9.

Parameters:: n (int) – the size of the alphabet.
Returns:: self
Return type:: Presentation
Raises:: LibsemigroupsError – if the value of n is greater than the maximum number of letters supported by Letter.