FroidurePin¶

class FroidurePin¶

This page contains the documentation for functionality in libsemigroups_pybind11 for the Froidure-Pin algorithm. The class FroidurePin implements the Froidure-Pin algorithm as described in the article "Algorithms for computing finite semigroups" by Veronique Froidure and Jean-Eric Pin.

A FroidurePin instance is defined by a generating set, and the main method is run(), which implements the Froidure-Pin Algorithm. If run() is invoked and finished() returns True, then the size, the left and right Cayley graphs are determined, and a confluent terminating presentation for the semigroup is known.

While FroidurePin is not a class the objects returned by FroidurePin have identical methods, and so we document FroidurePin as if it was a class.

Constructors¶

FroidurePin.__init__()

Overloaded function.

Generators¶

`FroidurePin.add_generator()`	Add a copy of an element to the generators.
`FroidurePin.add_generators()`	Add collection of generators.
`FroidurePin.closure()`	Add non-redundant generators in collection.
`FroidurePin.copy_closure()`	Copy and add non-redundant generators.
`FroidurePin.copy_add_generators()`	Copy and add a collection of generators.
`FroidurePin.number_of_generators()`	Returns the number of generators.
`FroidurePin.generator()`	Returns the generator with specified index.

Settings¶

`FroidurePin.batch_size()`	Overloaded function.
`FroidurePin.concurrency_threshold()`	Overloaded function.
`FroidurePin.immutable()`	Overloaded function.
`FroidurePin.max_threads()`	Overloaded function.
`FroidurePin.reserve()`	Requests the given capacity for elements.

Membership + comparison¶

`FroidurePin.contains()`	Test membership of an element.
`FroidurePin.current_position()`	Overloaded function.
`FroidurePin.position_to_sorted_position()`	Returns the sorted index of an element via its index.
`FroidurePin.position()`	Find the position of an element with enumeration if necessary.
`FroidurePin.sorted_position()`	Returns the sorted index of an element.
`FroidurePin.equal_to()`	Check equality of words in the generators.

Accessors¶

`FroidurePin.__iter__()`	Returns an iterator pointing to the first element.
`FroidurePin.at()`	Access element specified by index with bound checks.
`FroidurePin.current_size()`	Returns the number of elements so far enumerated.
`FroidurePin.size()`	Returns the size.
`FroidurePin.sorted_at()`	Access element specified by sorted index with bound checks.
`FroidurePin.sorted()`	Returns an iterator pointing to the first element (sorted).

Attributes¶

`FroidurePin.is_monoid()`	Check if the semigroup is a monoid.
`FroidurePin.is_finite()`	Check finiteness.
`FroidurePin.degree()`	Returns the degree of any and all elements.

Idempotents¶

`FroidurePin.is_idempotent()`	Check if an element is an idempotent via its index.
`FroidurePin.idempotents()`	Returns an iterator pointing at the first idempotent.
`FroidurePin.number_of_idempotents()`	Returns the number of idempotents.

Cayley graphs¶

`FroidurePin.left_cayley_graph()`	Returns the left Cayley graph
`FroidurePin.right_cayley_graph()`	Returns the right Cayley graph

Factorisation, products, and relations¶

`FroidurePin.current_length()`	Returns the length of the short-lex least word.
`FroidurePin.current_max_word_length()`	Returns the maximum length of a word in the generators so far computed.
`FroidurePin.current_number_of_rules()`	Returns the number of relations that have been found so far.
`FroidurePin.factorisation()`	Overloaded function.
`FroidurePin.length()`	Returns the length of the short-lex least word.
`FroidurePin.minimal_factorisation()`	Returns a short-lex least word representing an element given by index.
`FroidurePin.number_of_rules()`	Returns the total number of relations in the presentation.
`FroidurePin.product_by_reduction()`	Compute a product using the Cayley graph.
`FroidurePin.fast_product()`	Multiply elements via their indices.
`FroidurePin.rules()`	Returns an iterator pointing to the first rule (if any).
`FroidurePin.word_to_element()`	Convert a word in the generators to an element.

Prefixes and suffixes¶

`FroidurePin.final_letter()`	Returns the last letter of the element with specified index.
`FroidurePin.first_letter()`	Returns the first letter of the element with specified index.
`FroidurePin.prefix()`	Returns the index of the longest proper prefix.
`FroidurePin.suffix()`	Returns the position of the longest proper suffix.

Running and reporting¶

`FroidurePin.enumerate()`	Enumerate until at least a specified number of elements are found.
`FroidurePin.run()`	Run the algorithm until it finishes.
`FroidurePin.run_for()`	Run for a specified amount of time.
`FroidurePin.run_until()`	Run until a nullary predicate returns `True` or `finished()`.
`FroidurePin.kill()`	Stop running the algorithm (thread-safe).
`FroidurePin.dead()`	Check if the runner is dead.
`FroidurePin.finished()`	Check if the main algorithm has been run to completion or not.
`FroidurePin.started()`	Check if `run()` has been called at least once before.
`FroidurePin.report()`	Check if it is time to report.
`FroidurePin.report_every()`	Set the minimum elapsed time between reports.
`FroidurePin.report_why_we_stopped()`	Report why we stopped.
`FroidurePin.running()`	Check if currently running.
`FroidurePin.timed_out()`	Check if the main algorithm has or should timed out.
`FroidurePin.stopped()`	Check if the main algorithm has or should stop.
`FroidurePin.stopped_by_predicate()`	Check if the main algorithm was, or should be, stopped by the nullary predicate passed as first argument to `run_until()`.