Factorisation, products, and relations¶
This page contains information about the functionality of the
FroidurePin class related to factorisation, products, and
relations.
- FroidurePin.current_length(self: FroidurePin, pos: int) int¶
Returns the length of the short-lex least word equal to the element in position
pos(if any). No enumeration is performed.- Parameters
pos (int) -- the position
- Returns
An
int.
- FroidurePin.current_max_word_length(self: FroidurePin) int¶
Returns the maximum length of a word in the generators so far computed.
- Parameters
None
- Returns
An
int.
- FroidurePin.current_number_of_rules(self: FroidurePin) int¶
Returns the number of relations that have been found so far.
- Parameters
None
- Returns
An
int.
- FroidurePin.factorisation(self: FroidurePin, pos: int) List[int]¶
Returns a word representing an element given by index.
- Parameters
pos (int) - the index of the element whose factorisation is sought
- Returns
A
List[int].
- FroidurePin.factorisation(self: FroidurePin, x: Element) List[int]
Factorise an element as a word in the generators.
- Parameters
x (Element) - the possible element to factorise.
- Returns
A
List[int].
- FroidurePin.length(self: FroidurePin, pos: int) int¶
Returns the length of the short-lex least word equal to the element in position
pos(if any). Enumeration is triggered.- Parameters
pos (int) -- the position
- Returns
An
int.
- FroidurePin.minimal_factorisation(self: FroidurePin, pos: int) List[int]¶
Returns a short-lex least word representing an element given by index.
- Parameters
pos (int) - the index of the element whose factorisation is sought
- Returns
A
List[int].
- FroidurePin.number_of_rules(self: FroidurePin) int¶
Returns the total number of relations in the presentation.
- Parameters
None
- Returns
An
int.
- FroidurePin.product_by_reduction(self: FroidurePin, i: int, j: int) int¶
Compute a product using the Cayley graph.
- FroidurePin.fast_product(self: FroidurePin, i: int, j: int) int¶
Multiply elements via their indices.
- Parameters
i (int) -- the index of the first element to multiply
j (int :return: An
int.) -- the index of the second element to multiply
- FroidurePin.rules(self: FroidurePin) Iterator¶
Returns an iterator pointing to the first rule (if any).
- Parameters
None
- Returns
An iterator.
- FroidurePin.word_to_element(self: FroidurePin, w: List[int]) Element¶
Convert a word in the generators to an element.
- Parameters
w (List[int]) -- the word in the generators to evaluate.
- Returns
A copy of the element represented by the word
w.