def __init__(self, alphabet, rels):
# Check the alphabet
if not isinstance(alphabet, str):
raise TypeError('the first argument (alphabet) must be a string')
elif not all(alphabet.count(i) == 1 for i in alphabet):
raise ValueError('the first argument (alphabet) must be a '
'duplicate-free string')
# Corner case
if len(alphabet) == 0 and not len(rels) == 0:
raise ValueError('the empty semigroup must not have' +
' any relations')
# Check the relations
if not (isinstance(rels, list)
and all(isinstance(rel, list) for rel in rels)):
raise TypeError('the second argument (relations) must be a ' +
'list of lists')
elif not all(
len(rel) == 2 and isinstance(rel[0], str)
and isinstance(rel[1], str) for rel in rels):
raise TypeError('the second argument (relations) must be a ' +
'list of pairs of strings')
self._pure_letter_alphabet = True
for i in alphabet:
if not i in ('abcdefghijklmnopqrstuvwxyz1' +
'ABCDEFGHIJKLMNOPQRSTUVWXYZ'):
self._pure_letter_alphabet = False
break
for i, rel in enumerate(rels):
for j, word in enumerate(rel):
rels[i][j] = self._parse_word(word)
self.alphabet = alphabet
self.relations = rels
for rel in rels:
for word in rel:
self.check_word(word)
libsemigroups.FpSemigroupNC.__init__(self, len(alphabet), rels)
if not self.is_obviously_infinite():
Semigroup.__init__(self,
*[_FPSOME(self, i) for i in self.alphabet])
def factorisation(self, word):
'''
Factorises a given word into a list of generators each represented by
an integer starting at 0.
Args:
word (str): word to be factorised.
Returns:
list: factorisation into generators.
Examples:
>>> S = FpSemigroup('ab',[['a', 'aa'], ['b', 'bbb'], ['ab', 'ba']])
>>> S.factorisation('b')
[1]
>>> S.factorisation('aaabb')
[0, 1, 1]
'''
if self.is_obviously_infinite():
raise ValueError('given semigroup is infinite')
word = self._parse_word(word)
self.check_word(word)
Pyword = libsemigroups.PythonElementNC(_FPSOME(self, word))
return Semigroup.factorisation(self, Pyword)
def nridempotents(self):
if not self.is_finite():
raise ValueError('given semigroup is infinite')
return Semigroup.nridempotents(self)
def enumerate(self, limit):
if not self.is_finite():
raise ValueError('given semigroup is infinite')
return Semigroup.enumerate(self, limit)