def group_generators(self):
"""
Return the group generators of ``self``.
EXAMPLES::
sage: G = Groups.free(index_set=ZZ)
sage: G.group_generators()
Lazy family (Generator map from Integer Ring to
Free group indexed by Integer Ring(i))_{i in Integer Ring}
sage: G = Groups().free(index_set='abcde')
sage: sorted(G.group_generators())
[F['a'], F['b'], F['c'], F['d'], F['e']]
"""
if self._indices.cardinality() == infinity:
gen = PoorManMap(self.gen, domain=self._indices, codomain=self, name="Generator map")
return Family(self._indices, gen)
return Family(self._indices, self.gen)
def monoid_generators(self):
"""
Return the monoid generators of ``self``.
EXAMPLES::
sage: F = FreeAbelianMonoid(index_set=ZZ)
sage: F.monoid_generators()
Lazy family (Generator map from Integer Ring to
Free abelian monoid indexed by Integer Ring(i))_{i in Integer Ring}
sage: F = FreeAbelianMonoid(index_set=tuple('abcde'))
sage: sorted(F.monoid_generators())
[F['a'], F['b'], F['c'], F['d'], F['e']]
"""
if self._indices.cardinality() == infinity:
gen = PoorManMap(self.gen, domain=self._indices, codomain=self, name="Generator map")
return Family(self._indices, gen)
return Family(self._indices, self.gen)