def super_categories(self):
"""
EXAMPLES::
sage: PolyhedralSets(QQ).super_categories()
[Category of commutative magmas, Category of additive monoids]
"""
from sage.categories.magmas import Magmas
from sage.categories.additive_monoids import AdditiveMonoids
return [Magmas().Commutative(), AdditiveMonoids()]
def __init__(self, R, M, multiplicative=True):
self.base_monoid = M
if multiplicative:
category = Monoids().Commutative()
else:
category = AdditiveMonoids().AdditiveCommutative()
CombinatorialFreeModule.__init__(self,
R,
M,
category=category.Algebras(R))
def __init__(self):
r"""
TESTS::
sage: sys.path.append(os.getcwd()); from mac_lane import * # optional: standalone
sage: isinstance(pAdicValuation(QQ, 2).codomain(), DiscreteValuationCodomain)
True
"""
from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
from sage.categories.additive_monoids import AdditiveMonoids
UniqueRepresentation.__init__(self)
Parent.__init__(self,
facade=(QQ, FiniteEnumeratedSet([infinity,
-infinity])),
category=AdditiveMonoids())
def __init__(self):
r"""
TESTS::
sage: from sage.rings.valuation.value_group import DiscreteValuationCodomain
sage: isinstance(QQ.valuation(2).codomain(), DiscreteValuationCodomain)
True
"""
from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
from sage.categories.additive_monoids import AdditiveMonoids
UniqueRepresentation.__init__(self)
Parent.__init__(self,
facade=(QQ, FiniteEnumeratedSet([infinity,
-infinity])),
category=AdditiveMonoids())