def super_categories(self):
"""
EXAMPLES::
sage: Rings().super_categories()
[Category of rngs, Category of semirings]
"""
return [Rngs(), Semirings()]
def super_categories(self):
"""
EXAMPLES::
sage: Rings().super_categories()
[Category of rngs, Category of semirings]
"""
from sage.categories.rngs import Rngs
from sage.categories.semirings import Semirings
return [Rngs(), Semirings()]
def __init__(self):
r"""
TESTS::
sage: NN = NonNegativeIntegerSemiring(); NN
Non negative integer semiring
sage: NN.category()
Join of Category of semirings and Category of commutative monoids and Category of infinite enumerated sets and Category of facade sets
sage: TestSuite(NN).run()
"""
NonNegativeIntegers.__init__(self, category=(Semirings().Commutative(), InfiniteEnumeratedSets()) )
def __init__(self):
"""
Parent class for all Newton polygons.
sage: from sage.geometry.newton_polygon import ParentNewtonPolygon
sage: ParentNewtonPolygon()
Parent for Newton polygons
TESTS:
This class is a singleton.
sage: ParentNewtonPolygon() is ParentNewtonPolygon()
True
::
sage: TestSuite(ParentNewtonPolygon()).run()
"""
from sage.categories.semirings import Semirings
from sage.rings.rational_field import QQ
Parent.__init__(self, category=Semirings(), base=QQ)