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r""" A subset of sage.categories.all with just the basic categories needed for sage startup (i.e. to define ZZ, QQ, ...). """ from __future__ import absolute_import #***************************************************************************** # Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from .objects import Objects from .sets_cat import Sets, EmptySetError from .posets import Posets # For backward compatibility; will be deprecated at some point PartiallyOrderedSets = Posets OrderedSets = Posets
from .additive_magmas import AdditiveMagmas from .commutative_additive_semigroups import CommutativeAdditiveSemigroups from .commutative_additive_monoids import CommutativeAdditiveMonoids from .commutative_additive_groups import CommutativeAdditiveGroups
from .magmas import Magmas from .semigroups import Semigroups from .monoids import Monoids from .groups import Groups from .partially_ordered_monoids import PartiallyOrderedMonoids # For backward compatibility; might be deprecated at some point OrderedMonoids = PartiallyOrderedMonoids
from .rngs import Rngs from .semirings import Semirings from .rings import Rings from .domains import Domains from .division_rings import DivisionRings
from .commutative_rings import CommutativeRings from .integral_domains import IntegralDomains from .gcd_domains import GcdDomains from .principal_ideal_domains import PrincipalIdealDomains from .euclidean_domains import EuclideanDomains from .unique_factorization_domains import UniqueFactorizationDomains from .complete_discrete_valuation import CompleteDiscreteValuationRings
from .fields import Fields from .quotient_fields import QuotientFields from .finite_fields import FiniteFields from .discrete_valuation import DiscreteValuationRings, DiscreteValuationFields from .complete_discrete_valuation import CompleteDiscreteValuationRings, CompleteDiscreteValuationFields |