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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