source: sage/rings/all.py @ 4:99a35c84caf0

"""
Rings
"""

#*****************************************************************************
#       Copyright (C) 2005 William Stein <wstein@ucsd.edu>
#
#  Distributed under the terms of the GNU General Public License (GPL)
#
#    This code is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
#    General Public License for more details.
#
#  The full text of the GPL is available at:
#
#                  http://www.gnu.org/licenses/
#*****************************************************************************

# Ring base classes
from ring import Ring, is_Ring
from commutative_ring import CommutativeRing, is_CommutativeRing
from integral_domain import IntegralDomain, is_IntegralDomain
from dedekind_domain import DedekindDomain, is_DedekindDomain
from principal_ideal_domain import PrincipalIdealDomain, is_PrincipalIdealDomain
from euclidean_domain import EuclideanDomain, is_EuclideanDomain
from field import Field, is_Field, is_PrimeField

# Ring element base classes
from ring_element import RingElement, is_RingElement
from commutative_ring_element import CommutativeRingElement, is_CommutativeRingElement
from integral_domain_element import IntegralDomainElement, is_IntegralDomainElement
from dedekind_domain_element import DedekindDomainElement, is_DedekindDomainElement
from principal_ideal_domain_element import PrincipalIdealDomainElement, is_PrincipalIdealDomainElement
from euclidean_domain_element import EuclideanDomainElement, is_EuclideanDomainElement
from field_element import FieldElement, is_FieldElement


# Ideals
from ideal import Ideal, is_Ideal

# Quotient
from quotient_ring import QuotientRing

# Class Infinity containing the one element infinity
from infinity import infinity, is_Infinity

# Rational integers.
from integer_ring import IntegerRing, ZZ, Z, crt_basis
from integer import Integer

# Rational numbers
from rational_field import RationalField, QQ, Q, is_RationalField
from rational import Rational
Rationals = RationalField

# Integers modulo n.
from integer_mod_ring import IntegerModRing, Zmod, is_IntegerModRing
from integer_mod import IntegerMod, Mod, mod
Integers = IntegerModRing

# Finite fields
from finite_field import (FiniteField, is_FiniteField, GF, 
                          conway_polynomial, exists_conway_polynomial)
from finite_field_element import FiniteFieldElement

# Number field
from number_field.all import *

# Quotient of polynomial ring
from polynomial_quotient_ring import PolynomialQuotientRing, is_PolynomialQuotientRing
from polynomial_quotient_ring_element import PolynomialQuotientRingElement

# p-adic field
from padic_field import pAdicField, Qp, is_pAdicField
from padic import pAdic

# Real numbers
from real_field import RealField, is_RealField, is_RealNumber
Reals = RealField

# Complex numbers
from complex_field import ComplexField, is_ComplexField
from complex_number import ComplexNumber, is_ComplexNumber
Complexes = ComplexField

# Univariate Polynomial Rings
from polynomial_ring import PolynomialRing, polygen, is_PolynomialRing
from polynomial_element import Polynomial, is_Polynomial

# Multivariate Polynomial Rings
from multi_polynomial_ring import MPolynomialRing, is_MPolynomialRing, TermOrder
from multi_polynomial_element import MPolynomial, degree_lowest_rational_function, is_MPolynomialRingElement

# Power series ring in one variable
from power_series_ring import PowerSeriesRing, is_PowerSeriesRing
from power_series_ring_element import PowerSeries

# Laurent series ring in one variable
from laurent_series_ring import LaurentSeriesRing, is_LaurentSeriesRing
from laurent_series_ring_element import LaurentSeries

# Float interval arithmetic
from interval import IntervalRing, Interval

# Pseudo-ring of PARI objects.
from pari_ring import PariRing, Pari

# Big-oh notation
from big_oh import O

# Fraction field
from fraction_field import FractionField, is_FractionField
Frac = FractionField
from fraction_field_element import is_FractionFieldElement

# Arithmetic
from arith import *                   

from morphism import is_RingHomomorphism

from homset import is_RingHomset