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Matthias Koeppe
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sagelib |
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# Ring base classes | ||
from .ring import Ring | ||
from .ring import (Ring, Field, CommutativeRing, IntegralDomain, | ||
DedekindDomain, PrincipalIdealDomain, EuclideanDomain) | ||
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# Ring element base classes | ||
from sage.structure.element import (CommutativeAlgebraElement, | ||
RingElement, CommutativeRingElement, IntegralDomainElement, | ||
DedekindDomainElement, PrincipalIdealDomainElement, | ||
EuclideanDomainElement, FieldElement) | ||
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# Rational numbers | ||
from .rational import Rational | ||
from .rational_field import RationalField, QQ | ||
Rationals = RationalField | ||
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# Rational integers. | ||
from .integer_ring import IntegerRing, ZZ, crt_basis | ||
from .integer import Integer | ||
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# Integers modulo n. | ||
from sage.rings.finite_rings.integer_mod_ring import IntegerModRing, Zmod | ||
from sage.rings.finite_rings.integer_mod import IntegerMod, Mod, mod | ||
Integers = IntegerModRing | ||
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# Infinities | ||
from .infinity import infinity, Infinity, InfinityRing, unsigned_infinity, UnsignedInfinityRing | ||
oo = infinity | ||
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# Quotient | ||
from .quotient_ring import QuotientRing | ||
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# Localization | ||
from .localization import Localization | ||
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# Fraction field | ||
from .fraction_field import FractionField | ||
Frac = FractionField | ||
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# Function field | ||
from .function_field.all__sagemath_categories import * | ||
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# Double precision floating point numbers | ||
from .real_double import RealDoubleField, RDF, RealDoubleElement | ||
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# Ideals | ||
from .ideal import Ideal | ||
ideal = Ideal | ||
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# Semirings | ||
from .semirings.all import * | ||
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from .finite_rings.all__sagemath_categories import * | ||
from .number_field.all__sagemath_categories import * | ||
from .padics.all__sagemath_categories import * | ||
from .polynomial.all__sagemath_categories import * | ||
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# Power series rings | ||
from .power_series_ring import PowerSeriesRing | ||
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# Laurent series ring in one variable | ||
from .laurent_series_ring import LaurentSeriesRing | ||
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# Puiseux series ring | ||
from .puiseux_series_ring import PuiseuxSeriesRing | ||
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# Big-oh notation | ||
from .big_oh import O | ||
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# continued fractions | ||
from sage.rings.continued_fraction import (continued_fraction, | ||
continued_fraction_list) | ||
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# Lazy reals | ||
from .real_lazy import RealLazyField, RLF, ComplexLazyField, CLF | ||
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# Preliminary version of real numbers for doctesting without sage.rings.real_mpfr. | ||
# sage.rings.all redefines it. | ||
RealNumber = RR = RDF # used by the preparser to wrap real literals |
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# Quotient of polynomial ring | ||
from sage.rings.polynomial.polynomial_quotient_ring import PolynomialQuotientRing | ||
from sage.rings.polynomial.polynomial_quotient_ring_element import PolynomialQuotientRingElement | ||
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# Univariate Polynomial Rings | ||
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing | ||
from sage.rings.polynomial.polynomial_ring import polygen, polygens | ||
from sage.rings.polynomial.polynomial_element import Polynomial | ||
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# Multivariate Polynomial Rings | ||
from sage.rings.polynomial.term_order import TermOrder | ||
from sage.rings.polynomial.multi_polynomial_element import degree_lowest_rational_function | ||
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# Infinite Polynomial Rings | ||
from sage.rings.polynomial.infinite_polynomial_ring import InfinitePolynomialRing | ||
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# Laurent Polynomial Rings | ||
from sage.rings.polynomial.laurent_polynomial_ring import LaurentPolynomialRing | ||
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# Evaluation of cyclotomic polynomials | ||
from sage.rings.polynomial.cyclotomic import cyclotomic_value |