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- """Implementation of :class:`RealField` class. """
- from sympy.core.numbers import Float
- from sympy.polys.domains.field import Field
- from sympy.polys.domains.simpledomain import SimpleDomain
- from sympy.polys.domains.characteristiczero import CharacteristicZero
- from sympy.polys.domains.mpelements import MPContext
- from sympy.polys.polyerrors import CoercionFailed
- from sympy.utilities import public
- @public
- class RealField(Field, CharacteristicZero, SimpleDomain):
- """Real numbers up to the given precision. """
- rep = 'RR'
- is_RealField = is_RR = True
- is_Exact = False
- is_Numerical = True
- is_PID = False
- has_assoc_Ring = False
- has_assoc_Field = True
- _default_precision = 53
- @property
- def has_default_precision(self):
- return self.precision == self._default_precision
- @property
- def precision(self):
- return self._context.prec
- @property
- def dps(self):
- return self._context.dps
- @property
- def tolerance(self):
- return self._context.tolerance
- def __init__(self, prec=_default_precision, dps=None, tol=None):
- context = MPContext(prec, dps, tol, True)
- context._parent = self
- self._context = context
- self.dtype = context.mpf
- self.zero = self.dtype(0)
- self.one = self.dtype(1)
- def __eq__(self, other):
- return (isinstance(other, RealField)
- and self.precision == other.precision
- and self.tolerance == other.tolerance)
- def __hash__(self):
- return hash((self.__class__.__name__, self.dtype, self.precision, self.tolerance))
- def to_sympy(self, element):
- """Convert ``element`` to SymPy number. """
- return Float(element, self.dps)
- def from_sympy(self, expr):
- """Convert SymPy's number to ``dtype``. """
- number = expr.evalf(n=self.dps)
- if number.is_Number:
- return self.dtype(number)
- else:
- raise CoercionFailed("expected real number, got %s" % expr)
- def from_ZZ(self, element, base):
- return self.dtype(element)
- def from_ZZ_python(self, element, base):
- return self.dtype(element)
- def from_QQ(self, element, base):
- return self.dtype(element.numerator) / element.denominator
- def from_QQ_python(self, element, base):
- return self.dtype(element.numerator) / element.denominator
- def from_ZZ_gmpy(self, element, base):
- return self.dtype(int(element))
- def from_QQ_gmpy(self, element, base):
- return self.dtype(int(element.numerator)) / int(element.denominator)
- def from_AlgebraicField(self, element, base):
- return self.from_sympy(base.to_sympy(element).evalf(self.dps))
- def from_RealField(self, element, base):
- if self == base:
- return element
- else:
- return self.dtype(element)
- def from_ComplexField(self, element, base):
- if not element.imag:
- return self.dtype(element.real)
- def to_rational(self, element, limit=True):
- """Convert a real number to rational number. """
- return self._context.to_rational(element, limit)
- def get_ring(self):
- """Returns a ring associated with ``self``. """
- return self
- def get_exact(self):
- """Returns an exact domain associated with ``self``. """
- from sympy.polys.domains import QQ
- return QQ
- def gcd(self, a, b):
- """Returns GCD of ``a`` and ``b``. """
- return self.one
- def lcm(self, a, b):
- """Returns LCM of ``a`` and ``b``. """
- return a*b
- def almosteq(self, a, b, tolerance=None):
- """Check if ``a`` and ``b`` are almost equal. """
- return self._context.almosteq(a, b, tolerance)
- RR = RealField()
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