Source code for

"""Implementation of :class:`RealField` class. """

from __future__ import print_function, division

from import Field
from import SimpleDomain
from import CharacteristicZero
from import MPContext

from sympy.polys.polyerrors import DomainError, CoercionFailed
from sympy.core.numbers import Float
from sympy.utilities import public

[docs]@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) context._parent = self self._context = context self.dtype = context.mpf = self.dtype(0) = 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))
[docs] def to_sympy(self, element): """Convert ``element`` to SymPy number. """ return Float(element, self.dps)
[docs] 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_python(self, element, base): return self.dtype(element) 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_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)
[docs] def to_rational(self, element, limit=True): """Convert a real number to rational number. """ return self._context.to_rational(element, limit)
[docs] def get_ring(self): """Returns a ring associated with ``self``. """ return self
[docs] def get_exact(self): """Returns an exact domain associated with ``self``. """ from import QQ return QQ
[docs] def gcd(self, a, b): """Returns GCD of ``a`` and ``b``. """ return
[docs] def lcm(self, a, b): """Returns LCM of ``a`` and ``b``. """ return a*b
[docs] def almosteq(self, a, b, tolerance=None): """Check if ``a`` and ``b`` are almost equal. """ return self._context.almosteq(a, b, tolerance)