Source code for diofant.domains.realfield

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

from ..core import Float
from ..polys.polyerrors import CoercionFailed
from .characteristiczero import CharacteristicZero
from .field import Field
from .mpelements import MPContext
from .simpledomain import SimpleDomain


__all__ = 'RealField',


_reals_cache = {}


[docs]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 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 __new__(cls, prec=_default_precision, dps=None, tol=None): context = MPContext(prec, dps, tol) obj = super().__new__(cls) try: obj.dtype = _reals_cache[(context.prec, context.tolerance)] except KeyError: _reals_cache[(context.prec, context.tolerance)] = obj.dtype = context.mpf context._parent = obj obj._context = context obj._hash = hash((cls.__name__, obj.dtype, context.prec, context.tolerance)) obj.zero = obj.dtype(0) obj.one = obj.dtype(1) return obj def __eq__(self, other): return (isinstance(other, RealField) and self.precision == other.precision and self.tolerance == other.tolerance) def __hash__(self): return self._hash
[docs] def to_expr(self, element): """Convert ``element`` to Diofant number. """ return Float(element, self.dps)
[docs] def from_expr(self, expr): """Convert Diofant's number to ``dtype``. """ number = expr.evalf(self.dps) if number.is_Number: return self.dtype(number) else: raise CoercionFailed("expected real number, got %s" % expr)
def _from_PythonIntegerRing(self, element, base): return self.dtype(element) def _from_PythonRationalField(self, element, base): return self.dtype(element.numerator) / element.denominator def _from_GMPYIntegerRing(self, element, base): return self.dtype(int(element)) def _from_GMPYRationalField(self, element, base): return self.dtype(int(element.numerator)) / int(element.denominator) def _from_AlgebraicField(self, element, base): return self.from_expr(base.to_expr(element)) 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_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 self.one
[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)
RR = RealField()