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