Source code for sympy.polys.domains.gmpyrationalfield

"""Implementation of :class:`GMPYRationalField` class. """


from sympy.polys.domains.groundtypes import (
    GMPYRational, SymPyRational,
    gmpy_numer, gmpy_denom, factorial as gmpy_factorial,
)
from sympy.polys.domains.rationalfield import RationalField
from sympy.polys.polyerrors import CoercionFailed
from sympy.utilities import public



@public
class GMPYRationalField(RationalField):
    """Rational field based on GMPY's ``mpq`` type.

    This will be the implementation of :ref:`QQ` if ``gmpy`` or ``gmpy2`` is
    installed. Elements will be of type ``gmpy.mpq``.
    """

    dtype = GMPYRational
    zero = dtype(0)
    one = dtype(1)
    tp = type(one)
    alias = 'QQ_gmpy'

    def __init__(self):
        pass



    def get_ring(self):
        """Returns ring associated with ``self``. """
        from sympy.polys.domains import GMPYIntegerRing
        return GMPYIntegerRing()




    def to_sympy(self, a):
        """Convert ``a`` to a SymPy object. """
        return SymPyRational(int(gmpy_numer(a)),
                             int(gmpy_denom(a)))




    def from_sympy(self, a):
        """Convert SymPy's Integer to ``dtype``. """
        if a.is_Rational:
            return GMPYRational(a.p, a.q)
        elif a.is_Float:
            from sympy.polys.domains import RR
            return GMPYRational(*map(int, RR.to_rational(a)))
        else:
            raise CoercionFailed("expected ``Rational`` object, got %s" % a)




    def from_ZZ_python(K1, a, K0):
        """Convert a Python ``int`` object to ``dtype``. """
        return GMPYRational(a)




    def from_QQ_python(K1, a, K0):
        """Convert a Python ``Fraction`` object to ``dtype``. """
        return GMPYRational(a.numerator, a.denominator)




    def from_ZZ_gmpy(K1, a, K0):
        """Convert a GMPY ``mpz`` object to ``dtype``. """
        return GMPYRational(a)




    def from_QQ_gmpy(K1, a, K0):
        """Convert a GMPY ``mpq`` object to ``dtype``. """
        return a




    def from_GaussianRationalField(K1, a, K0):
        """Convert a ``GaussianElement`` object to ``dtype``. """
        if a.y == 0:
            return GMPYRational(a.x)




    def from_RealField(K1, a, K0):
        """Convert a mpmath ``mpf`` object to ``dtype``. """
        return GMPYRational(*map(int, K0.to_rational(a)))




    def exquo(self, a, b):
        """Exact quotient of ``a`` and ``b``, implies ``__truediv__``.  """
        return GMPYRational(a) / GMPYRational(b)




    def quo(self, a, b):
        """Quotient of ``a`` and ``b``, implies ``__truediv__``. """
        return GMPYRational(a) / GMPYRational(b)




    def rem(self, a, b):
        """Remainder of ``a`` and ``b``, implies nothing.  """
        return self.zero




    def div(self, a, b):
        """Division of ``a`` and ``b``, implies ``__truediv__``. """
        return GMPYRational(a) / GMPYRational(b), self.zero




    def numer(self, a):
        """Returns numerator of ``a``. """
        return a.numerator




    def denom(self, a):
        """Returns denominator of ``a``. """
        return a.denominator




    def factorial(self, a):
        """Returns factorial of ``a``. """
        return GMPYRational(gmpy_factorial(int(a)))