"""Rational number type based on Python integers. """

from sympy.core.numbers import igcd
from sympy.printing.defaults import DefaultPrinting
from sympy.polys.polyutils import PicklableWithSlots
from sympy.polys.domains.domainelement import DomainElement

import operator

class PythonRational(DefaultPrinting, PicklableWithSlots, DomainElement):
    """
    Rational number type based on Python integers.

    This was supposed to be needed for compatibility with older Python
    versions which don't support Fraction. However, Fraction is very
    slow so we don't use it anyway.

    Examples
    ========

    >>> from sympy.polys.domains import PythonRational

    >>> PythonRational(1)
    1
    >>> PythonRational(2, 3)
    2/3
    >>> PythonRational(14, 10)
    7/5

    """

    __slots__ = ['p', 'q']

    def parent(self):
        from sympy.polys.domains import PythonRationalField
        return PythonRationalField()

    def __init__(self, p, q=None):
        if q is None:
            self.p = p
            self.q = 1
        else:
            if not q:
                raise ZeroDivisionError('rational number')
            elif q < 0:
                p, q = -p, -q

            g = igcd(p, q)

            self.p = p//g
            self.q = q//g

    @classmethod
    def new(cls, p, q):
        obj = object.__new__(cls)
        obj.p = p
        obj.q = q
        return obj

    def __hash__(self):
        if self.q == 1:
            return hash(self.p)
        else:
            return hash((self.p, self.q))

    def __int__(self):
        return int(float(self.p)/self.q)

    def __float__(self):
        return float(self.p)/self.q

    def __abs__(self):
        return self.new(abs(self.p), self.q)

    def __pos__(self):
        return self.new(+self.p, self.q)

    def __neg__(self):
        return self.new(-self.p, self.q)

    def __add__(self, other):
        if isinstance(other, PythonRational):
            p = self.p*other.q + self.q*other.p
            q = self.q*other.q
        elif isinstance(other, int):
            p = self.p + self.q*other
            q = self.q
        else:
            return NotImplemented

        return self.__class__(p, q)

    def __radd__(self, other):
        if not isinstance(other, int):
            return NotImplemented

        p = self.p + self.q*other
        q = self.q

        return self.__class__(p, q)

    def __sub__(self, other):
        if isinstance(other, PythonRational):
            p = self.p*other.q - self.q*other.p
            q = self.q*other.q
        elif isinstance(other, int):
            p = self.p - self.q*other
            q = self.q
        else:
            return NotImplemented

        return self.__class__(p, q)

    def __rsub__(self, other):
        if not isinstance(other, int):
            return NotImplemented

        p = self.q*other - self.p
        q = self.q

        return self.__class__(p, q)

    def __mul__(self, other):
        if isinstance(other, PythonRational):
            p = self.p*other.p
            q = self.q*other.q
        elif isinstance(other, int):
            p = self.p*other
            q = self.q
        else:
            return NotImplemented

        return self.__class__(p, q)

    def __rmul__(self, other):
        if not isinstance(other, int):
            return NotImplemented

        p = self.p*other
        q = self.q

        return self.__class__(p, q)

    def __div__(self, other):
        if isinstance(other, PythonRational):
            p = self.p*other.q
            q = self.q*other.p
        elif isinstance(other, int):
            p = self.p
            q = self.q*other
        else:
            return NotImplemented

        return self.__class__(p, q)

    __truediv__ = __div__

    def __rdiv__(self, other):
        if not isinstance(other, int):
            return NotImplemented

        p = self.q*other
        q = self.p

        return self.__class__(p, q)

    __rtruediv__ = __rdiv__

    def __mod__(self, other):
        return self.__class__(0)

    def __divmod__(self, other):
        return (self//other, self % other)

    def __pow__(self, exp):
        p, q = self.p, self.q

        if exp < 0:
            p, q, exp = q, p, -exp

        return self.new(p**exp, q**exp)

    def __bool__(self):
        return self.p != 0

    def __eq__(self, other):
        if isinstance(other, PythonRational):
            return self.q == other.q and self.p == other.p
        elif isinstance(other, int):
            return self.q == 1 and self.p == other
        else:
            return False

    def __ne__(self, other):
        return not self.__eq__(other)

    def _cmp(self, other, op):
        try:
            diff = self - other
        except TypeError:
            return NotImplemented
        else:
            return op(diff.p, 0)

    def __lt__(self, other):
        return self._cmp(other, operator.lt)

    def __le__(self, other):
        return self._cmp(other, operator.le)

    def __gt__(self, other):
        return self._cmp(other, operator.gt)

    def __ge__(self, other):
        return self._cmp(other, operator.ge)

    @property
    def numer(self):
        return self.p

    @property
    def denom(self):
        return self.q

    numerator = numer
    denominator = denom
