def div(self, other):  # Factors
        """Return ``self`` and ``other`` with ``gcd`` removed from each.
        This is optimized for the case when there are many factors in common.

        Examples
        ========

        >>> from sympy.core.exprtools import Factors
        >>> from sympy.abc import x, y, z
        >>> from sympy import S

        >>> a = Factors((x*y**2).as_powers_dict())
        >>> a.div(a)
        (Factors({}), Factors({}))
        >>> a.div(x*z)
        (Factors({y: 2}), Factors({z: 1}))

        The ``/`` operator only gives ``quo``:

        >>> a/x
        Factors({y: 2})

        Factors treats its factors as though they are all in the numerator, so
        if you violate this assumption the results will be correct but will
        not strictly correspond to the numerator and denominator of the ratio:

        >>> a.div(x/z)
        (Factors({y: 2}), Factors({z: -1}))

        Factors is also naive about bases: it does not attempt any denesting
        of Rational-base terms, for example the following does not become
        2**(2*x)/2.

        >>> Factors(2**(2*x + 2)).div(S(8))
        (Factors({2: 2*x + 2}), Factors({8: 1}))

        factor_terms can clean up such Rational-bases powers:

        >>> from sympy.core.exprtools import factor_terms
        >>> n, d = Factors(2**(2*x + 2)).div(S(8))
        >>> n.as_expr()/d.as_expr()
        2**(2*x + 2)/8
        >>> factor_terms(_)
        2**(2*x)/2

        """
        quo, rem = dict(self.factors), {}

        if not isinstance(other, Factors):
            other = Factors(other)
            if other.is_zero:
                raise ZeroDivisionError
            if self.is_zero:
                return (Factors(S.Zero), Factors())

        for factor, exp in other.factors.items():
            if factor in quo:
                d = quo[factor] - exp
                if _isnumber(d):
                    if d <= 0:
                        del quo[factor]

                    if d >= 0:
                        if d:
                            quo[factor] = d

                        continue

                    exp = -d

                else:
                    r = quo[factor].extract_additively(exp)
                    if r is not None:
                        if r:
                            quo[factor] = r
                        else:  # should be handled already
                            del quo[factor]
                    else:
                        other_exp = exp
                        sc, sa = quo[factor].as_coeff_Add()
                        if sc:
                            oc, oa = other_exp.as_coeff_Add()
                            diff = sc - oc
                            if diff > 0:
                                quo[factor] -= oc
                                other_exp = oa
                            elif diff < 0:
                                quo[factor] -= sc
                                other_exp = oa - diff
                            else:
                                quo[factor] = sa
                                other_exp = oa
                        if other_exp:
                            rem[factor] = other_exp
                        else:
                            assert factor not in rem
                    continue

            rem[factor] = exp

        return Factors(quo), Factors(rem)
dataset/ETHPy150Open sympy/sympy/sympy/core/exprtools.py/Factors.div/original