def test_float_handling():
    def test(e1, e2):
        return len(e1.atoms(Float)) == len(e2.atoms(Float))
    assert solve(x - 0.5, rational=True)[0].is_Rational
    assert solve(x - 0.5, rational=False)[0].is_Float
    assert solve(x - S.Half, rational=False)[0].is_Rational
    assert solve(x - 0.5, rational=None)[0].is_Float
    assert solve(x - S.Half, rational=None)[0].is_Rational
    assert test(nfloat(1 + 2*x), 1.0 + 2.0*x)
    for contain in [list, tuple, set]:
        ans = nfloat(contain([1 + 2*x]))
        assert type(ans) is contain and test(list(ans)[0], 1.0 + 2.0*x)
    k, v = nfloat({2*x: [1 + 2*x]}).items()[0]
    assert test(k, 2*x) and test(v[0], 1.0 + 2.0*x)
    assert test(nfloat(cos(2*x)), cos(2.0*x))
    assert test(nfloat(3*x**2), 3.0*x**2)
    assert test(nfloat(3*x**2, exponent=True), 3.0*x**2.0)
    assert test(nfloat(exp(2*x)), exp(2.0*x))
    assert test(nfloat(x/3), x/3.0)
    assert test(nfloat(x**4 + 2*x + cos(S(1)/3) + 1),
            x**4 + 2.0*x + 1.94495694631474)

def test_return_root_of():
    f = x ** 5 - 15 * x ** 3 - 5 * x ** 2 + 10 * x + 20
    s = list(solveset_complex(f, x))
    for root in s:
        assert root.func == RootOf

    # if one uses solve to get the roots of a polynomial that has a RootOf
    # solution, make sure that the use of nfloat during the solve process
    # doesn't fail. Note: if you want numerical solutions to a polynomial
    # it is *much* faster to use nroots to get them than to solve the
    # equation only to get RootOf solutions which are then numerically
    # evaluated. So for eq = x**5 + 3*x + 7 do Poly(eq).nroots() rather
    # than [i.n() for i in solve(eq)] to get the numerical roots of eq.
    assert (
        nfloat(list(solveset_complex(x ** 5 + 3 * x ** 3 + 7, x))[0], exponent=False)
        == RootOf(x ** 5 + 3 * x ** 3 + 7, 0).n()
    )

    sol = list(solveset_complex(x ** 6 - 2 * x + 2, x))
    assert all(isinstance(i, RootOf) for i in sol) and len(sol) == 6

    f = x ** 5 - 15 * x ** 3 - 5 * x ** 2 + 10 * x + 20
    s = list(solveset_complex(f, x))
    for root in s:
        assert root.func == RootOf

    s = x ** 5 + 4 * x ** 3 + 3 * x ** 2 + S(7) / 4
    assert solveset_complex(s, x) == FiniteSet(*Poly(s * 4, domain="ZZ").all_roots())

    # XXX: this comparison should work without converting the FiniteSet to list
    # See #7876
    eq = x * (x - 1) ** 2 * (x + 1) * (x ** 6 - x + 1)
    assert list(solveset_complex(eq, x)) == list(
        FiniteSet(
            -1,
            0,
            1,
            RootOf(x ** 6 - x + 1, 0),
            RootOf(x ** 6 - x + 1, 1),
            RootOf(x ** 6 - x + 1, 2),
            RootOf(x ** 6 - x + 1, 3),
            RootOf(x ** 6 - x + 1, 4),
            RootOf(x ** 6 - x + 1, 5),
        )
    )

#.........这里部分代码省略.........

    # TODO: Apply different strategies, considering expression pattern:
    # is it a purely rational function? Is there any trigonometric function?...
    # See also https://github.com/sympy/sympy/pull/185.

    def shorter(*choices):
        '''Return the choice that has the fewest ops. In case of a tie,
        the expression listed first is selected.'''
        if not has_variety(choices):
            return choices[0]
        return min(choices, key=measure)

    # rationalize Floats
    floats = False
    if rational is not False and expr.has(Float):
        floats = True
        expr = nsimplify(expr, rational=True)

    expr = bottom_up(expr, lambda w: w.normal())
    expr = Mul(*powsimp(expr).as_content_primitive())
    _e = cancel(expr)
    expr1 = shorter(_e, _mexpand(_e).cancel())  # issue 6829
    expr2 = shorter(together(expr, deep=True), together(expr1, deep=True))

    if ratio is S.Infinity:
        expr = expr2
    else:
        expr = shorter(expr2, expr1, expr)
    if not isinstance(expr, Basic):  # XXX: temporary hack
        return expr

    expr = factor_terms(expr, sign=False)

    # hyperexpand automatically only works on hypergeometric terms
    expr = hyperexpand(expr)

    expr = piecewise_fold(expr)

    if expr.has(BesselBase):
        expr = besselsimp(expr)

    if expr.has(TrigonometricFunction, HyperbolicFunction):
        expr = trigsimp(expr, deep=True)

    if expr.has(log):
        expr = shorter(expand_log(expr, deep=True), logcombine(expr))

    if expr.has(CombinatorialFunction, gamma):
        # expression with gamma functions or non-integer arguments is
        # automatically passed to gammasimp
        expr = combsimp(expr)

    if expr.has(Sum):
        expr = sum_simplify(expr)

    if expr.has(Product):
        expr = product_simplify(expr)

    from sympy.physics.units import Quantity
    from sympy.physics.units.util import quantity_simplify

    if expr.has(Quantity):
        expr = quantity_simplify(expr)

    short = shorter(powsimp(expr, combine='exp', deep=True), powsimp(expr), expr)
    short = shorter(short, cancel(short))
    short = shorter(short, factor_terms(short), expand_power_exp(expand_mul(short)))
    if short.has(TrigonometricFunction, HyperbolicFunction, ExpBase):
        short = exptrigsimp(short)

    # get rid of hollow 2-arg Mul factorization
    hollow_mul = Transform(
        lambda x: Mul(*x.args),
        lambda x:
        x.is_Mul and
        len(x.args) == 2 and
        x.args[0].is_Number and
        x.args[1].is_Add and
        x.is_commutative)
    expr = short.xreplace(hollow_mul)

    numer, denom = expr.as_numer_denom()
    if denom.is_Add:
        n, d = fraction(radsimp(1/denom, symbolic=False, max_terms=1))
        if n is not S.One:
            expr = (numer*n).expand()/d

    if expr.could_extract_minus_sign():
        n, d = fraction(expr)
        if d != 0:
            expr = signsimp(-n/(-d))

    if measure(expr) > ratio*measure(original_expr):
        expr = original_expr

    # restore floats
    if floats and rational is None:
        expr = nfloat(expr, exponent=False)

    return expr