<commit_before>from sympy import (
    Abs, Dummy, Eq, Gt,
    LambertW, Piecewise, Poly, Rational, S, Symbol, Matrix,
    acos, atan, atanh, cos, erf, erfinv, erfc, erfcinv,
    exp, log, pi, sin, sinh, sqrt, symbols,
    tan, tanh, atan2, arg,
    Lambda, imageset, cot, acot, I, EmptySet, Union, E, Interval, oo)

from sympy.core.function import nfloat
from sympy.functions.elementary.complexes import im, re
from sympy.functions.elementary.hyperbolic import HyperbolicFunction
from sympy.functions.elementary.trigonometric import TrigonometricFunction

from sympy.polys.rootoftools import RootOf

from sympy.sets import FiniteSet

from sympy.utilities.pytest import XFAIL, raises, skip
from sympy.utilities.randtest import verify_numerically as tn
from sympy.physics.units import cm


from sympy.solvers.solveset import (
    solveset_real, domain_check, solveset_complex, linear_eq_to_matrix,
    linsolve, _is_function_class_equation, invert_real, invert_complex,
    solveset)

a = Symbol('a', real=True)
b = Symbol('b', real=True)
c = Symbol('c', real=True)
x = Symbol('x', real=True)
y = Symbol('y', real=True)
z = Symbol('z', real=True)
q = Symbol('q', real=True)
m = Symbol('m', real=True)
n = Symbol('n', real=True)


def test_invert_real():
    x = Dummy(real=True)
    n = Symbol('n')
    d = Dummy()
    assert solveset(abs(x) - n, x) == solveset(abs(x) - d, x) == EmptySet()

    n = Symbol('n', real=True)
    assert invert_real(x + 3, y, x) == (x, FiniteSet(y - 3))
    assert invert_real(x*3, y, x) == (x, FiniteSet(y / 3))

    assert invert_real(exp(x), y, x) == (x, FiniteSet(log(y)))
    assert invert_real(exp(3*x), y, x) == (x, FiniteSet(log(y) / 3))
    assert invert_real(exp(x + 3), y, x) == (x, FiniteSet(log(y) - 3))

    assert invert_real(exp(x) + 3, y, x) == (x, FiniteSet(log(y - 3)))
    assert invert_real(exp(x)*3, y, x) == (x, FiniteSet(log(y / 3)))

    assert invert_real(log(x), y, x) == (x, FiniteSet(exp(y)))
    assert invert_real(log(3*x), y, x) == (x, FiniteSet(exp(y) / 3))
    assert invert_real(log(x + 3), y, x) == (x, FiniteSet(exp(y) - 3))

    assert invert_real(Abs(x), y, x) == (x, FiniteSet(-y, y))

    assert invert_real(2**x, y, x) == (x, FiniteSet(log(y)/log(2)))
    assert invert_real(2**exp(x), y, x) == (x, FiniteSet(log(log(y)/log(2))))

    assert invert_real(x**2, y, x) == (x, FiniteSet(sqrt(y), -sqrt(y)))
    assert invert_real(x**Rational(1, 2), y, x) == (x, FiniteSet(y**2))

    raises(ValueError, lambda: invert_real(x, x, x))
    raises(ValueError, lambda: invert_real(x**pi, y, x))
    raises(ValueError, lambda: invert_real(S.One, y, x))

    assert invert_real(x**31 + x, y, x) == (x**31 + x, FiniteSet(y))<commit_msg>Fix Failing test in solveset<commit_after>from sympy import (
    Abs, Dummy, Eq, Gt,
    LambertW, Piecewise, Poly, Rational, S, Symbol, Matrix,
    acos, atan, atanh, cos, erf, erfinv, erfc, erfcinv,
    exp, log, pi, sin, sinh, sqrt, symbols,
    tan, tanh, atan2, arg,
    Lambda, imageset, cot, acot, I, EmptySet, Union, E, Interval, Intersection,
    oo)

from sympy.core.function import nfloat
from sympy.functions.elementary.complexes import im, re
from sympy.functions.elementary.hyperbolic import HyperbolicFunction
from sympy.functions.elementary.trigonometric import TrigonometricFunction

from sympy.polys.rootoftools import RootOf

from sympy.sets import FiniteSet

from sympy.utilities.pytest import XFAIL, raises, skip
from sympy.utilities.randtest import verify_numerically as tn
from sympy.physics.units import cm


from sympy.solvers.solveset import (
    solveset_real, domain_check, solveset_complex, linear_eq_to_matrix,
    linsolve, _is_function_class_equation, invert_real, invert_complex,
    solveset)

a = Symbol('a', real=True)
b = Symbol('b', real=True)
c = Symbol('c', real=True)
x = Symbol('x', real=True)
y = Symbol('y', real=True)
z = Symbol('z', real=True)
q = Symbol('q', real=True)
m = Symbol('m', real=True)
n = Symbol('n', real=True)


def test_invert_real():
    x = Dummy(real=True)
    n = Symbol('n')
    d = Dummy()
    assert solveset(abs(x) - n, x) == Intersection(S.Reals, FiniteSet(-n, n))

    n = Symbol('n', real=True)
    assert invert_real(x + 3, y, x) == (x, FiniteSet(y - 3))
    assert invert_real(x*3, y, x) == (x, FiniteSet(y / 3))

    assert invert_real(exp(x), y, x) == (x, FiniteSet(log(y)))
    assert invert_real(exp(3*x), y, x) == (x, FiniteSet(log(y) / 3))
    assert invert_real(exp(x + 3), y, x) == (x, FiniteSet(log(y) - 3))

    assert invert_real(exp(x) + 3, y, x) == (x, FiniteSet(log(y - 3)))
    assert invert_real(exp(x)*3, y, x) == (x, FiniteSet(log(y / 3)))

    assert invert_real(log(x), y, x) == (x, FiniteSet(exp(y)))
    assert invert_real(log(3*x), y, x) == (x, FiniteSet(exp(y) / 3))
    assert invert_real(log(x + 3), y, x) == (x, FiniteSet(exp(y) - 3))

    assert invert_real(Abs(x), y, x) == (x, FiniteSet(-y, y))

    assert invert_real(2**x, y, x) == (x, FiniteSet(log(y)/log(2)))
    assert invert_real(2**exp(x), y, x) == (x, FiniteSet(log(log(y)/log(2))))

    assert invert_real(x**2, y, x) == (x, FiniteSet(sqrt(y), -sqrt(y)))
    assert invert_real(x**Rational(1, 2), y, x) == (x, FiniteSet(y**2))

    raises(ValueError, lambda: invert_real(x, x, x))
    raises(ValueError, lambda: invert_real(x**pi, y, x))
    raises(ValueError, lambda: invert_real(S.One, y, x))

    assert invert_real(x**31 + x, y, x) == (x**31 + x, FiniteSet(y))
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