def test_maximum():
x, y = symbols('x y')
assert maximum(sin(x), x) is S.One
assert maximum(sin(x), x, Interval(0, 1)) == sin(1)
assert maximum(tan(x), x) is oo
assert maximum(tan(x), x, Interval(-pi/4, pi/4)) is S.One
assert maximum(sin(x)*cos(x), x, S.Reals) == S.Half
assert simplify(maximum(sin(x)*cos(x), x, Interval(pi*Rational(3, 8), pi*Rational(5, 8)))
) == sqrt(2)/4
assert maximum((x+3)*(x-2), x) is oo
assert maximum((x+3)*(x-2), x, Interval(-5, 0)) == S(14)
assert maximum((x+3)/(x-2), x, Interval(-5, 0)) == Rational(2, 7)
assert simplify(maximum(-x**4-x**3+x**2+10, x)
) == 41*sqrt(41)/512 + Rational(5419, 512)
assert maximum(exp(x), x, Interval(-oo, 2)) == exp(2)
assert maximum(log(x) - x, x, S.Reals) is S.NegativeOne
assert maximum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
) is S.One
assert maximum(cos(x)-sin(x), x, S.Reals) == sqrt(2)
assert maximum(y, x, S.Reals) == y
assert maximum(abs(a**3 + a), a, Interval(0, 2)) == 10
assert maximum(abs(60*a**3 + 24*a), a, Interval(0, 2)) == 528
assert maximum(abs(12*a*(5*a**2 + 2)), a, Interval(0, 2)) == 528
raises(ValueError, lambda : maximum(sin(x), x, S.EmptySet))
raises(ValueError, lambda : maximum(log(cos(x)), x, S.EmptySet))
raises(ValueError, lambda : maximum(1/(x**2 + y**2 + 1), x, S.EmptySet))
raises(ValueError, lambda : maximum(sin(x), sin(x)))
raises(ValueError, lambda : maximum(sin(x), x*y, S.EmptySet))
raises(ValueError, lambda : maximum(sin(x), S.One))
def test_maximum():
x, y = symbols('x y')
assert maximum(sin(x), x) == S.One
assert maximum(sin(x), x, Interval(0, 1)) == sin(1)
assert maximum(tan(x), x) == oo
assert maximum(tan(x), x, Interval(-pi / 4, pi / 4)) == S.One
assert maximum(sin(x) * cos(x), x, S.Reals) == S.Half
assert simplify(
maximum(sin(x) * cos(x), x, Interval(3 * pi / 8,
5 * pi / 8))) == sqrt(2) / 4
assert maximum((x + 3) * (x - 2), x) == oo
assert maximum((x + 3) * (x - 2), x, Interval(-5, 0)) == S(14)
assert maximum((x + 3) / (x - 2), x, Interval(-5, 0)) == S(2) / 7
assert simplify(maximum(-x**4 - x**3 + x**2 + 10,
x)) == 41 * sqrt(41) / 512 + S(5419) / 512
assert maximum(exp(x), x, Interval(-oo, 2)) == exp(2)
assert maximum(log(x) - x, x, S.Reals) == -S.One
assert maximum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))) == S.One
assert maximum(cos(x) - sin(x), x, S.Reals) == sqrt(2)
assert maximum(y, x, S.Reals) == y
raises(ValueError, lambda: maximum(sin(x), x, S.EmptySet))
raises(ValueError, lambda: maximum(log(cos(x)), x, S.EmptySet))
raises(ValueError, lambda: maximum(1 / (x**2 + y**2 + 1), x, S.EmptySet))
raises(ValueError, lambda: maximum(sin(x), sin(x)))
raises(ValueError, lambda: maximum(sin(x), x * y, S.EmptySet))
raises(ValueError, lambda: maximum(sin(x), S(1)))
def test_issue_19869():
t = symbols('t')
assert (maximum(sqrt(3) * (t - 1) / (3 * sqrt(t**2 + 1)),
t)) == sqrt(3) / 3
def test_maximum():
x, y = symbols('x y')
assert maximum(sin(x), x) == S.One
assert maximum(sin(x), x, Interval(0, 1)) == sin(1)
assert maximum(tan(x), x) == oo
assert maximum(tan(x), x, Interval(-pi/4, pi/4)) == S.One
assert maximum(sin(x)*cos(x), x, S.Reals) == S.Half
assert simplify(maximum(sin(x)*cos(x), x, Interval(3*pi/8, 5*pi/8))
) == sqrt(2)/4
assert maximum((x+3)*(x-2), x) == oo
assert maximum((x+3)*(x-2), x, Interval(-5, 0)) == S(14)
assert maximum((x+3)/(x-2), x, Interval(-5, 0)) == S(2)/7
assert simplify(maximum(-x**4-x**3+x**2+10, x)
) == 41*sqrt(41)/512 + S(5419)/512
assert maximum(exp(x), x, Interval(-oo, 2)) == exp(2)
assert maximum(log(x) - x, x, S.Reals) == -S.One
assert maximum(cos(x), x, Union(Interval(0, 5), Interval(-6, -3))
) == S.One
assert maximum(cos(x)-sin(x), x, S.Reals) == sqrt(2)
assert maximum(y, x, S.Reals) == y
raises(ValueError, lambda : maximum(sin(x), x, S.EmptySet))
raises(ValueError, lambda : maximum(log(cos(x)), x, S.EmptySet))
raises(ValueError, lambda : maximum(1/(x**2 + y**2 + 1), x, S.EmptySet))
raises(ValueError, lambda : maximum(sin(x), sin(x)))
raises(ValueError, lambda : maximum(sin(x), x*y, S.EmptySet))
raises(ValueError, lambda : maximum(sin(x), S(1)))
