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)))