text: from sympy import Symbol, exp, log, oo, S, I, sqrt
  from sympy.calculus.singularities import (
      singularities,
      is_increasing,
      is_strictly_increasing,
      is_decreasing,
      is_strictly_decreasing,
      is_monotonic
  )
  from sympy.sets import Interval, FiniteSet
  from sympy.utilities.pytest import XFAIL, raises
  from sympy.abc import x, y
  
  
  def test_singularities():
      x = Symbol('x')
      assert singularities(x**2, x) == S.EmptySet
      assert singularities(x/(x**2 + 3*x + 2), x) == FiniteSet(-2, -1)
      assert singularities(1/(x**2 + 1), x) == FiniteSet(I, -I)
      assert singularities(x/(x**3 + 1), x) == \
          FiniteSet(-1, (1 - sqrt(3) * I) / 2, (1 + sqrt(3) * I) / 2)
      assert singularities(1/(y**2 + 2*I*y + 1), y) == \
          FiniteSet(-I + sqrt(2)*I, -I - sqrt(2)*I)
  
      x = Symbol('x', real=True)
      assert singularities(1/(x**2 + 1), x) == S.EmptySet
  
  
  @XFAIL
  def test_singularities_non_rational():
      x = Symbol('x', real=True)
  
      assert singularities(exp(1/x), x) == FiniteSet(0)
      assert singularities(log((x - 2)**2), x) == FiniteSet(2)
  
  
  def test_is_increasing():
      """Test whether is_increasing returns correct value."""
      a = Symbol('a', negative=True)
  
      assert is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
      assert is_increasing(-x**2, Interval(-oo, 0))
      assert not is_increasing(-x**2, Interval(0, oo))
      assert not is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
      assert is_increasing(x**2 + y, Interval(1, oo), x)
      assert is_increasing(-x**2*a, Interval(1, oo), x)
      assert is_increasing(1)
  
  
  def test_is_strictly_increasing():
      """Test whether is_strictly_increasing returns correct value."""
      assert is_strictly_increasing(
          4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
      assert is_strictly_increasing(
          4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
      assert not is_strictly_increasing(
          4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
      assert not is_strictly_increasing(-x**2, Interval(0, oo))
      assert not is_strictly_decreasing(1)
  
  
  def test_is_decreasing():
      """Test whether is_decreasing returns correct value."""
      b = Symbol('b', positive=True)
  
      assert is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
      assert is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
      assert not is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
      assert not is_decreasing(-x**2, Interval(-oo, 0))
      assert not is_decreasing(-x**2*b, Interval(-oo, 0), x)
  
  
  def test_is_strictly_decreasing():
      """Test whether is_strictly_decreasing returns correct value."""
      assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
      assert not is_strictly_decreasing(
          1/(x**2 - 3*x), Interval.Ropen(-oo, S(3)/2))
      assert not is_strictly_decreasing(-x**2, Interval(-oo, 0))
      assert not is_strictly_decreasing(1)
      assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
  
  
  def test_is_monotonic():
      """Test whether is_monotonic returns correct value."""
      assert is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
      assert is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
      assert is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
      assert not is_monotonic(-x**2, S.Reals)
      assert is_monotonic(x**2 + y + 1, Interval(1, 2), x)
      raises(NotImplementedError, lambda: is_monotonic(x**2 + y + 1))
  