def test_equals():
assert (-3 - sqrt(5) + (-sqrt(10) / 2 - sqrt(2) / 2) ** 2).equals(0)
assert (x ** 2 - 1).equals((x + 1) * (x - 1))
assert (cos(x) ** 2 + sin(x) ** 2).equals(1)
assert (a * cos(x) ** 2 + a * sin(x) ** 2).equals(a)
r = sqrt(2)
assert (-1 / (r + r * x) + 1 / r / (1 + x)).equals(0)
assert factorial(x + 1).equals((x + 1) * factorial(x))
assert sqrt(3).equals(2 * sqrt(3)) is False
assert (sqrt(5) * sqrt(3)).equals(sqrt(3)) is False
assert (sqrt(5) + sqrt(3)).equals(0) is False
assert (sqrt(5) + pi).equals(0) is False
assert meter.equals(0) is False
assert (3 * meter ** 2).equals(0) is False
# from integrate(x*sqrt(1+2*x), x);
# diff is zero, but differentiation does not show it
i = 2 * sqrt(2) * x ** (S(5) / 2) * (1 + 1 / (2 * x)) ** (S(5) / 2) / 5 + 2 * sqrt(2) * x ** (S(3) / 2) * (
1 + 1 / (2 * x)
) ** (S(5) / 2) / (-6 - 3 / x)
ans = sqrt(2 * x + 1) * (6 * x ** 2 + x - 1) / 15
diff = i - ans
assert diff.equals(0) is not False # should be True, but now it's None
# XXX TODO add a force=True option to equals to posify both
# self and other before beginning comparisions
p = Symbol("p", positive=True)
assert diff.subs(x, p).equals(0) is True
def test_equals():
assert (-3 - sqrt(5) + (-sqrt(10) / 2 - sqrt(2) / 2)**2).equals(0)
assert (x**2 - 1).equals((x + 1) * (x - 1))
assert (cos(x)**2 + sin(x)**2).equals(1)
assert (a * cos(x)**2 + a * sin(x)**2).equals(a)
r = sqrt(2)
assert (-1 / (r + r * x) + 1 / r / (1 + x)).equals(0)
assert factorial(x + 1).equals((x + 1) * factorial(x))
assert sqrt(3).equals(2 * sqrt(3)) is False
assert (sqrt(5) * sqrt(3)).equals(sqrt(3)) is False
assert (sqrt(5) + sqrt(3)).equals(0) is False
assert (sqrt(5) + pi).equals(0) is False
assert meter.equals(0) is False
assert (3 * meter**2).equals(0) is False
# from integrate(x*sqrt(1+2*x), x);
# diff is zero only when assumptions allow
i = 2*sqrt(2)*x**(S(5)/2)*(1 + 1/(2*x))**(S(5)/2)/5 + \
2*sqrt(2)*x**(S(3)/2)*(1 + 1/(2*x))**(S(5)/2)/(-6 - 3/x)
ans = sqrt(2 * x + 1) * (6 * x**2 + x - 1) / 15
diff = i - ans
assert diff.equals(0) is False
assert diff.subs(x, -S.Half / 2) == 7 * sqrt(2) / 120
# there are regions for x for which the expression is True, for
# example, when x < -1/2 or x > 0 the expression is zero
p = Symbol('p', positive=True)
assert diff.subs(x, p).equals(0) is True
assert diff.subs(x, -1).equals(0) is True
def test_equals():
assert (-3 - sqrt(5) + (-sqrt(10)/2 - sqrt(2)/2)**2).equals(0)
assert (x**2 - 1).equals((x + 1)*(x - 1))
assert (cos(x)**2 + sin(x)**2).equals(1)
assert (a*cos(x)**2 + a*sin(x)**2).equals(a)
r = sqrt(2)
assert (-1/(r + r*x) + 1/r/(1 + x)).equals(0)
assert factorial(x + 1).equals((x + 1)*factorial(x))
assert sqrt(3).equals(2*sqrt(3)) is False
assert (sqrt(5)*sqrt(3)).equals(sqrt(3)) is False
assert (sqrt(5) + sqrt(3)).equals(0) is False
assert (sqrt(5) + pi).equals(0) is False
assert meter.equals(0) is False
assert (3*meter**2).equals(0) is False
# from integrate(x*sqrt(1+2*x), x);
# diff is zero only when assumptions allow
i = 2*sqrt(2)*x**(S(5)/2)*(1 + 1/(2*x))**(S(5)/2)/5 + \
2*sqrt(2)*x**(S(3)/2)*(1 + 1/(2*x))**(S(5)/2)/(-6 - 3/x)
ans = sqrt(2*x + 1)*(6*x**2 + x - 1)/15
diff = i - ans
assert diff.equals(0) is False
assert diff.subs(x, -S.Half/2) == 7*sqrt(2)/120
# there are regions for x for which the expression is True, for
# example, when x < -1/2 or x > 0 the expression is zero
p = Symbol('p', positive=True)
assert diff.subs(x, p).equals(0) is True
assert diff.subs(x, -1).equals(0) is True
def test_equals():
assert (-3 - sqrt(5) + (-sqrt(10) / 2 - sqrt(2) / 2)**2).equals(0)
assert (x**2 - 1).equals((x + 1) * (x - 1))
assert (cos(x)**2 + sin(x)**2).equals(1)
assert (a * cos(x)**2 + a * sin(x)**2).equals(a)
r = sqrt(2)
assert (-1 / (r + r * x) + 1 / r / (1 + x)).equals(0)
assert factorial(x + 1).equals((x + 1) * factorial(x))
assert sqrt(3).equals(2 * sqrt(3)) is False
assert (sqrt(5) * sqrt(3)).equals(sqrt(3)) is False
assert (sqrt(5) + sqrt(3)).equals(0) is False
assert (sqrt(5) + pi).equals(0) is False
assert meter.equals(0) is False
assert (3 * meter**2).equals(0) is False
# from integrate(x*sqrt(1+2*x), x);
# diff is zero, but differentiation does not show it
i = 2*sqrt(2)*x**(S(5)/2)*(1 + 1/(2*x))**(S(5)/2)/5 + \
2*sqrt(2)*x**(S(3)/2)*(1 + 1/(2*x))**(S(5)/2)/(-6 - 3/x)
ans = sqrt(2 * x + 1) * (6 * x**2 + x - 1) / 15
diff = i - ans
assert diff.equals(0) is not False # should be True, but now it's None
# XXX TODO add a force=True option to equals to posify both
# self and other before beginning comparisions
p = Symbol('p', positive=True)
assert diff.subs(x, p).equals(0) is True
