def test_as_sum_midpoint1():
e = Integral(sqrt(x**3 + 1), (x, 2, 10))
assert e.as_sum(1, method="midpoint") == 8 * sqrt(217)
assert e.as_sum(2, method="midpoint") == 4 * sqrt(65) + 12 * sqrt(57)
assert e.as_sum(3, method="midpoint") == 8*sqrt(217)/3 + \
8*sqrt(3081)/27 + 8*sqrt(52809)/27
assert e.as_sum(4, method="midpoint") == 2*sqrt(730) + \
4*sqrt(7) + 4*sqrt(86) + 6*sqrt(14)
assert abs(e.as_sum(4, method="midpoint").evalf() - e.evalf()) < 0.5
e = Integral(sqrt(x**3 + y**3), (x, 2, 10), (y, 0, 10))
pytest.raises(NotImplementedError, lambda: e.as_sum(4))
def test_as_sum_midpoint1():
e = Integral(sqrt(x**3 + 1), (x, 2, 10))
assert e.as_sum(1, method="midpoint") == 8*sqrt(217)
assert e.as_sum(2, method="midpoint") == 4*sqrt(65) + 12*sqrt(57)
assert e.as_sum(3, method="midpoint") == 8*sqrt(217)/3 + \
8*sqrt(3081)/27 + 8*sqrt(52809)/27
assert e.as_sum(4, method="midpoint") == 2*sqrt(730) + \
4*sqrt(7) + 4*sqrt(86) + 6*sqrt(14)
assert abs(e.as_sum(4, method="midpoint").evalf() - e.evalf()) < 0.5
e = Integral(sqrt(x**3 + y**3), (x, 2, 10), (y, 0, 10))
pytest.raises(NotImplementedError, lambda: e.as_sum(4))
def test_literal_evalf_is_number_is_zero_is_comparable():
f = Function('f')
# the following should not be changed without a lot of dicussion
# `foo.is_number` should be equivalent to `not foo.free_symbols`
# it should not attempt anything fancy; see is_zero, is_constant
# and equals for more rigorous tests.
assert f(1).is_number is True
i = Integral(0, (x, x, x))
# expressions that are symbolically 0 can be difficult to prove
# so in case there is some easy way to know if something is 0
# it should appear in the is_zero property for that object;
# if is_zero is true evalf should always be able to compute that
# zero
assert i.evalf() == 0
assert i.is_zero
assert i.is_number is False
assert i.evalf(2, strict=False) == 0
# issue sympy/sympy#10272
n = sin(1)**2 + cos(1)**2 - 1
assert n.is_comparable is not True
assert n.evalf(2, strict=False).is_comparable is not True
