def test_euler_maclaurin():
# Exact polynomial sums with E-M
def check_exact(f, a, b, m, n):
A = Sum(f, (k, a, b))
s, e = A.euler_maclaurin(m, n)
assert (e == 0) and (s.expand() == A.doit())
check_exact(k**4, a, b, 0, 2)
check_exact(k**4 + 2 * k, a, b, 1, 2)
check_exact(k**4 + k**2, a, b, 1, 5)
check_exact(k**5, 2, 6, 1, 2)
check_exact(k**5, 2, 6, 1, 3)
assert Sum(x - 1, (x, 0, 2)).euler_maclaurin(m=30, n=30,
eps=2**-15) == (0, 0)
# Not exact
assert Sum(k**6, (k, a, b)).euler_maclaurin(0, 2)[1] != 0
# Numerical test
for m, n in [(2, 4), (2, 20), (10, 20), (18, 20)]:
A = Sum(1 / k**3, (k, 1, oo))
s, e = A.euler_maclaurin(m, n)
assert abs((s - zeta(3)).evalf()) < e.evalf()
def test_euler_maclaurin():
pytest.raises(ValueError, lambda: Sum(x - y, (x, 0, 2),
(y, 0, 2)).euler_maclaurin())
# Exact polynomial sums with E-M
def check_exact(f, a, b, m, n):
A = Sum(f, (k, a, b))
s, e = A.euler_maclaurin(m, n)
assert (e == 0) and (s.expand() == A.doit())
check_exact(k**4, a, b, 0, 2)
check_exact(k**4 + 2*k, a, b, 1, 2)
check_exact(k**4 + k**2, a, b, 1, 5)
check_exact(k**5, 2, 6, 1, 2)
check_exact(k**5, 2, 6, 1, 3)
assert Sum(x-1, (x, 0, 2)).euler_maclaurin(m=30, n=30, eps=2**-15) == (0, 0)
# Not exact
assert Sum(k**6, (k, a, b)).euler_maclaurin(0, 2)[1] != 0
# Numerical test
for m, n in [(2, 4), (2, 20), (10, 20), (18, 20)]:
A = Sum(1/k**3, (k, 1, oo))
s, e = A.euler_maclaurin(m, n)
assert abs((s - zeta(3)).evalf()) < e.evalf()
def check_exact(f, a, b, m, n):
A = Sum(f, (k, a, b))
s, e = A.euler_maclaurin(m, n)
assert (e == 0) and (s.expand() == A.doit())
def check_exact(f, a, b, m, n):
A = Sum(f, (k, a, b))
s, e = A.euler_maclaurin(m, n)
assert (e == 0) and (s.expand() == A.doit())
