def test_issue_11151():
z = S.Zero
e = Sum(z, (x, 1, 2))
assert e != z # it shouldn't evaluate
# when it does evaluate, this is what it should give
assert evalf(e, 15, {}) == \
evalf(z, 15, {}) == (None, None, 15, None)
# so this shouldn't fail
assert (e / 2).n() == 0
# this was where the issue appeared
expr0 = Sum(x**2 + x, (x, 1, 2))
expr1 = Sum(0, (x, 1, 2))
expr2 = expr1 / expr0
assert simplify(factor(expr2) - expr2) == 0
def test_issue_11151():
z = S.Zero
e = Sum(z, (x, 1, 2))
assert e != z # it shouldn't evaluate
# when it does evaluate, this is what it should give
assert evalf(e, 15, {}) == \
evalf(z, 15, {}) == (None, None, 15, None)
# so this shouldn't fail
assert (e/2).n() == 0
# this was where the issue appeared
expr0 = Sum(x**2 + x, (x, 1, 2))
expr1 = Sum(0, (x, 1, 2))
expr2 = expr1/expr0
assert simplify(factor(expr2) - expr2) == 0
def test_evalf_with_bounded_error():
cases = [
# zero
(Rational(0), None, 1),
# zero im part
(pi, None, 10),
# zero real part
(pi * I, None, 10),
# re and im nonzero
(2 - 3 * I, None, 5),
# similar tests again, but using eps instead of m
(Rational(0), Rational(1, 2), None),
(pi, Rational(1, 1000), None),
(pi * I, Rational(1, 1000), None),
(2 - 3 * I, Rational(1, 1000), None),
# very large eps
(2 - 3 * I, Rational(1000), None),
# case where x already small, hence some cancelation in p = m + n - 1
(Rational(1234, 10**8), Rational(1, 10**12), None),
]
for x0, eps, m in cases:
a, b, _, _ = evalf(x0, 53, {})
c, d, _, _ = _evalf_with_bounded_error(x0, eps, m)
if eps is None:
eps = 2**(-m)
z = make_mpc((a or fzero, b or fzero))
w = make_mpc((c or fzero, d or fzero))
assert abs(w - z) < eps
# eps must be positive
raises(ValueError, lambda: _evalf_with_bounded_error(pi, Rational(0)))
raises(ValueError, lambda: _evalf_with_bounded_error(pi, -pi))
raises(ValueError, lambda: _evalf_with_bounded_error(pi, I))
def test_issue_22849():
a = -8 + 3 * sqrt(3)
x = AlgebraicNumber(a)
assert evalf(a, 1, {}) == evalf(x, 1, {})
