def test_integrate_primitive():
DE = DifferentialExtension(extension={"D": [Poly(1, x), Poly(1 / x, t)], "Tfuncs": [log]})
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x * log(x), -1, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x / log(x), x), False)
DE = DifferentialExtension(
extension={"D": [Poly(1, x), Poly(1 / x, t1), Poly(1 / (x + 1), t2)], "Tfuncs": [log, Lambda(i, log(i + 1))]}
)
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == (
0,
NonElementaryIntegral(log(x) / log(1 + x), x),
False,
)
DE = DifferentialExtension(
extension={"D": [Poly(1, x), Poly(1 / x, t1), Poly(1 / (x * t1), t2)], "Tfuncs": [log, Lambda(i, log(log(i)))]}
)
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == (
0,
NonElementaryIntegral(log(log(x)) / log(x), x),
False,
)
DE = DifferentialExtension(extension={"D": [Poly(1, x), Poly(1 / x, t0)], "Tfuncs": [log]})
assert integrate_primitive(
Poly(x ** 2 * t0 ** 3 + (3 * x ** 2 + x) * t0 ** 2 + (3 * x ** 2 + 2 * x) * t0 + x ** 2 + x, t0),
Poly(x ** 2 * t0 ** 4 + 4 * x ** 2 * t0 ** 3 + 6 * x ** 2 * t0 ** 2 + 4 * x ** 2 * t0 + x ** 2, t0),
DE,
) == (-1 / (log(x) + 1), NonElementaryIntegral(1 / (log(x) + 1), x), False)
def test_integrate_primitive():
DE = DifferentialExtension(
extension={"D": [Poly(1, x), Poly(1 / x, t)], "Tfuncs": [log]}
)
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x * log(x), -1, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (
0,
NonElementaryIntegral(x / log(x), x),
False,
)
DE = DifferentialExtension(
extension={
"D": [Poly(1, x), Poly(1 / x, t1), Poly(1 / (x + 1), t2)],
"Tfuncs": [log, Lambda(i, log(i + 1))],
}
)
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == (
0,
NonElementaryIntegral(log(x) / log(1 + x), x),
False,
)
DE = DifferentialExtension(
extension={
"D": [Poly(1, x), Poly(1 / x, t1), Poly(1 / (x * t1), t2)],
"Tfuncs": [log, Lambda(i, log(log(i)))],
}
)
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == (
0,
NonElementaryIntegral(log(log(x)) / log(x), x),
False,
)
DE = DifferentialExtension(
extension={"D": [Poly(1, x), Poly(1 / x, t0)], "Tfuncs": [log]}
)
assert integrate_primitive(
Poly(
x ** 2 * t0 ** 3
+ (3 * x ** 2 + x) * t0 ** 2
+ (3 * x ** 2 + 2 * x) * t0
+ x ** 2
+ x,
t0,
),
Poly(
x ** 2 * t0 ** 4
+ 4 * x ** 2 * t0 ** 3
+ 6 * x ** 2 * t0 ** 2
+ 4 * x ** 2 * t0
+ x ** 2,
t0,
),
DE,
) == (-1 / (log(x) + 1), NonElementaryIntegral(1 / (log(x) + 1), x), False)
def test_integrate_primitive():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)],
'Tfuncs': [log]})
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x*log(x), -1, True)
# (x*log(x) - x, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x/log(x), x), False)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'Tfuncs': [log, lambda x: log(x + 1)]})
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == \
(0, NonElementaryIntegral(log(x)/log(1 + x), x), False)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x*t1), t2)],
'Tfuncs': [log, lambda x: log(log(x))]})
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == \
(0, NonElementaryIntegral(log(log(x))/log(x), x), False)
def test_integrate_primitive():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)],
'Tfuncs': [log]})
assert integrate_primitive(Poly(t, t), Poly(1, t), DE) == (x*log(x), -1, True)
# (x*log(x) - x, True)
assert integrate_primitive(Poly(x, t), Poly(t, t), DE) == (0, NonElementaryIntegral(x/log(x), x), False)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'Tfuncs': [log, lambda x: log(x + 1)]})
assert integrate_primitive(Poly(t1, t2), Poly(t2, t2), DE) == \
(0, NonElementaryIntegral(log(x)/log(1 + x), x), False)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x*t1), t2)],
'Tfuncs': [log, lambda x: log(log(x))]})
assert integrate_primitive(Poly(t2, t2), Poly(t1, t2), DE) == \
(0, NonElementaryIntegral(log(log(x))/log(x), x), False)