def test_is_deriv_k():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'exts': [None, 'log', 'log'], 'extargs': [None, x, x + 1]})
assert is_deriv_k(Poly(2*x**2 + 2*x, t2), Poly(1, t2), DE) == \
([(t1, 1), (t2, 1)], t1 + t2, 2)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(t2, t2)],
'exts': [None, 'log', 'exp'], 'extargs': [None, x, x]})
assert is_deriv_k(Poly(x**2*t2**3, t2), Poly(1, t2), DE) == \
([(x, 3), (t1, 2)], 2*t1 + 3*x, 1)
# TODO: Add more tests, including ones with exponentials
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/x, t1)],
'exts': [None, 'log'], 'extargs': [None, x**2]})
assert is_deriv_k(Poly(x, t1), Poly(1, t1), DE) == \
([(t1, S(1)/2)], t1/2, 1)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/(1 + x), t0)],
'exts': [None, 'log'], 'extargs': [None, x**2 + 2*x + 1]})
assert is_deriv_k(Poly(1 + x, t0), Poly(1, t0), DE) == \
([(t0, S(1)/2)], t0/2, 1)
# Issue 10798
# DE = DifferentialExtension(log(1/x), x)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-1/x, t)],
'exts': [None, 'log'], 'extargs': [None, 1/x]})
assert is_deriv_k(Poly(1, t), Poly(x, t), DE) == ([(t, 1)], t, 1)
def test_is_deriv_k():
DE = DifferentialExtension(
extension={
'D': [Poly(1, x),
Poly(1 / x, t1),
Poly(1 / (x + 1), t2)],
'L_K': [1, 2],
'E_K': [],
'L_args': [x, x + 1],
'E_args': []
})
assert is_deriv_k(Poly(2*x**2 + 2*x, t2), Poly(1, t2), DE) == \
([(t1, 1), (t2, 1)], t1 + t2, 2)
DE = DifferentialExtension(
extension={
'D': [Poly(1, x), Poly(1 / x, t1),
Poly(t2, t2)],
'L_K': [1],
'E_K': [2],
'L_args': [x],
'E_args': [x]
})
assert is_deriv_k(Poly(x**2*t2**3, t2), Poly(1, t2), DE) == \
([(x, 3), (t1, 2)], 2*t1 + 3*x, 1)
# TODO: Add more tests, including ones with exponentials
DE = DifferentialExtension(
extension={
'D': [Poly(1, x), Poly(2 / x, t1)],
'L_K': [1],
'E_K': [],
'L_args': [x**2],
'E_args': []
})
assert is_deriv_k(Poly(x, t1), Poly(1, t1), DE) == \
([(t1, S(1)/2)], t1/2, 1)
DE = DifferentialExtension(
extension={
'D': [Poly(1, x), Poly(2 / (1 + x), t0)],
'L_K': [1],
'E_K': [],
'L_args': [x**2 + 2 * x + 1],
'E_args': []
})
assert is_deriv_k(Poly(1 + x, t0), Poly(1, t0), DE) == \
([(t0, S(1)/2)], t0/2, 1)
# Issue 10798
# DE = DifferentialExtension(log(1/x), x)
DE = DifferentialExtension(
extension={
'D': [Poly(1, x), Poly(-1 / x, t)],
'L_K': [1],
'E_K': [],
'L_args': [1 / x],
'E_args': []
})
assert is_deriv_k(Poly(1, t), Poly(x, t), DE) == ([(t, 1)], t, 1)
def test_is_deriv_k():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'exts': [None, 'log', 'log'], 'extargs': [None, x, x + 1]})
assert is_deriv_k(Poly(2*x**2 + 2*x, t2), Poly(1, t2), DE) == \
([(t1, 1), (t2, 1)], t1 + t2, 2)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(t2, t2)],
'exts': [None, 'log', 'exp'], 'extargs': [None, x, x]})
assert is_deriv_k(Poly(x**2*t2**3, t2), Poly(1, t2), DE) == \
([(x, 3), (t1, 2)], 2*t1 + 3*x, 1)
# TODO: Add more tests, including ones with exponentials
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/x, t1)],
'exts': [None, 'log'], 'extargs': [None, x**2]})
assert is_deriv_k(Poly(x, t1), Poly(1, t1), DE) == \
([(t1, S.Half)], t1/2, 1)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/(1 + x), t0)],
'exts': [None, 'log'], 'extargs': [None, x**2 + 2*x + 1]})
assert is_deriv_k(Poly(1 + x, t0), Poly(1, t0), DE) == \
([(t0, S.Half)], t0/2, 1)
# Issue 10798
# DE = DifferentialExtension(log(1/x), x)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(-1/x, t)],
'exts': [None, 'log'], 'extargs': [None, 1/x]})
assert is_deriv_k(Poly(1, t), Poly(x, t), DE) == ([(t, 1)], t, 1)
def test_is_deriv_k():
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(1/(x + 1), t2)],
'L_K': [1, 2], 'E_K': [], 'L_args': [x, x + 1], 'E_args': []})
assert is_deriv_k(Poly(2*x**2 + 2*x, t2), Poly(1, t2), DE) == \
([(t1, 1), (t2, 1)], t1 + t2, 2)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t1), Poly(t2, t2)],
'L_K': [1], 'E_K': [2], 'L_args': [x], 'E_args': [x]})
assert is_deriv_k(Poly(x**2*t2**3, t2), Poly(1, t2), DE) == \
([(x, 3), (t1, 2)], 2*t1 + 3*x, 1)
# TODO: Add more tests, including ones with exponentials
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/x, t1)],
'L_K': [1], 'E_K': [], 'L_args': [x**2], 'E_args': []})
assert is_deriv_k(Poly(x, t1), Poly(1, t1), DE) == \
([(t1, S(1)/2)], t1/2, 1)
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(2/(1 + x), t0)],
'L_K': [1], 'E_K': [], 'L_args': [x**2 + 2*x + 1], 'E_args': []})
assert is_deriv_k(Poly(1 + x, t0), Poly(1, t0), DE) == \
([(t0, S(1)/2)], t0/2, 1)
