def test_diff_no_eval_derivative():
class My(Expr):
def __new__(cls, x):
return Expr.__new__(cls, x)
# My doesn't have its own _eval_derivative method
assert My(x).diff(x).func is Derivative
assert My(x).diff(x, 3).func is Derivative
assert re(x).diff(x, 2) == Derivative(re(x), (x, 2)) # issue 15518
assert diff(NDimArray([re(x), im(x)]), (x, 2)) == NDimArray(
[Derivative(re(x), (x, 2)), Derivative(im(x), (x, 2))])
# it doesn't have y so it shouldn't need a method for this case
assert My(x).diff(y) == 0
def __init__(self, iterable):
from sympy.matrices.matrices import MatrixBase
from sympy.tensor.array import NDimArray
if not isinstance(iterable, (Iterable, MatrixBase)):
raise NotImplementedError("Data type not yet supported")
if isinstance(iterable, list):
iterable = NDimArray(iterable)
self._iter = iterable
self._idx = 0
def test_diff_nth_derivative():
f = Function("f")
n = Symbol("n", integer=True)
expr = diff(sin(x), (x, n))
expr2 = diff(f(x), (x, 2))
expr3 = diff(f(x), (x, n))
assert expr.subs(sin(x), cos(-x)) == Derivative(cos(-x), (x, n))
assert expr.subs(n, 1).doit() == cos(x)
assert expr.subs(n, 2).doit() == -sin(x)
assert expr2.subs(Derivative(f(x), x), y) == Derivative(y, x)
# Currently not supported (cannot determine if `n > 1`):
# assert expr3.subs(Derivative(f(x), x), y) == Derivative(y, (x, n-1))
assert expr3 == Derivative(f(x), (x, n))
assert diff(x, (x, n)) == Piecewise((x, Eq(n, 0)), (1, Eq(n, 1)),
(0, True))
assert diff(2 * x, (x, n)).dummy_eq(
Sum(
Piecewise(
(
2 * x * factorial(n) / (factorial(y) * factorial(-y + n)),
Eq(y, 0) & Eq(Max(0, -y + n), 0),
),
(
2 * factorial(n) / (factorial(y) * factorial(-y + n)),
Eq(y, 0) & Eq(Max(0, -y + n), 1),
),
(0, True),
),
(y, 0, n),
))
# TODO: assert diff(x**2, (x, n)) == x**(2-n)*ff(2, n)
exprm = x * sin(x)
mul_diff = diff(exprm, (x, n))
assert isinstance(mul_diff, Sum)
for i in range(5):
assert mul_diff.subs(n, i).doit() == exprm.diff((x, i)).expand()
exprm2 = 2 * y * x * sin(x) * cos(x) * log(x) * exp(x)
dex = exprm2.diff((x, n))
assert isinstance(dex, Sum)
for i in range(7):
assert dex.subs(n, i).doit().expand() == exprm2.diff((x, i)).expand()
assert (cos(x) * sin(y)).diff([[x, y, z]]) == NDimArray(
[-sin(x) * sin(y), cos(x) * cos(y), 0])
