def test_issue_11726():
x, t = symbols("x t")
f = symbols("f", cls=Function)
X, T = symbols("X T", cls=Function)
u = f(x, t)
eq = u.diff(x, 2) - u.diff(t, 2)
res = pde_separate(eq, u, [T(x), X(t)])
assert res == [D(T(x), x, x) / T(x), D(X(t), t, t) / X(t)]
def test_issue_11726():
x, t = symbols("x t")
f = symbols("f", cls=Function)
X, T = symbols("X T", cls=Function)
u = f(x, t)
eq = u.diff(x, 2) - u.diff(t, 2)
res = pde_separate(eq, u, [T(x), X(t)])
assert res == [D(T(x), x, x)/T(x),D(X(t), t, t)/X(t)]
def test_pde_separate():
x, y, z, t = symbols("x,y,z,t")
F, T, X, Y, Z, u = map(Function, 'FTXYZu')
eq = Eq(D(u(x, t), x), D(u(x, t), t) * exp(u(x, t)))
raises(ValueError, lambda: pde_separate(eq, u(x, t), [X(x), T(t)], 'div'))
def test_pde_separate():
x, y, z, t = symbols("x,y,z,t")
F, T, X, Y, Z, u = map(Function, 'FTXYZu')
eq = Eq(D(u(x, t), x), D(u(x, t), t)*exp(u(x, t)))
raises(ValueError, lambda: pde_separate(eq, u(x, t), [X(x), T(t)], 'div'))