def test_replace_arrays_partial_derivative():
x, y, z, t = symbols("x y z t")
expr = PartialDerivative(A(i), A(j))
assert expr.replace_with_arrays({A(i): [x, y]}, [i, j]) == Array([[1, 0], [0, 1]])
expr = PartialDerivative(A(i), A(-i))
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 0
expr = PartialDerivative(A(-i), A(i))
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 0
def test_replace_arrays_partial_derivative():
x, y, z, t = symbols("x y z t")
expr = PartialDerivative(A(i), A(j))
assert expr.replace_with_arrays({A(i): [x, y]}, [i, j]) == Array([[1, 0],
[0, 1]])
expr = PartialDerivative(A(i), A(-i))
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 0
expr = PartialDerivative(A(-i), A(i))
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 0
def test_replace_arrays_partial_derivative():
x, y, z, t = symbols("x y z t")
# d(A^i)/d(A_j) = d(g^ik A_k)/d(A_j) = g^ik delta_jk
expr = PartialDerivative(A(i), A(-j))
assert expr.get_free_indices() == [i, j]
assert expr.get_indices() == [i, j]
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, 1)
}, [i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, -1)
}, [i, j]) == Array([[1, 0], [0, -1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, 1)
}, [i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, -1)
}, [i, j]) == Array([[1, 0], [0, -1]])
expr = PartialDerivative(A(i), A(j))
assert expr.get_free_indices() == [i, -j]
assert expr.get_indices() == [i, -j]
assert expr.replace_with_arrays({A(i): [x, y]}, [i, -j]) == Array([[1, 0],
[0, 1]])
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, 1)
}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, -1)
}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, 1)
}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, -1)
}, [i, -j]) == Array([[1, 0], [0, 1]])
expr = PartialDerivative(A(-i), A(-j))
expr.get_free_indices() == [-i, j]
expr.get_indices() == [-i, j]
assert expr.replace_with_arrays({A(-i): [x, y]}, [-i, j]) == Array([[1, 0],
[0,
1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, 1)
}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(-i): [x, y],
L: diag(1, -1)
}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, 1)
}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({
A(i): [x, y],
L: diag(1, -1)
}, [-i, j]) == Array([[1, 0], [0, 1]])
expr = PartialDerivative(A(i), A(i))
assert expr.get_free_indices() == []
assert expr.get_indices() == [L_0, -L_0]
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 2
expr = PartialDerivative(A(-i), A(-i))
assert expr.get_free_indices() == []
assert expr.get_indices() == [-L_0, L_0]
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 2
expr = PartialDerivative(H(i, j) + H(j, i), A(i))
assert expr.get_indices() == [L_0, j, -L_0]
assert expr.get_free_indices() == [j]
expr = PartialDerivative(H(i, j) + H(j, i), A(k)) * B(-i)
assert expr.get_indices() == [L_0, j, -k, -L_0]
assert expr.get_free_indices() == [j, -k]
expr = PartialDerivative(A(i) * (H(-i, j) + H(j, -i)), A(j))
assert expr.get_indices() == [L_0, -L_0, L_1, -L_1]
assert expr.get_free_indices() == []
expr = A(j) * A(-j) + expr
assert expr.get_indices() == [L_0, -L_0, L_1, -L_1]
assert expr.get_free_indices() == []
expr = A(i) * (B(j) * PartialDerivative(C(-j), D(i)) +
C(j) * PartialDerivative(D(-j), B(i)))
assert expr.get_indices() == [L_0, L_1, -L_1, -L_0]
assert expr.get_free_indices() == []
expr = A(i) * PartialDerivative(C(-j), D(i))
assert expr.get_indices() == [L_0, -j, -L_0]
assert expr.get_free_indices() == [-j]
def test_replace_arrays_partial_derivative():
x, y, z, t = symbols("x y z t")
# d(A^i)/d(A_j) = d(g^ik A_k)/d(A_j) = g^ik delta_jk
expr = PartialDerivative(A(i), A(-j))
assert expr.get_free_indices() == [i, j]
assert expr.get_indices() == [i, j]
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, [i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, [i, j]) == Array([[1, 0], [0, -1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, 1)}, [i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, -1)}, [i, j]) == Array([[1, 0], [0, -1]])
expr = PartialDerivative(A(i), A(j))
assert expr.get_free_indices() == [i, -j]
assert expr.get_indices() == [i, -j]
assert expr.replace_with_arrays({A(i): [x, y]}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, 1)}, [i, -j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, -1)}, [i, -j]) == Array([[1, 0], [0, 1]])
expr = PartialDerivative(A(-i), A(-j))
expr.get_free_indices() == [-i, j]
expr.get_indices() == [-i, j]
assert expr.replace_with_arrays({A(-i): [x, y]}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, 1)}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(-i): [x, y], L: diag(1, -1)}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, [-i, j]) == Array([[1, 0], [0, 1]])
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, [-i, j]) == Array([[1, 0], [0, 1]])
expr = PartialDerivative(A(i), A(i))
assert expr.get_free_indices() == []
assert expr.get_indices() == [L_0, -L_0]
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 2
expr = PartialDerivative(A(-i), A(-i))
assert expr.get_free_indices() == []
assert expr.get_indices() == [-L_0, L_0]
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, 1)}, []) == 2
assert expr.replace_with_arrays({A(i): [x, y], L: diag(1, -1)}, []) == 2