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