code: def test_eval_partial_derivative_single_1st_rank_tensors_by_tensor():
      expr1 = PartialDerivative(A(i), A(j))
      assert expr1._perform_derivative() - L.delta(i, -j) == 0
  
      expr2 = PartialDerivative(A(i), A(-j))
      assert (
          expr2._perform_derivative()
          - L.metric(i, L_0) * L.delta(-L_0, j)
          == 0
      )
  
      expr3 = PartialDerivative(A(-i), A(-j))
      assert expr3._perform_derivative() - L.delta(-i, j) == 0
  
      expr4 = PartialDerivative(A(-i), A(j))
      assert (
          expr4._perform_derivative()
          - L.metric(-i, -L_0) * L.delta(L_0, -j)
          == 0
      )
  
      expr5 = PartialDerivative(A(i), B(j))
      expr6 = PartialDerivative(A(i), C(j))
      expr7 = PartialDerivative(A(i), D(j))
      expr8 = PartialDerivative(A(i), H(j, k))
      assert expr5._perform_derivative() == 0
      assert expr6._perform_derivative() == 0
      assert expr7._perform_derivative() == 0
      assert expr8._perform_derivative() == 0
  
      expr9 = PartialDerivative(A(i), A(i))
      assert expr9._perform_derivative() - L.delta(L_0, -L_0) == 0
  
      expr10 = PartialDerivative(A(-i), A(-i))
      assert expr10._perform_derivative() - L.delta(-L_0, L_0) == 0
  
imports: from sympy import sin, cos
  from sympy.testing.pytest import raises
  from sympy.tensor.toperators import PartialDerivative
  from sympy.tensor.tensor import TensorIndexType, tensor_indices, TensorHead, tensor_heads
  from sympy.core.numbers import Rational
  from sympy.core.symbol import symbols
  from sympy.matrices.dense import diag
  from sympy.tensor.array import Array
  from sympy.core.random import randint
label_desc: Use image node_id 10 for calling a global function with example usage: test_eval_partial_derivative_single_1st_rank_tensors_by_tensor() without return types