code: def test_root_system():
      c = RootSystem("A3")
      assert c.cartan_type == TypeA(3)
      assert c.simple_roots() == {
          1: [1, -1, 0, 0],
          2: [0, 1, -1, 0],
          3: [0, 0, 1, -1],
      }
      assert c.root_space() == "alpha[1] + alpha[2] + alpha[3]"
      assert c.cartan_matrix() == Matrix(
          [[2, -1, 0], [-1, 2, -1], [0, -1, 2]]
      )
      assert c.dynkin_diagram() == "0---0---0\n1   2   3"
      assert c.add_simple_roots(1, 2) == [1, 0, -1, 0]
      assert c.all_roots() == {
          1: [1, -1, 0, 0],
          2: [1, 0, -1, 0],
          3: [1, 0, 0, -1],
          4: [0, 1, -1, 0],
          5: [0, 1, 0, -1],
          6: [0, 0, 1, -1],
          7: [-1, 1, 0, 0],
          8: [-1, 0, 1, 0],
          9: [-1, 0, 0, 1],
          10: [0, -1, 1, 0],
          11: [0, -1, 0, 1],
          12: [0, 0, -1, 1],
      }
      assert c.add_as_roots([1, 0, -1, 0], [0, 0, 1, -1]) == [
          1,
          0,
          0,
          -1,
      ]
  
imports: from sympy.liealgebras.root_system import RootSystem
  from sympy.liealgebras.type_a import TypeA
  from sympy.matrices import Matrix
label_desc: Use image node_id 1 for calling a global function with example usage: test_root_system() without return types