code: def test_conversion():
      f = [x**2 + y**2, 2 * z]
      g = [
          ((1, 0, 0, 1), QQ(2)),
          ((0, 2, 0, 0), QQ(1)),
          ((0, 0, 2, 0), QQ(1)),
      ]
      assert sdm_to_vector(g, [x, y, z], QQ) == f
      assert sdm_from_vector(f, lex, QQ) == g
      assert sdm_from_vector([x, 1], lex, QQ) == [
          ((1, 0), QQ(1)),
          ((0, 1), QQ(1)),
      ]
      assert sdm_to_vector([((1, 1, 0, 0), 1)], [x, y, z], QQ, n=3) == [
          0,
          x,
          0,
      ]
      assert sdm_from_vector([0, 0], lex, QQ, gens=[x, y]) == sdm_zero()
  
imports: from sympy.polys.distributedmodules import sdm_monomial_mul, sdm_monomial_deg, sdm_monomial_divides, sdm_add, sdm_LM, sdm_LT, sdm_mul_term, sdm_zero, sdm_deg, sdm_LC, sdm_from_dict, sdm_spoly, sdm_ecart, sdm_nf_mora, sdm_groebner, sdm_from_vector, sdm_to_vector, sdm_monomial_lcm
  from sympy.polys.orderings import lex, grlex, InverseOrder
  from sympy.polys.domains import QQ
  from sympy.abc import x, y, z
label_desc: Use image node_id 16 for calling a global function with example usage: test_conversion() without return types