code: def test_gf_trace_map():
      f = ZZ.map([1, 1, 4, 9, 1])
      a = [1, 1, 1]
      c = ZZ.map([1, 0])
      b = gf_pow_mod(c, 11, f, 11, ZZ)
  
      assert gf_trace_map(a, b, c, 0, f, 11, ZZ) == (
          [1, 1, 1],
          [1, 1, 1],
      )
      assert gf_trace_map(a, b, c, 1, f, 11, ZZ) == (
          [5, 2, 10, 3],
          [5, 3, 0, 4],
      )
      assert gf_trace_map(a, b, c, 2, f, 11, ZZ) == (
          [5, 9, 5, 3],
          [10, 1, 5, 7],
      )
      assert gf_trace_map(a, b, c, 3, f, 11, ZZ) == ([1, 10, 6, 0], [7])
      assert gf_trace_map(a, b, c, 4, f, 11, ZZ) == (
          [1, 1, 1],
          [1, 1, 8],
      )
      assert gf_trace_map(a, b, c, 5, f, 11, ZZ) == (
          [5, 2, 10, 3],
          [5, 3, 0, 0],
      )
      assert gf_trace_map(a, b, c, 11, f, 11, ZZ) == (
          [1, 10, 6, 0],
          [10],
      )
  
imports: from sympy.polys.galoistools import gf_crt, gf_crt1, gf_crt2, gf_int, gf_degree, gf_strip, gf_trunc, gf_normal, gf_from_dict, gf_to_dict, gf_from_int_poly, gf_to_int_poly, gf_neg, gf_add_ground, gf_sub_ground, gf_mul_ground, gf_add, gf_sub, gf_add_mul, gf_sub_mul, gf_mul, gf_sqr, gf_div, gf_rem, gf_quo, gf_exquo, gf_lshift, gf_rshift, gf_expand, gf_pow, gf_pow_mod, gf_gcdex, gf_gcd, gf_lcm, gf_cofactors, gf_LC, gf_TC, gf_monic, gf_eval, gf_multi_eval, gf_compose, gf_compose_mod, gf_trace_map, gf_diff, gf_irreducible, gf_irreducible_p, gf_irred_p_ben_or, gf_irred_p_rabin, gf_sqf_list, gf_sqf_part, gf_sqf_p, gf_Qmatrix, gf_Qbasis, gf_ddf_zassenhaus, gf_ddf_shoup, gf_edf_zassenhaus, gf_edf_shoup, gf_berlekamp, gf_factor_sqf, gf_factor, gf_value, linear_congruence, _csolve_prime_las_vegas, csolve_prime, gf_csolve, gf_frobenius_map, gf_frobenius_monomial_base
  from sympy.polys.polyerrors import ExactQuotientFailed
  from sympy.polys import polyconfig
  from sympy.polys.domains import ZZ
  from sympy.core.numbers import pi
  from sympy.ntheory.generate import nextprime
  from sympy.testing.pytest import raises
label_desc: Use image node_id 24 for calling a global function with example usage: test_gf_trace_map() without return types