code: def _do_test_benchmark_minpoly():
      R, x, y, z = ring("x,y,z", QQ, lex)
  
      F = [x**3 + x + 1, y**2 + y + 1, (x + y) * z - (x**2 + y)]
      G = [
          x
          + QQ(155, 2067) * z**5
          - QQ(355, 689) * z**4
          + QQ(6062, 2067) * z**3
          - QQ(3687, 689) * z**2
          + QQ(6878, 2067) * z
          - QQ(25, 53),
          y
          + QQ(4, 53) * z**5
          - QQ(91, 159) * z**4
          + QQ(523, 159) * z**3
          - QQ(387, 53) * z**2
          + QQ(1043, 159) * z
          - QQ(308, 159),
          z**6
          - 7 * z**5
          + 41 * z**4
          - 82 * z**3
          + 89 * z**2
          - 46 * z
          + 13,
      ]
  
      assert groebner(F, R) == G
  
imports: from sympy.polys.groebnertools import groebner, sig, sig_key, lbp, lbp_key, critical_pair, cp_key, is_rewritable_or_comparable, Sign, Polyn, Num, s_poly, f5_reduce, groebner_lcm, groebner_gcd, is_groebner, is_reduced
  from sympy.polys.fglmtools import _representing_matrices
  from sympy.polys.orderings import lex, grlex
  from sympy.polys.rings import ring, xring
  from sympy.polys.domains import ZZ, QQ
  from sympy.testing.pytest import slow
  from sympy.polys import polyconfig
label_desc: Use image node_id 4 for calling a global function with example usage: _do_test_benchmark_minpoly() without return types