code: def test_representing_matrices():
      R, x, y = ring("x,y", QQ, grlex)
  
      basis = [(0, 0), (0, 1), (1, 0), (1, 1)]
      F = [x**2 - x - 3 * y + 1, -2 * x + y**2 + y - 1]
  
      assert _representing_matrices(basis, F, R) == [
          [
              [QQ(0, 1), QQ(0, 1), -QQ(1, 1), QQ(3, 1)],
              [QQ(0, 1), QQ(0, 1), QQ(3, 1), -QQ(4, 1)],
              [QQ(1, 1), QQ(0, 1), QQ(1, 1), QQ(6, 1)],
              [QQ(0, 1), QQ(1, 1), QQ(0, 1), QQ(1, 1)],
          ],
          [
              [QQ(0, 1), QQ(1, 1), QQ(0, 1), -QQ(2, 1)],
              [QQ(1, 1), -QQ(1, 1), QQ(0, 1), QQ(6, 1)],
              [QQ(0, 1), QQ(2, 1), QQ(0, 1), QQ(3, 1)],
              [QQ(0, 1), QQ(0, 1), QQ(1, 1), -QQ(1, 1)],
          ],
      ]
  
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 26 for calling a global function with example usage: test_representing_matrices() without return types