code: def test_macaulay_example_one():
      """Tests the Macaulay for example from [Bruce97]_"""
  
      x, y, z = symbols("x, y, z")
      a_1_1, a_1_2, a_1_3 = symbols("a_1_1, a_1_2, a_1_3")
      a_2_2, a_2_3, a_3_3 = symbols("a_2_2, a_2_3, a_3_3")
      b_1_1, b_1_2, b_1_3 = symbols("b_1_1, b_1_2, b_1_3")
      b_2_2, b_2_3, b_3_3 = symbols("b_2_2, b_2_3, b_3_3")
      c_1, c_2, c_3 = symbols("c_1, c_2, c_3")
  
      f_1 = (
          a_1_1 * x**2
          + a_1_2 * x * y
          + a_1_3 * x * z
          + a_2_2 * y**2
          + a_2_3 * y * z
          + a_3_3 * z**2
      )
      f_2 = (
          b_1_1 * x**2
          + b_1_2 * x * y
          + b_1_3 * x * z
          + b_2_2 * y**2
          + b_2_3 * y * z
          + b_3_3 * z**2
      )
      f_3 = c_1 * x + c_2 * y + c_3 * z
  
      mac = MacaulayResultant([f_1, f_2, f_3], [x, y, z])
  
      assert mac.degrees == [2, 2, 1]
      assert mac.degree_m == 3
  
      assert mac.monomial_set == [
          x**3,
          x**2 * y,
          x**2 * z,
          x * y**2,
          x * y * z,
          x * z**2,
          y**3,
          y**2 * z,
          y * z**2,
          z**3,
      ]
      assert mac.monomials_size == 10
      assert mac.get_row_coefficients() == [
          [x, y, z],
          [x, y, z],
          [x * y, x * z, y * z, z**2],
      ]
  
      matrix = mac.get_matrix()
      assert matrix.shape == (mac.monomials_size, mac.monomials_size)
      assert mac.get_submatrix(matrix) == Matrix(
          [[a_1_1, a_2_2], [b_1_1, b_2_2]]
      )
  
file_path: sympy/sympy/polys/tests/test_multivariate_resultants.py
imports: from sympy.matrices.dense import Matrix
  from sympy.polys.polytools import factor
  from sympy.core import symbols
  from sympy.tensor.indexed import IndexedBase
  from sympy.polys.multivariate_resultants import DixonResultant, MacaulayResultant
label_desc: Use image node_id 14 for calling a global function with example usage: test_macaulay_example_one() without return types