code: def _w_1():
      R, x, y, z = ring("x,y,z", ZZ)
      return (
          4 * x**6 * y**4 * z**2
          + 4 * x**6 * y**3 * z**3
          - 4 * x**6 * y**2 * z**4
          - 4 * x**6 * y * z**5
          + x**5 * y**4 * z**3
          + 12 * x**5 * y**3 * z
          - x**5 * y**2 * z**5
          + 12 * x**5 * y**2 * z**2
          - 12 * x**5 * y * z**3
          - 12 * x**5 * z**4
          + 8 * x**4 * y**4
          + 6 * x**4 * y**3 * z**2
          + 8 * x**4 * y**3 * z
          - 4 * x**4 * y**2 * z**4
          + 4 * x**4 * y**2 * z**3
          - 8 * x**4 * y**2 * z**2
          - 4 * x**4 * y * z**5
          - 2 * x**4 * y * z**4
          - 8 * x**4 * y * z**3
          + 2 * x**3 * y**4 * z
          + x**3 * y**3 * z**3
          - x**3 * y**2 * z**5
          - 2 * x**3 * y**2 * z**3
          + 9 * x**3 * y**2 * z
          - 12 * x**3 * y * z**3
          + 12 * x**3 * y * z**2
          - 12 * x**3 * z**4
          + 3 * x**3 * z**3
          + 6 * x**2 * y**3
          - 6 * x**2 * y**2 * z**2
          + 8 * x**2 * y**2 * z
          - 2 * x**2 * y * z**4
          - 8 * x**2 * y * z**3
          + 2 * x**2 * y * z**2
          + 2 * x * y**3 * z
          - 2 * x * y**2 * z**3
          - 3 * x * y * z
          + 3 * x * z**3
          - 2 * y**2
          + 2 * y * z**2
      )
  
imports: from sympy.core import Add, Mul, Symbol, sympify, Dummy, symbols
  from sympy.core.containers import Tuple
  from sympy.core.singleton import S
  from sympy.ntheory import nextprime
  from sympy.polys.densearith import dmp_add_term, dmp_neg, dmp_mul, dmp_sqr
  from sympy.polys.densebasic import dmp_zero, dmp_one, dmp_ground, dup_from_raw_dict, dmp_raise, dup_random
  from sympy.polys.domains import ZZ
  from sympy.polys.factortools import dup_zz_cyclotomic_poly
  from sympy.polys.polyclasses import DMP
  from sympy.polys.polytools import Poly, PurePoly
  from sympy.polys.polyutils import _analyze_gens
  from sympy.utilities import subsets, public, filldedent
  from sympy.polys.rings import ring
label_desc: Use image node_id 19 for calling a global function with example usage: _w_1() and returns: unknown