code: def dmp_fateman_poly_F_1(n, K):
      """Fateman's GCD benchmark: trivial GCD"""
      u = [K(1), K(0)]
  
      for i in range(n):
          u = [dmp_one(i, K), u]
  
      v = [K(1), K(0), K(0)]
  
      for i in range(0, n):
          v = [dmp_one(i, K), dmp_zero(i), v]
  
      m = n - 1
  
      U = dmp_add_term(u, dmp_ground(K(1), m), 0, n, K)
      V = dmp_add_term(u, dmp_ground(K(2), m), 0, n, K)
  
      f = [[-K(3), K(0)], [], [K(1), K(0), -K(1)]]
  
      W = dmp_add_term(v, dmp_ground(K(1), m), 0, n, K)
      Y = dmp_raise(f, m, 1, K)
  
      F = dmp_mul(U, V, n, K)
      G = dmp_mul(W, Y, n, K)
  
      H = dmp_one(n, K)
  
      return F, G, H
  
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 7 for calling a global function with example usage: dmp_fateman_poly_F_1(n, K) and returns: F,  G,  H