code: def _dmp_simplify_gcd(f, g, u, K):
      """Try to eliminate `x_0` from GCD computation in `K[X]`."""
      df = dmp_degree(f, u)
      dg = dmp_degree(g, u)
  
      if df > 0 and dg > 0:
          return None
  
      if not (df or dg):
          F = dmp_LC(f, K)
          G = dmp_LC(g, K)
      else:
          if not df:
              F = dmp_LC(f, K)
              G = dmp_content(g, u, K)
          else:
              F = dmp_content(f, u, K)
              G = dmp_LC(g, K)
  
      v = u - 1
      h = dmp_gcd(F, G, v, K)
  
      cff = [dmp_quo(cf, h, v, K) for cf in f]
      cfg = [dmp_quo(cg, h, v, K) for cg in g]
  
      return [h], cff, cfg
  
imports: from sympy.polys.densearith import dup_sub_mul, dup_neg, dmp_neg, dmp_add, dmp_sub, dup_mul, dmp_mul, dmp_pow, dup_div, dmp_div, dup_rem, dup_quo, dmp_quo, dup_prem, dmp_prem, dup_mul_ground, dmp_mul_ground, dmp_mul_term, dup_quo_ground, dmp_quo_ground, dup_max_norm, dmp_max_norm
  from sympy.polys.densebasic import dup_strip, dmp_raise, dmp_zero, dmp_one, dmp_ground, dmp_one_p, dmp_zero_p, dmp_zeros, dup_degree, dmp_degree, dmp_degree_in, dup_LC, dmp_LC, dmp_ground_LC, dmp_multi_deflate, dmp_inflate, dup_convert, dmp_convert, dmp_apply_pairs
  from sympy.polys.densetools import dup_clear_denoms, dmp_clear_denoms, dup_diff, dmp_diff, dup_eval, dmp_eval, dmp_eval_in, dup_trunc, dmp_ground_trunc, dup_monic, dmp_ground_monic, dup_primitive, dmp_ground_primitive, dup_extract, dmp_ground_extract
  from sympy.polys.galoistools import gf_int, gf_crt
  from sympy.polys.polyconfig import query
  from sympy.polys.polyerrors import MultivariatePolynomialError, HeuristicGCDFailed, HomomorphismFailed, NotInvertible, DomainError
label_desc: Use image node_id 29 for calling a global function with example usage: _dmp_simplify_gcd(f, g, u, K) and returns: list,  cff,  cfg, None