code: def groebner_gcd(f, g):
      """Computes GCD of two polynomials using Groebner bases."""
      if f.ring != g.ring:
          raise ValueError("Values should be equal")
      domain = f.ring.domain
  
      if not domain.is_Field:
          fc, f = f.primitive()
          gc, g = g.primitive()
          gcd = domain.gcd(fc, gc)
  
      H = (f * g).quo([groebner_lcm(f, g)])
  
      if len(H) != 1:
          raise ValueError("Length should be 1")
      h = H[0]
  
      if not domain.is_Field:
          return gcd * h
      else:
          return h.monic()
  
imports: from sympy.core.symbol import Dummy
  from sympy.polys.monomials import monomial_mul, monomial_lcm, monomial_divides, term_div
  from sympy.polys.orderings import lex
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.polyconfig import query
label_desc: Use image node_id 28 for calling a global function with example usage: groebner_gcd(f, g) and returns: unknown, h