code: def dmp_ground_monic(f, u, K):
      """
      Divide all coefficients by ``LC(f)`` in ``K[X]``.
  
      Examples
      ========
  
      >>> from sympy.polys import ring, ZZ, QQ
  
      >>> R, x,y = ring("x,y", ZZ)
      >>> f = 3*x**2*y + 6*x**2 + 3*x*y + 9*y + 3
  
      >>> R.dmp_ground_monic(f)
      x**2*y + 2*x**2 + x*y + 3*y + 1
  
      >>> R, x,y = ring("x,y", QQ)
      >>> f = 3*x**2*y + 8*x**2 + 5*x*y + 6*x + 2*y + 3
  
      >>> R.dmp_ground_monic(f)
      x**2*y + 8/3*x**2 + 5/3*x*y + 2*x + 2/3*y + 1
  
      """
      if not u:
          return dup_monic(f, K)
  
      if dmp_zero_p(f, u):
          return f
  
      lc = dmp_ground_LC(f, u, K)
  
      if K.is_one(lc):
          return f
      else:
          return dmp_exquo_ground(f, lc, u, K)
  
imports: from sympy.polys.densearith import dup_add_term, dmp_add_term, dup_lshift, dup_add, dmp_add, dup_sub, dmp_sub, dup_mul, dmp_mul, dup_sqr, dup_div, dup_rem, dmp_rem, dmp_expand, dup_mul_ground, dmp_mul_ground, dup_quo_ground, dmp_quo_ground, dup_exquo_ground, dmp_exquo_ground
  from sympy.polys.densebasic import dup_strip, dmp_strip, dup_convert, dmp_convert, dup_degree, dmp_degree, dmp_to_dict, dmp_from_dict, dup_LC, dmp_LC, dmp_ground_LC, dup_TC, dmp_TC, dmp_zero, dmp_ground, dmp_zero_p, dup_to_raw_dict, dup_from_raw_dict, dmp_zeros
  from sympy.polys.polyerrors import MultivariatePolynomialError, DomainError
  from sympy.utilities import variations
  from math import ceil, log
label_desc: Use image node_id 21 for calling a global function with example usage: dmp_ground_monic(f, u, K) and returns: dup_monic, f, f, dmp_exquo_ground