code: def normal_denom(fa, fd, ga, gd, DE):
      """
      Normal part of the denominator.
  
      Explanation
      ===========
  
      Given a derivation D on k[t] and f, g in k(t) with f weakly
      normalized with respect to t, either raise NonElementaryIntegralException,
      in which case the equation Dy + f*y == g has no solution in k(t), or the
      quadruplet (a, b, c, h) such that a, h in k[t], b, c in k<t>, and for any
      solution y in k(t) of Dy + f*y == g, q = y*h in k<t> satisfies
      a*Dq + b*q == c.
  
      This constitutes step 1 in the outline given in the rde.py docstring.
      """
      dn, ds = splitfactor(fd, DE)
      en, es = splitfactor(gd, DE)
  
      p = dn.gcd(en)
      h = en.gcd(en.diff(DE.t)).quo(p.gcd(p.diff(DE.t)))
  
      a = dn * h
      c = a * h
      if c.div(en)[1]:
          # en does not divide dn*h**2
          raise NonElementaryIntegralException
      ca = c * ga
      ca, cd = ca.cancel(gd, include=True)
  
      ba = a * fa - dn * derivation(h, DE) * fd
      ba, bd = ba.cancel(fd, include=True)
  
      # (dn*h, dn*h*f - dn*Dh, dn*h**2*g, h)
      return (a, (ba, bd), (ca, cd), h)
  
imports: from operator import mul
  from functools import reduce
  from sympy.core import oo
  from sympy.core.symbol import Dummy
  from sympy.polys import Poly, gcd, ZZ, cancel
  from sympy.functions.elementary.complexes import im, re
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.integrals.risch import gcdex_diophantine, frac_in, derivation, splitfactor, NonElementaryIntegralException, DecrementLevel, recognize_log_derivative
label_desc: Use image node_id 4 for calling a global function with example usage: normal_denom(fa, fd, ga, gd, DE) and returns: a,  ba,  bd,  ca,  cd,  h