code: def save_monomial_index(filename, monomial_index):
      
      monomial_translation = [''] * (len(monomial_index) + 1)
      for key, k in monomial_index.items():
          monomial_translation[k] = convert_monomial_to_string(key)
      file_ = open(filename, 'w')
      for k in range(len(monomial_translation)):
          file_.write('%s %s\n' % (k, monomial_translation[k]))
      file_.close()
docs: Save a monomial dictionary for debugging purposes.
  
      :param filename: The name of the file to save to.
      :type filename: str.
      :param monomial_index: The monomial index of the SDP relaxation.
      :type monomial_index: dict of :class:`sympy.core.expr.Expr`.