docs: def formula_to_dbid(formula_str, backslash_fix=False):
      """
      Convert a LaTeX formula to the database index.
  
      Parameters
      ----------
      formula_str : string
          The formula as LaTeX code.
      backslash_fix : boolean
          If this is set to true, then it will be checked if the same formula
          exists with a preceeding backslash.
  
      Returns
      -------
      int :
          The database index.
      """
      global __formula_to_dbid_cache
      if __formula_to_dbid_cache is None:
          mysql = utils.get_mysql_cfg()
          connection = pymysql.connect(host=mysql['host'],
                                       user=mysql['user'],
                                       passwd=mysql['passwd'],
                                       db=mysql['db'],
                                       charset='utf8mb4',
                                       cursorclass=pymysql.cursors.DictCursor)
          cursor = connection.cursor()
  
          # Get all formulas that should get examined
          sql = ("SELECT `id`, `formula_in_latex` FROM `wm_formula` ")
          cursor.execute(sql)
          formulas = cursor.fetchall()
          __formula_to_dbid_cache = {}
          for fm in formulas:
              __formula_to_dbid_cache[fm['formula_in_latex']] = fm['id']
      if formula_str in __formula_to_dbid_cache:
          return __formula_to_dbid_cache[formula_str]
      elif backslash_fix and ('\\%s' % formula_str) in __formula_to_dbid_cache:
          return __formula_to_dbid_cache['\\%s' % formula_str]
      else:
          logging.info("Symbol '%s' was not found. Add it to write-math.com.",
                       formula_str)
          mysql = utils.get_mysql_cfg()
          connection = pymysql.connect(host=mysql['host'],
                                       user=mysql['user'],
                                       passwd=mysql['passwd'],
                                       db=mysql['db'],
                                       charset='utf8mb4',
                                       cursorclass=pymysql.cursors.DictCursor)
          cursor = connection.cursor()
          sql = ("INSERT INTO `wm_formula` (`user_id`, `formula_name`, "
                 "`formula_in_latex`, "
                 "`mode`, `package`) VALUES ("
                 "'10', %s, %s, 'bothmodes', NULL);")
          if len(formula_str) < 20:
              logging.info("Insert formula %s.", formula_str)
          cursor.execute(sql, (formula_str, formula_str))
          connection.commit()
          __formula_to_dbid_cache[formula_str] = connection.insert_id()
          return __formula_to_dbid_cache[formula_str]