Should I polish a cast iron pan for use on a glass cooktop? There was a question asked here about using cast iron on glass top ranges. In the responses, there was a link to an article about cast iron equipment. Here is a quote.


  There is also an almost comically simple alternative for a more
  permanent fix. It's one of those ideas like the safety pin or the
  paper clip: blindingly obvious in hindsight, but not apparent at once.
  Just sandpaper the pan or pot bottom smooth! Readers have reported to
  us that they have done just that, with excellent results. We don't
  have details, but we'd guess that two grades of sandpaper, a coarse
  then a fine for polishing off, would do the job. 


I am getting my first brand-new electric glass-top range, and I don't want to ruin it. The quote said they are guessing, but with Stack Exchange, there is no guessing just real experiences. How do you polish the cast iron to make the bottom smoother? Did you see an improvement?
This will be a short answer as there is not much to say: 

I have used cast iron pans on my glass stove top for about five years, and the surface does not show any scratches or marks. I have not taken any special care to protect the surface, and certainly have not polished the iron.