Once again, thanks to all that contributed to my small storage of knowledge involving this and other points of classic concern. Just to review, the problem is that when I received the Gios from the shop, the seat post (SR) was cracked, and after I soaked overnight in ammonia, and attempted extraction the seatpost broke one inch below the top of the seatpost lug. All advice has been helpful and encouraging, but I am beginning to make my cuts with a hand saw handle that allows the use of bi-metal saws-all type blades and even though I have completed three cuts, there is no extraction yet. My wife says to remain "Zen" and just continue in total focus, and eventually a solution will come. My hope is to give the post at least four complete cuts and then to soak in ammonia again, to achieve the best possible penetration of caustic that is possible. Because I have nothing to grab onto, I will probably have to plan for an extended campaign. If anyone has any advise specific to how to extract a post that has broken off below the lug, please feel more than free to offer it, or even to offer encouragement.
Thanks to all, I am Garth Libre in Miami Shores,, still hopeful, still enthusiastic.