While you can't run Sage directly on the iPhone, you can certainly
connect to a Sage notebook server and use Sage via the web interface.
If you don't have your own Sage server set up, you could use
http://www.sagenb.org
--Mike
You could also presumably write an iphone app that uses Sage via an
internet connection "behind the scenes" to do computation. This app
would of course only
work if one was online.
That said, what do you want to do with polynomial equations? "Support
polynomial equations" is too vague.
-- William