* ''Goal'' -- Finally finish incorporating the changes of #6084, which conceptually splits the precision a polynomial is defined up to from an approximation of the coefficients. 
 * ''Type'' -- precision handling, speed improvements
 * ''Priority'' -- High
 * ''Difficulty'' -- Annoying
 * ''Prerequisites'' -- None
 * ''Background'' -- 
 * ''Contributors'' -- David Roe
 * ''Progress'' - I've been almost done with this for a long time now.  At this point the code has bit-rotted to some extent and there are doctests to fix.  It's also going to be a big project to referee
 * ''Related Tickets'' -- 

== Discussion ==

== Tasks ==

 1. Rescue the code from [[http://trac.sagemath.org/sage_trac/ticket/6084 | #6084]] and get it in a state where it can be reviewed.