* ''Goal'' -- Separate precision from approximation for power series. Include precision types that give information about the valuations for ALL coefficients (not just the first n). Write functions for solving p-adic differential equations. 
 * ''Type'' -- speed improvements, precision handling, advanced functionality
 * ''Priority'' -- Medium-Low
 * ''Difficulty'' -- Medium-Hard
 * ''Prerequisites'' -- [[../PolynomialPrecision | polynomial precision]]
 * ''Background'' -- Take a look at this book: Kedlaya, Kiran.  p-adic Differential Equations, Cambridge Studies in Advanced Mathematics 125, Cambridge Univ. Press, 2010.
 * ''Contributors'' -- 
 * ''Progress'' - not started
 * ''Related Tickets'' -- 

== Discussion ==

== Tasks ==

 1. Write precision classes for power series, analogous to those for polynomials. 

 1. Write a subclass of `PowerSeries_poly` to take advantage of these precision structures.  Implement nontrivial power series functionality using an approximation and the precision object.

 1. Implement cool stuff for p-adic differential equations.  :-)