*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*-- 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

- Write precision classes for power series, analogous to those for polynomials.
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.Implement cool stuff for p-adic differential equations.