padics/UnivariatePowerSeriesPadic

• 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

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

2. 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.

3. Implement cool stuff for p-adic differential equations.