We'll be drawing our projects from the following sources.

The wiki page for enhancements to p-adics in Sage.

The list of open p-adic tickets on Trac.

- Computational projects proposed by participants on Sunday afternoon.

## Projects

Power Series -- separate precision from arithmetic, come up with applications that it will be used for: power series that converge in a particular p-adic disc. Modules over these rings.

Factoring -- work on factoring of polynomials over local fields.

Templates -- templates for elements of p-adic fields.

Symbolic Integration -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage.

Logarithms and Exponentials -- logarithms and exponentials for p-adic extension fields.

Function Fields -- implementing p-adic function fields

Witt Vectors -- Witt vectors over general rings.

Completions -- Completions of number fields.

Linear Algebra -- think. then implement.

Inversion -- Speed up inversion.

nth roots -- Implement nth roots for p-adic elements.

Panayi's root finding algorithm -- Implement Panayi's p-adic root finding algorithm. (Simon Spicer; on hold)

Trac 12545: create highly optimized p-adic L-series implementation for various special cases (William Stein, Jennifer Balakrishnan, Simon Spicer)

Trac 812: p-adic L-series via overconvergent modular symbols (William Stein, Jennifer Balakrishnan, Simon Spicer)

Report and fix bugs in the p-adics -- some of our funding comes from this objective.

Bruhat Tits Tree -- Cameron and Marc's code into Sage.

Trac 8335: lattices of finite fields -- See also Trac 12117, Trac 12125, Trac 7240 and Trac 12133.

Trac 8240: conversion to and from residue fields of p-adic fields -- depends on Trac 12062, Trac 12053, Trac 12064, and Trac 12077, which all need review.

Additional Functions -- Implement the Artin-Hasse Exponential and the p-adic gamma function

Not directly related to p-adics but:

/SkewPolynomials -- Ring of skew polynomials over a finite field

## Miscellaneous

Here are my emacs files:

My sage.el file -- Download and put somewhere convenient

My pyrex.el file -- Download and put somewhere convenient

My .emacs file -- put in your home directory and edit the following two lines to the appropriate paths for the above files:

- (load "/Users/Roed/sage/sage-4.0/data/emacs/sage-mode.el")
- (load "/Users/Roed/sage/sage-4.0/data/emacs/pyrex-mode.el")