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.
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 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
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")