Diff for "padicSageDays/Projects"

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.

• FLINT 2 -- Get FLINT 2 into Sage. See #12173.

• 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")