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== Sunday Project Proposals == == Projects ==
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 * [[/PowerSeries]] -- 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.
 * [[/SymbolicIntegration]] -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage.
 * [[/LogarithmsForExt]] -- logarithms and exponentials for p-adic extension fields.
 * [[/FunctionFields]] -- Hess' automorphism algorithm for finding isomorphisms between function fields.
 * [[/WittVectors]] -- Witt vectors over general rings.
 * [[/HilbertSymbols]] -- General Hilbert symbols for p-adic fields.
 * [[/Completions]] -- Completions of number fields.
 * [[/LinearAlgebra]] -- think. then implement.		  * [[/PowerSeries|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|Factoring]] -- work on factoring of polynomials over local fields.
 * [[/Templates|Templates]] -- templates for elements of p-adic fields.
 * [[/SymbolicIntegration|Symbolic Integration]] -- symbolic integration over p-adics. p-adic Igusa zeta functions. Get rational functions in a symbolic p. Look at Denef's webpage.
 * [[/LogarithmsForExt|Logarithms and Exponentials]] -- logarithms and exponentials for p-adic extension fields.
 * [[/FunctionFields|Function Fields]] -- implementing p-adic function fields
 * [[/WittVectors|Witt Vectors]] -- Witt vectors over general rings.
 * [[/Completions|Completions]] -- Completions of number fields.
 * [[/LinearAlgebra|Linear Algebra]] -- think. then implement.
 * [[/Inversion|Inversion]] -- Speed up inversion.
 * [[/nthRoots|nth roots]] -- Implement nth roots for p-adic elements.
 * [[/PadicRootAlgorithm|Panayi's root finding algorithm]] -- Implement Panayi's p-adic root finding algorithm. (Simon Spicer; on hold)
 * [[http://trac.sagemath.org/sage_trac/ticket/12545|Trac 12545: create highly optimized p-adic L-series implementation for various special cases]] (William Stein, Jennifer Balakrishnan, Simon Spicer)
 * [[http://trac.sagemath.org/sage_trac/ticket/812|Trac 812: p-adic L-series via overconvergent modular symbols]] (William Stein, Jennifer Balakrishnan, Simon Spicer)
 * [[/BugSquash|Report and fix bugs in the p-adics]] -- some of our funding comes from this objective.
 * [[/BruhatTitsTree|Bruhat Tits Tree]] -- Cameron and Marc's code into Sage.
 * [[/FLINT2|FLINT 2]] -- Get FLINT 2 into Sage. See [[http://trac.sagemath.org/sage_trac/ticket/12173|#12173]].
 * [[http://trac.sagemath.org/sage_trac/ticket/8335|Trac 8335: lattices of finite fields]] -- See also [[http://trac.sagemath.org/sage_trac/ticket/12117|Trac 12117]], [[http://trac.sagemath.org/sage_trac/ticket/12125|Trac 12125]], [[http://trac.sagemath.org/sage_trac/ticket/7240|Trac 7240]] and [[http://trac.sagemath.org/sage_trac/ticket/12133|Trac 12133]].
 * [[http://trac.sagemath.org/sage_trac/ticket/8240|Trac 8240: conversion to and from residue fields of p-adic fields]] -- depends on [[http://trac.sagemath.org/sage_trac/ticket/12062|Trac 12062]], [[http://trac.sagemath.org/sage_trac/ticket/12053|Trac 12053]], [[http://trac.sagemath.org/sage_trac/ticket/12064|Trac 12064]], and [[http://trac.sagemath.org/sage_trac/ticket/12077|Trac 12077]], which all need review.
 * [[/AdditionalFunctions|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:

 * [[http://sage.math.washington.edu/home/roed/sage.el|My sage.el file]] -- Download and put somewhere convenient
 * [[http://sage.math.washington.edu/home/roed/pyrex.el|My pyrex.el file]] -- Download and put somewhere convenient
 * [[http://sage.math.washington.edu/home/roed/.emacs|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")

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

Projects

Not directly related to p-adics but:

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")

padicSageDays/Projects (last edited 2012-02-22 22:45:40 by roed)