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| As the workshop progresses we'll be using this space to organize work on these projects. You should feel free now to add projects you'd like to see worked on either to this page or the [[padics|the enhancements page]]. | == Projects == * [[/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. * [[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) * [[http://trac.sagemath.org/sage_trac/ticket/812|Trac 812: p-adic L-series via overconvergent modular symbols]] (William Stein, Jennifer Balakrishnan) * [[/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/8241|Trac 8241: 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 == 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.
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.
Trac 12545: create highly optimized p-adic L-series implementation for various special cases (William Stein, Jennifer Balakrishnan)
Trac 812: p-adic L-series via overconvergent modular symbols (William Stein, Jennifer Balakrishnan)
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 8241: 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
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")