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| == Sunday Project Proposals == | == Projects == |
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| * [[/FunctionFields|Function Fields]] -- Hess' automorphism algorithm for finding isomorphisms between function fields. | * [[/FunctionFields|Function Fields]] -- implementing p-adic function fields |
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| * [[/HilbertSymbols|Hilbert symbols]] -- General Hilbert symbols for p-adic fields. | |
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| * [[/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) |
* [[/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) |
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| * [[/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 |
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")