Dear Sage lovers,
I've recently written several patches/packages related to p-adics
in Sage. Here is an overview of what I've done:
. an implementation of Frobenius endormophisms over p-adic
rings (as morphism - the method x.frobenius() already exists)
. an implementation of Newton polygons as a separated class
. an implementation of several useful function on polynomials over
p-adic rings and fields (like Hensel lift, slope factorization)
. an implementation of bounded convergent series over ultrametic
balls (this includes in particular power series over rings like
Z_p); this patch is undocumented yet
. (very early stage) based on some discussions with David Roe, a
package implementating a new approch to p-adics (and actually,
more generally to inexact elements): the main feature is that
approximation and precision are now completely separated objects
(which should allow at some point more flexibility).
This package also provides a first implementation of lazy p-adics.
and hopefully, coming soon (I'm working on this currently):
. an implementation of several useful decompositions of matrices
over p-adics (like Hermite form, Smith form, LU factorization)
together with a special implementation of modules over p-adic
rings and vector spaces over p-adic fields
All of this is available online on the CETHop website:
http://cethop.math.cnrs.fr/prodscient/algos.html
(webpage written in french, sorry).
Also available are some demo worksheets:
https://cethop.math.cnrs.fr:8443/pub/
The page:
https://cethop.math.cnrs.fr:8443/
provides an access to a sage session (via the Notebook) where all
the above patches are applied. You can then use them inline if you
don't want to install them on your computer. If you want an account
on this Notebook, please just email and ask me.
Until now, I've not submitted these patches to the trac server. I
actually would like to have some feedback before. So please, don't
hesitate to comment on my work.
By the way, I have the vague project to organize Sage Days (about
p-adics) in September in Rennes. Could you please tell me if you
could be interested and available at that time?
Best wishes,
--Xavier
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