Differential Geometry via SAGE
mikarm
teaching) and use SAGE for two or three years in the research work and
in the teaching as well.
SAGE includes rather developed methods in algebra, number theory,
algebraic geometry, etc. but lacks the differential geometry.
Therefore I would like to contribute to the SAGE development in this
direction.
To start with, I wrote a class 'parametrized_surface3d', made a
worksheet "Ellipsoid via SAGE" which demonstrates the methods of the
class in work and put it as a ticket to trac.sagemath.org
http://trac.sagemath.org/sage_trac/ticket/10132
Joris Vankerschaver inserted serious improvement to the code and made
a sage patch
http://trac.sagemath.org/sage_trac/attachment/ticket/10132/trac_10132_differential_geometry_sage.patch
I plan to write also the similar classes for curves on the plane and
in the 3-dimensional space, as well as a class for a surface given
implicitly. The further plans are Riemannian geometry, etc. (see the
discussion http://trac.sagemath.org/sage_trac/ticket/10132)
Also, I hope I will write a text-book "Elementary differential
geometry via SAGE" which in some sense will be similar to A.Gray's
book "Differential geometry via Mathematica".
The good thing is collaborate in development of differential geometry
in SAGE. One possibility to organize such a collaboration is, as it
was proposed by Andrey Novoseltsev, to make a wiki, which I will do
soon.
Any other ideas or suggestions?
William Stein
Run a Sage Days workshop!? I might be able to fund one, if you could
think of a group of relevant people to invite, dates that would work,
etc. It would be best if it were in Seattle. I might be able to get
Jack Lee, a professor here and author of one of the best books on
differential geometry (and Mathematica packages) involved too.
If you serious about organizing a Sage Days workshop, let me know. I
have some new funding for these during the next three years. They can
be a great way to get momentum, ideas, people, etc. Here's a list of
some so far: http://wiki.sagemath.org/Workshops
William
mikarm
At the same time, better first to get some results and to have at
least a small group working in this direction,
in order to have some base for discussion (not only good intentions,
but some real things). Let us look how the things will go.
If good, I think we should organize this event.
I did not know that Mathematica includes packages in differential
geometry, maybe because I haven't used it for a long time.
I know that Maple has a lot of differential geometry implemented, but
also I have no real experience in it, because I prefer the open source
tools.
Last years I used maxima, and then Sage.
Anyway, the experience of professor Jack Lee surely can help much in
the development of differential geometry in the Sage.
Mikhail
William Stein
>> Run a Sage Days workshop!?
>
> Good idea, thanks a lot!
> At the same time, better first to get some results and to have at
> least a small group working in this direction,
> in order to have some base for discussion (not only good intentions,
> but some real things). Let us look how the things will go.
> If good, I think we should organize this event.
That's a great plan. Just let me know later if/when you decide, and
I'll see what is possible/fundable, etc.
>
> I did not know that Mathematica includes packages in differential
> geometry, maybe because I haven't used it for a long time.
I don't have any personal experience with it easier, but have heard
about it from other people. I don't know if it is included in
Mathematica or not.
> I know that Maple has a lot of differential geometry implemented, but
> also I have no real experience in it, because I prefer the open source
> tools.
Same here :-)
> Last years I used maxima, and then Sage.
> Anyway, the experience of professor Jack Lee surely can help much in
> the development of differential geometry in the Sage.
>
> Mikhail
>
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--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org