#10132: Differential Geometry via Sage
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Reporter: mikarm | Owner: mhampton
Type: enhancement | Status: new
Priority: major | Milestone:
Component: geometry | Keywords: differential geometry,
parametrized surface
Author: Mikhail Malakhaltsev | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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I am working in the field of differential geometry (research and 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', and made a
worksheet "Ellipsoid via SAGE" which demonstrates the methods of the class
in work. I attached the corresponding files to this ticket.
Note that, at this moment, the class is not optimized from the programing
point of view (calculation time, catching exeptions, etc), but somehow it
works.
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, though the
life is short :) so I do not know if I will be able to complete this
program. Anyway, 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".
So I would be thankful if I could get answers on the following questions:
1) What do you think, is it important to include the differential
geometric stuff to SAGE?
2) Are there other people who work in the same direction? It would be good
if I could cooperate with them.
3) What recommendations can you give concerning the code of the class for
I could take into account in my future work.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10132>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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