#10132: Parametrization of (metric) surfaces in 3D euclidean space
---------------------------+------------------------------------------------
Reporter: mikarm | Owner: mikarm
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: geometry | Keywords: differential geometry,
parametrized surface
Work_issues: | Upstream: N/A
Reviewer: vdelecroix | Author: Mikhail Malakhaltsev
Merged: | Dependencies:
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Changes (by vdelecroix):
* status: needs_review => needs_work
* reviewer: => vdelecroix
Old description:
> Apply trac_10123_final_allfiles_done.patch
>
> It was tested under sage-4.6.2.
New description:
This patch aims to implement a class for embedded surfaces in the
euclidean space R^3 described by a parametrization. Its focus on the
computation of metric invariants (first and second fundamental forms,
Gaussian curvature, ...) and more involved geometry (geodesics, ...).
Apply trac_10123_final_allfiles_done.patch
It was tested under sage-4.6.2.
--
Comment:
Hello,
That's nice to see some Riemannian geometry to come in ! Before I'm
playing with the patch and be involved into details, I have some general
preliminary remarks
0) The description of this patch (on this webpage) should contains few
words about what you intend to developp. I wrote few lines of description
that you can modify.
1) '''patch errors'''
* the patch trac_10123_final_allfiles_done.patch does not contain the
modification of "setup.py" which is needed to take into account
modification of Sage sources
* I get a minor error for patching index.rst in the doc with sage-4.6.2
2) '''name logic'''
* There is a directory sage/geometry/ which is the directory intended
for... geometry. It would be better to put all Riemannian geometry inside.
* "riemann" is a very ambiguous name as there is the Riemaniann geometry
which deals with manifolds with metric, Riemann surface which are complex
curves, Riemann hypothesis, ... perhaps riemannian_manifolds (repository
are always plural) is safer and more comprehensive.
* the vector (resp. matrix) manipulation for simplifications of
coordinates should be put elsewhere because it has nothing to do with
riemannian geometry. The ideal way to do is to implement a new class for
vectors on symbolic ring (look at the repertory sage/modules). But that
job is a patch in its own. The simplest way I see is that you move this
file as sage/modules/vector_symbolic_ring.py and inside its preambule
write a word about your needs (ie simplification of coordinates) and make
an explicit link to your file. That way, when somebody else comes in to
implement the class for vector on symbolic rings he will modify your
functions on Riemannian manifolds accordingly.
3) '''about a class for generic manifolds:''' I do not think the class
GenericManifold would be interesting. If anyway you intend to add it, it
should be put in another file in another place. If you start such generic
stuff, your ParametrizedSurface3D should derive from something like
EmbeddedRiemannianManifold. And if so, you have to implement a class for
morphisms between RiemannianManifolds... it will be painful !
4) In your file you mention "PatchOfCoordinates" without any reference to
the corresponding file ! I think it would be very useful to use it right
now in order to be able to have a parametrization defined on a restricted
domain... In a soon future it can be used to write differential equations
on the surface itself.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10132#comment:44>
Sage <http://www.sagemath.org>
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