#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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Comment(by jvkersch):
Hi Mikhail,
Thanks for your comments. I agree with the outline of the necessary work,
and I've gone ahead removing the old version of the methods and checking
whether the code still works with Sage 4.6 (it does). I've also made a
start on caching the remaining methods (I worked on `natural_frame`) and
the numerical treatment of parallel transport.
With parallel transport, I noticed something weird: as a test, I asked the
code to do parallel transport along a great circle on the sphere, and I
found that the numerical equations blow up! I can't see any theoretical
reason why this should be a difficult numerical problem, and the code
seems fine too. So I'm a bit puzzled...
As for the remaining issues, I don't know how to deal with the assumption
in the computation of the mean curvature, but I'll look at it again during
the weekend.
I agree that it would be good to deal with a greater variety of surfaces.
I wanted to implement Costa's surface (just as a preliminary test), but I
didn't know how to deal with the Weierstrass p-functions in the parametric
representation...
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10132#comment:17>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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