#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 mikarm):
Joris,
I really appreciate that you participate actively in the development of
the package.
Thank you very much, I am sure that together we will go much faster and
efficiently.
These days I also had a lot of work, but hope at the weekend I will have
time to try new version of the package you submitted.
One thing I should say concerning your idea:
"The most significant is that I think that the member functions such as
natural_frame, first_fundamental_form_coefficients,
second_order_natural_frame, etc. should always just return a
dictionary/list with all of the components. The current situation is that
these functions take an optional argument, and when that argument is
specified only that component is returned."
Certainly I agree that this change simplifies code and goes "along the
Sage line".
However, my experience in calculations in differential geometry (by hand
and using a computer programs), is that often the calculations are really
hard (imagine that we deal with a surface whose equations are given by
special functions or something else of this type rather than elementary
surfaces like the ellipsoid, the catenoid, etc.
In addition, in my opinion, computer calculations are to be combined with
some theoretical arguments, calculation by hand, etc. So, it is very real
the situation when the user needs to calculate only one component of a
tensor and does not need to spend time on the calculation of the whole
thing.
At the same time, another user may wish to have the complete information,
because he needs it for some reasons.
The way out of this contradiction is, I think, to have two algorithms
within one package. One is to calculate everything and to cash it, and
then use.
Another is to calculate one thing on user's request (then in order to find
other, e.g. components of a tensor, he will spend more time than if he
would use the first algorithm, but it is his choice :).
Maybe you have other solutions which are more efficient than this one.
Anyway, at the weekend I plan to play with the improved version of the
package you submitted here, and will comment on it.
Again thank you, it is more interesting to work together!
Mikhail
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10132#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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