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',  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?

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