On 28.03.2012 17:06, krastanov.ste...@gmail.com wrote:
(1) I think it would be good to extend the "usage" section to give some non-trivial examples. It does not matter if you make the particulars of input/output forms up, just show what you envision your code should be able to do at the end of the summer, in a best-case scenario.I will extend that part.
Great. Let us know of changes.
(2) Add details on how you plan to implement things. What new classes will here be, what data structures do they hold? E.g. a manifold is typicaly constructed from patching open subsets of R^n along diffeomorphisms - but I am not aware of sympy code to represent even open balls (I could be wrong, obviously).OK.(3) Are there any non-trivial algorithms that you think could be implemented? (For example, might it be feasible to compute the euler characteristic of a Manifold via the Hopf index theorem?)Most of the paper that I referred to is about working independently of coordinates, then at the end choosing a coordinate system and deriving something useful in that system (differential equation about something, finding an integral, a pullback, a connection).
That sounds very sensible. I would love to e.g. put a symbolic metric on a manifold and get out symbolically the Christoffel symbols.
When those are found, it is the rest of sympy that comes into play. For example in the case of Hoph theorem, it would be easy to get equations for the vector field, check them for zeros, get the maps around those zeroes and then rely on something in sympy to find the index of those maps. However, this is the naive algorithm which assumes perfect solvers and so on, so probably it won't work.
Sure, I was just fantasizing ;).
So, about data structures and algorithms: nothing nontrivial, it will depend on what is already in sympy. I will add examples of interesting results possible with this project.
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