Thank you for this - I am studying it and it definitely has some of
the flavour of what i'm thinking of.  Once I understand it better I
can say more.

On Jul 30, 10:47 am, Alan Bromborsky <abro...@verizon.net> wrote:
> Marco wrote:
> > I was very impressed by the description of SymPy here:
>
> >http://www.euroscipy.org/presentations/slides/index.html
>
> > and especially slide 14 "Internals: Object oriented model".
>
> > I have a couple of general questions about how Object-oriented SymPy
> > is. I'm a mathematician and would like to use or extend SymPy to do
> > abstract differential geometry.
>
> > 1. Where/how can I see a diagram of the structure of the classes in
> > SymPy?
> > 2. Is SymPy at all modeled after category theory, which organizes
> > mathematics in an essentially object-oriented way?
> > 3. Is there a SymPy approach to, for example, vector spaces?  I do
> > *not* mean matrix algebra or computations in components.  I mean an
> > actual abstract vector space, where objects would be vectors and one
> > could take linear combinations of vectors.  I'm asking this question
> > as an example of a more general question - whether SymPy has been used
> > to do "abstract" computations on mathematical objects such as vector
> > spaces, manifolds, etc. (as mathematicians often do) rather than
> > explicit ones in numbers or polynomials.
>
> You might want to look at the following documentation since geometric
> algebra includes vector spaces:
>
> http://docs.sympy.org/modules/galgebra/GA/GAsympy.html

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