Hello everyone,

I'd like to apply for GSoC-2012 studentship with SymPy.  I can't call
myself a Python expert, but I've been regularly doing moderately
complex stuff in Python for more than four years already.  I have some
basic experience with SymPy; I was much better at it a couple years
ago, but I wasn't sufficiently clever then to contribute.

Right now I'm pursuing my MSc in Mathematics and Informatics.  This
semester is algebra-biased: I'm studying quasigroups, lattices,
Gröbner bases.  As extracurricular activities, I'm studying category
theory and probability.  I'd be happy to apply any part of the
knowledge I (will) have by contributing to SymPy.

I've scanned https://github.com/sympy/sympy/wiki/gsoc-2012-Ideas , and
there are a couple ideas which make me drool in happiness :-) My
favourite is "implement symbolic (formal) logics and set theory".  I
haven't ever had serious courses in either of these subjects, but I
hope the patchy knowledge I have can be quite easily fixed to yield
the proper coverage.

One of the other ideas that interest me is "Groebner bases and their
applications in geometry, simplification and integration".  I've only
started the course in Gröbner bases, so I can't claim being
knowledgeable, but I will have graduated the course by the beginning
of May, which is before the start of coding time, and which means that
I should be quite prepared to work on this task by that time.

There's extra motivation for me to work on Gröbner bases: a part of
the research I'm part of now focuses on this object.

Finally, I'd like to suggest an idea of my own.  Since I'm studying
category theory now (and I don't think I'm ever going to put this
instrument aside), I'm dealing with commutative diagrams quite often.
It would be great to have a tool which would be able to allow one
solve typical problems about commutative diagrams, like:

  * check if the diagram is commutative,

  * for a given value in some source node of the diagram graph, show
    the values obtained in other nodes of the diagram,

  * find one (or more) isomorphic embeddings of a given diagram into
    another given diagram.

I totally understand that this is far from being detailed and far from
being anything concrete at the moment, but if the SymPy community
approved of such functionality, I'd be willing to produce further
reasoning and go into much detail.

Conclusion: I'd be happy to work one of the following (or something
similar):

  * formal logic and set theory

  * Gröbner bases

  * a tool for commutative diagrams

I hope that I did manage to express my enthusiasm sufficiently well
:-)

I'll now try and fix some of the bugs, listed here
http://code.google.com/p/sympy/issues/list .

Sergiu

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