Let me first say that it would be quite amazing to have sympy code to
check commutativity of diagrams. However, I think there is a reason that
"no" computer programs for category theory exist so far: most proofs in
category theory are trivial! As soon as you have formalized your diagram
enough to put it into a computer, it should be obvious how to prove
commutativity.
There are of course counterexamples, in particularly when applying
category theory to algebraic geometry, commutative algebra and algebraic
topology (probably in other areas too, but these are the ones I know).
But there morphism are defined in complicated, explicit ways, and
checking commutativity rarely uses only "trivial" commutativity rules.
All this should not discourage you. But it seems to me that, as mentors,
we will be having a very hard time to decide how good chances are that
at the end of the summer, you will actually have ended up with useful
code. I guess your inclusion of a drawing algorithm improves matters a
bit: even if the part on checking commutativity does not really work (in
practice, maybe, ...), being able to type a diagram in some natural
fashion into sympy and then producing tikz code that can be pasted into
latex would probably already be enormously helpful.
One comment regarding drawing of diagrams. You write that they are often
drawn in a grid-like fashion. I think this is a bit of a misperception:
obviously squares tend to be drawn in grids, but there is no reason to
do this with more complicated diagrams; the only thing that matters is
clarity. Diagrams in books are often drawn in grids, simply because
typesetting them is a pain!
Best,
Tom
On 06.04.2012 00:19, Sergiu Ivanov wrote:
Hello,
I have finally managed to draft the proposal for my pet project idea:
https://github.com/sympy/sympy/wiki/GSoC-2012-Application-Sergiu-Ivanov:-Category-Theory-Module
I tried very hard to submit it earlier, but it took me much more time
than I had initially expected. Sorry for the late submission :-(
As far as I remember, it will still be possible to comment on
proposals after the deadline (which is coming in less than 24 hours),
which, I think, can be a good way for fixing something in a proposal.
I will still be able to edit the version on the wiki.
I hope this is acceptable.
I will get back to answer E-mails very soon.
Sergiu
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