On Wed, Feb 15, 2012 at 10:34 PM, Aaron Meurer <asmeu...@gmail.com> wrote: > > The best chances to be accepted are to sell yourself, not so much your > project.
Hm, sounds reasonable, although different from the perspective I was used to adopt. >> In this case, I'll have to confess that I've been musing on the >> perspective of working on Karr a couple days, and I feel like I'm more >> attracted to the problems listed here >> https://github.com/sympy/sympy/wiki/gsoc-2012-Ideas under the title >> Polynomials module. My interest decreases the way the ideas are >> ordered there, i.e., I like the idea about the Groebner bases most. >> Therefore, in accordance with your suggestion (I believe) I'll find >> some papers on this topic and, specifically, Faugere F4 (since F5 has >> already been implemented, I think). > > From what I remember, there were problems implementing F4 because of > our linear algebra module (i.e., the matrices) were too slow to really > make the algorithm efficient. So if you want to implement an > algorithm that uses linear algebra extensively, you'll probably need > to improve the matrices as well (which could in itself be a project). Hm, I see. In that case, I'll take a look at the code of SymPy linear algebra module and see if I can derive any definite conclusion. >> (BTW, I'm not saying that Karr is not interesting, it's just that I >> don't somehow feel emotionally attached to it :-) ) > > Then don't do it. This was just a suggestion. We definitely want you > to do a project that you want to do, as this greatly increases its > chances of success. Thank you for you attitude! >> >> I am, of course, still willing to work on the commutative diagram >> tool, but I'm only in case you deem it relevant *and* important :-) > > Is category theory used outside category theory? If so, maybe you > could give an example showing how the module might be used to solve > some actual problem. I remember reading that category theory has been > called "general abstract nonsense" which is probably why I'm still > having a hard time grasping onto it, or at least its usefulness. I'll > try to read through the Wikipedia article as well. Yes, some people still call category theory "general abstract nonsense" :-) I've seen a lot of *good* textbooks on ring theory and/or module theory which included chapters introducing the basics of category theory. From my own experience I can tell that category theoretic approach offers a much better perspective over a certain area of mathematics, since it allows you to do cross-area comparisons. I'm not yet sufficiently good in category theory to give you concrete examples, but: you can use category theory to correctly reduce problems in one area (finite automata, for instance) to better known problems in a different area (group theory, for instance). Moreover, there are some remarkable results (again, I can't be concrete, since I don't really understand the complex stuff yet) that can be applied in concrete categories to relatively easily describe and prove complex stuff. Category theory is being adopted throughout algebra and topology right now; I hope to contribute to bringing it to formal languages and computability. The easiest benefit from adopting category theory is much better systematisation and unification of terminology (consider the traditional terms "homomorphisms" and "homeomorphisms", which are both morphisms in corresponding categories). Sergiu -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
