[Haskell-cafe] [GSoC] A proposal for GSoC regarding computational algebra

[Hiromi ISHII]

Hello cafe,

I'm so happy to know that there are people interetested in my proposal!
I really thank carter (in freenode chat), Edward and Dominic in advance.


Edward:

> I suppose given your library's use of my algebra package and other components under the hood, etc. I'd probably be the most likely mentor. 
> 
> I'd be willing to work with you, and likely to fold it in/replace much of the existing algebra machinery, which I confess is woefully under-maintained.
Thanks! `algebra` packge provides fine-grained abstraction for algebraic structures (though it does not provide the class for noetherian rings), so I adopted for my purpose. I suppose that the `algebra` is more general purpose library than my `computational-algebra`, which is currently concentrated on computation in polynomial rings or quotient ring.

> Usually, proposals to write a new library have a hard time getting accepted to GSOC, but you do already have a decent sized body of work there.

Sounds great. Yes, in fact, my proposal is not building new library but to improve (my personal) existing library.


Dominic:

> I might be. Can you give some use cases?
The current applications of my interest are elimination theory and solving multivariate nonlinear equation systems.
Here are some example: https://github.com/konn/computational-algebra/blob/master/examples/solve.hs
Another example is purely mathematical things: for example, we can calculate ideal operations in polynomial rings and basic operation in quotient ring. There are application also in the area of statistics, robotics and cryptology, but I don't know much about them.

> I should point out I do a fair amount of numerical work and this typically involves linear
> algebra but from a numerical point of view.
That sounds interesting. Linear computations required by F4 and F5 algorithm is purely symbolic ones, but there might be common technique.

> I am also quite interested in computational algebraic topology but I suspect you are not
> proposing to work on that?
Sadly not. I don't know much about *algebraic topology*, but my project can be applied to *algebraic geometry* because some computations in commutative algebra can be done with Groebner basis. 

-- Hiromi ISHII
konn.jinro at gmail.com