As far as I know, everything that has been implemented is already in
the codebase, with the exception of
https://github.com/sympy/sympy/pull/563.  I've CC'd Jeremias (the
student who worked on it last year) and Mateusz (his mentor), to see
if they have any more comments.  As far as I know, Mario's suggestion
is valid.

If Mateusz is free, he'll likely be the one to mentor such a project.
Otherwise, I don't know.  Mario, would you be willing to help out with
such a project, if not directly mentor it.  I think your knowledge of
Groebner bases is probably the strongest.  We can help out where your
knowledge of the codebase is lacking.

Otherwise, I'll do it, though I'll have to update my own knowledge of
Groebner bases and these algorithms (which would not be a bad thing).

As for the linear algebra, I'm not sure it's something you could just
do really quickly, though feel free to look into it.  What we need to
do is make things faster, and one way would be to restructure things
in Matrix so that they are similar to the way they are in Poly.
Otherwise, from my understanding, the algorithms that use linear
algebra are not really faster, as they kind of assume that the linear
algebra will be fast(er).

Aaron Meurer

On Sat, Mar 10, 2012 at 2:08 PM, Sergiu Ivanov
<unlimitedscol...@gmail.com> wrote:
> Hello,
>
> I'd like to hear a definitive word on the status of Groebner bases in
> SymPy.  The ideas page says (just like it did a couple weeks ago) that
> there was a project on this topic last year, and then it invites the
> student to contact the developers, which I hereby do :-)
>
> In the source tree, I can see the file sympy/polys/groebnertools.py,
> which contains the implementation of Buchberger and F5B algorithms.
> I've seen some suggestions for further improvement on the list (
> https://groups.google.com/forum/?fromgroups#!topic/sympy/EI47kQM6S8c
> ), however neither of them has made it into the official ideas page.
>
> I'd be interested in working on (improving) Groebner bases, so it
> would be great to settle on a task which I could start preparing for.
> I would also be very glad to hear from the people who are willing to
> mentor such a task.
>
> The ideas page says that Groebner bases in SymPy would benefit from
> improvements to linear algebra.  I absolutely don't mind (moreover,
> I'd like it) to include a couple of such improvements into my eventual
> proposal.  Moreover, I could actually try to make a couple such
> improvements right away, as a part of satisfying the patch
> requirement.
>
> A slight disclaimer is that I'm still not completely through my
> Groebner bases course at the uni, so I'm by far not an expert in this
> domain.  I do believe though that my passion for and (something that I
> consider to be) general knowledge of algebra, and, particularly of
> modules and rings, will be sufficient to eventually grasp any
> Groebner-bases-related idea.
>
> Sergiu
>
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