On Aug 2, 2:59 am, john_perry_usm <john.pe...@usm.edu> wrote:
> Raphael,
>
> > Also, I read back in April that there was a plan to implement
> > Faugere's F4 algorithm. As the systems I want to solve are very large,
> > I would be particularly interested in that or any related tools that
> > are in development. (Anyone working on an XL variant?)
>
> There is some work being done to implement F4 & F5 in Singular, which
> would then make it into Sage, but the work proceeds slowly. A working
> F5 implementation for Singular exists (I have a copy), but it's not
> very optimized and does not use linear algebra, and so it is a little
> slower than Singular's default slimgb.
>
> If I understand correctly, they are currently working on a complete
> revision of Singular's linear algebra, to allow for efficient
> implementations of F4 & F5. I've forwarded this email to Christian
> Eder, to whom we owe the current F5 implementation in Singular. He
> will correct me if I'm wrong, & perhaps comment further.
>
A linear algebra based method could be very interesting. As an
example, if there were a way to export the presumably very large
linear algebra problem that needs to be solved, then one option would
be to run that separately on one of the many large clusters available
(over MPI say). Just a thought.
Raphael
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