Hey Burcin,

Thank you for the link.

I should have some time in the next couple of days to look at this.
Assuming there are no major unexpected complications --- I wouldn't
want to start an involved process of completely rewriting something
like quotient fields here --- I'll hopefully have enough time to start
& finish this.

Sebastian

On Jan 5, 12:57 pm, Burcin Erocal <bur...@erocal.org> wrote:
> Hi Sebastian,
>
> On Tue, 5 Jan 2010 04:10:08 -0800 (PST)
>
> Sebastian Pancratz <s...@pancratz.org> wrote:
> > Dear all,
>
> > When looking at trac ticket #7730 (which essentially ends with saying
> > that GCD computations over multivariate polynomial rings are slow), I
> > noticed that the current implementation of multiplication in fraction
> > fields computes the product (a/b) * (c/d) by first computing a*c and
> > b*d, and then dividing out common factors (in the case of exact
> > underlying rings).
>
> > I am wondering whether there is a good reason for doing this.
>
> I believe the reason is that no one implemented anything else.
>
> When I read the paragraph above, I couldn't believe we still used naive
> multiplication, especially since I implemented the Henrici
> multiplication ages ago. Apparently, I never submitted the patch,
> waiting to include other improvements with it indefinitely.
>
> I found my old patch, which had a modification date of "Wed Apr 09
> 09:24:45 2008", and rebased it to 4.3. The new version is here:
>
> http://sage.math.washington.edu/home/burcin/henrici_mul.patch
>
> It probably needs more work to add more doctests, etc.
>
> Note that you can also do a similar trick for derivatives. It would be
> great if you implemented that as well.
>
> Can you handle the rest of the submission & review process? I am very
> busy with thesis related work these days.
>
> Thank you.
>
> Cheers,
> Burcin

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