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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