Dear Michel,
On Mon, Mar 09, 2009 at 12:03:34AM -0700, Michel wrote:
> A long time ago I made a FractionFIeld implementation which would
> cache factorizations of denominators. instead of taking gcd's all the
> time
>
> http://markmail.org/message/7hxox5cbz5knxjse#query:new%20implementation%20of%20fraction%20field+page:1+mid:5bf3l37bsim34m4g+state:results
>
> It is usually much faster than the naive implementation but it is
> possible
> to make examples where it is slower (see the above thread). That's
> why it was rejected.
Cool, thanks so much for your pointer and your patch!
In combinatorics, when playing with rational generating series, we
have *lots* of fractions with denominators that factor well. So this
gives quite a few applications to your code.
Let me dream a bit. I very much like the idea of Factored(Ring), where
elements are kept in factored form as long as possible, as is done in
FriCas (thanks Martin for the pointer). I would like to have several
variants to choose from:
- PartiallyFactored(Ring)
The factors are not guaranteed to be relatively prime
- RelativelyPrimeFactored(Ring)
The factors are guaranteed to be relatively prime, but not necessarily
prime themselves
- FullyFactored(Ring)
The factors are all guaranteed to be prime
In each case, the gcd function would do its best to exploit the
structure (e.g. remember which factors are readily relatively prime).
As readily pointed out, this is very modular, and leaves the user with
the choice of the appropriate implementation of fraction field for his
particular application (as the discussion pointed out there won't be
one perfect implementation optimal in all cases). For example for my
application, I ideally would use Ring /
GcdFreePartiallyFactored(Ring). As a starter, I could do with
FractionField(PartiallyFactored(Ring)).
How much work would it be to adapt your patch in this direction? I
definitely volunteer for testing and reviewing it! In fact, your
patch would be very welcome on the Sage-combinat patch server so that
we can easily start playing with it (even though it's not only about
combinatorics).
Best regards,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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