On May 27, 2007, at 11:47 , David Harvey wrote:
> On May 27, 2007, at 2:21 PM, Michel wrote:
[snip]
> Well I have another idea, I'm not sure to what extent this is already
> implemented in your factor_cache.pyx, or to what extent it even makes
> sense. (I haven't actually looked at your code yet.)
>
> It sounds like this factor caching thing actually has nothing to do
> with fraction fields as such. Rather it sounds like one could
> implement
> a wrapper around a generic ring which remembers factorisations of
> elements. I'm imagining something like
>
> R = some ring
> S = FactorCache(R)
>
> So now S is a ring, whose elements are products of elements of R.
> Multiplication does the obvious thing, addition and subtraction I
> suppose checks for common factors and just expands the rest? (I
> suppose
> this is very much like the Factorization class already in SAGE, except
> it would support arithmetic. Or maybe the Factorization class already
> supports arithmetic, I don't know.)
>
> Then you would just write
>
> K = FractionField(S)
>
> Would it even be necessary to write special code in the fraction field
> class if it was done this way? (Hmmm.... thinking aloud in public
> here....)
An intriguing idea... A couple of questions:
Should this be a implementation concept, rather than an "API
concept"? Not quite sure what I am asking, but this feels to me like
a good idea for implementation, but not for "the user" to fiddle
with. What is the difference between R and S for your average user?
Would FractionField(R) and FractionField(S) be the same?
How does this relate to rings like Z[\sqrt{-5}]? Keeping
factorizations around for these seems problematic...
Justin
--
Justin C. Walker, Curmudgeon-At-Large
Institute for the Absorption of Federal Funds
--------
If you're not confused,
You're not paying attention
--------
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
