On Fri, Aug 22, 2008 at 10:33 AM, John Cremona <[EMAIL PROTECTED]> wrote:
>
> Forgive the self-reply.
>
> Looking at factorization.py I was all ready to fix all the problems I
> could see -- using Sequence to get a common universe for the bases on
> construction, cache this base_ring, only allow operations between
> factorizations with the same base_ring, and so on.
>
> But then I saw what appeared to be a totally weird example:
>
>            sage: F = Factorization([(ZZ^3, 2), (ZZ^2, 5)], cr=True); F
>            (Ambient free module of rank 2 over the principal ideal
> domain Integer Ring)^5 *
>            (Ambient free module of rank 3 over the principal ideal
> domain Integer Ring)^2
>
> This bears no relation at all to what I thought the Factorization
> class was for.  Doing a search_src showed that this is designed in to
> support splitting of modular symbols spaces (and similar).
>
> This leaves a question almost certainly for William:  is it really
> sensible to have one class serve both as the structure to hold "prime
> factorizations" for UFDs and other rings, as well as to hold lists of
> subspaces with multiplicities?

I use one word for both: "factorization" :-)

> If so, perhaps we need to refactor this to have a base class which
> just handles the basics, with (at least) 2 derived classes, one for
> rings factorizations and one for additive decompositions?

Sure, go for it.  As long as I don't have to do the work, it sounds
good to me.

-- William

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