Ralf Hemmecke wrote:
> On 06/12/2010 01:50 PM, Waldek Hebisch wrote:
> > Bill Page wrote:
> >> Ralf,
> >>
> >> I think that the map
> >>
> >> coerce : Fraction Polynomial Complex Integer -> %
> >>
> >> which is apparently x+-> [x,x]
> >>
> >> in
> >>
> >> )sh DirectProduct(2,Fraction Polynomial Complex Integer)
> >>
> >> should not be called a coercion.
> >
> > Good spot. AFAICS that coercion is defined because we have
> >
> > if R has SetCategory then FullyRetractableTo R
> >
> > in DirectProductCategory. IMHO this does not make sense.
> > But before removing it one have to fix a few places in algebra
> > (at least retract in SquareMatrix) where the retraction from direct
> > product to scalars is used.
>
> Waldek,
>
> what exactly is the problem?
>
> coerce: R -> %
>
> or
>
> retract % -> R
>
> for % being DirectProduct(ndim, R)?
Your orignal problem is due to coerce. I think that
FullyRetractableTo is problematic because there are many
different reasonable definitions. OTOH if we put ring
structure on DirectProduct then only the current one
remains to be reasonable.
> Bill and me discussed the coercion. If you check hyperdoc for
> DirectProduct and click on "origin" for the function "coerce", then you
> see that coerce: R -> % comes from Algebra(R). It just needs that R is a
> CommutativeRing. Thus, removing FullyRetractableTo R will probably have
> no effect on my original problem.
Right, coerce also comes from Algebra(R). I would say that
retract and coerce make sense if we treat DirectProduct as
a ring. But when we multiply DirectProduct by an matrix
the ring structure of DirectProduct is irrelevant.
--
Waldek Hebisch
[email protected]
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/fricas-devel?hl=en.
