I feel like I'm jumping into this discussion late, but it's something
I've been thinking about too...
On Oct 28, 2006, at 7:05 PM, William Stein wrote:
> Regarding ring and algebra elements, suppose x is in a ring R and y
> is in a K-algebra S. We want to define what "x * y" means. The
> most natural thing to me would be
>
> x * y is K._coerce_(x) * y
>
> and that's it. If no coerce map exists, fail.
>
> Am I missing something? The above rule is definitely easy to
> understand.
>
> William
I think if there is a natural coercion S -> R, one should also be
able to do
x * y = x * y.base_extend(R)
Right now something like
sage: R.<x> = ZZ['x']
sage: (1/2) * (x^2-x)
throws an "unable to find a common parent" type error. I am wondering
if there are any (many) other cases where there is an unambiguous
common parent that is not the parent of either "sibling." I think
there should be generic code able to handle this for elements defined
over a basering (e.g. polynomials, series, matrices, etc.) but
perhaps there are other such situations too (e.g. the product of
elements of two extensions of Q, though I haven't given thought to
how messy this could become).
Robert
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