On Nov 2, 2006, at 11:02 PM, Robert Bradshaw wrote:

> 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).

This is much harder. I agree it would be nice, but how would you  
handle something like

sage: R.<x> = ZZ["x"]
sage: S.<y> = ZZ["y"]
sage: x*y

??

David


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