On Sat, 28 Oct 2006 18:19:52 -0700, David Harvey
<[EMAIL PROTECTED]> wrote:
> I'm a bit worried about ambiguous situations arising, although I
> can't think of any specific examples. If both objects are module
> elements (or algebra elements) then everything's ok I think. I'm more
> worried about multiplying a ring element by an algebra element; it
> feels like it might be possible to get an ambiguous situation where
> you don't know whether to coerce yourself towards a scalar
> multiplication or an algebra multiplication.
David Kohel told me that in MAGMA he often had troubles like this
involving matrices. I don't remember specific example -- maybe, e.g.,
if X is a 2x2 matrix whose entries are themselves 2x2 matrices, how
do you multiply and add them?
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
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