Ralf,

On Thu, Jun 10, 2010 at 6:40 PM, Ralf Hemmecke <[email protected]> wrote:
> ...
> With the definition of
>
> Module(R:CommutativeRing): Category == BiModule(R,R)
>  add
>    if not(R is %) then x:%*r:R == r*x
>
> I think, it is quite sufficient when
>
> SquareMatrixCategory(ndim,R,Row,Col): Category == Definition where
>  Definition ==> Join(DifferentialExtension R, BiModule(R, R),_
>     ...
>
> which is the current definition.
>

Ok.

>> If it did, then I think the question of coercion would be moot.
>
> But note, my question was about looking for an appropriate operation *
> (or rather an appropriate coercion) so that
>
>  R and SquareMatrix(2,Fraction R)
>
> can be connected.
>

That was not clear to me.  And in fact such a coercion does seem to be
applied in the case R = Integer.

> As written in
> http://groups.google.com/group/fricas-devel/browse_thread/thread/63f43b33d26ecb6d
> , Fraction R and SquareMatrix(2, Fraction R) is not a problem.
>

Sorry I did not notice when you originally pointed this out.  Now I
see the difference between (97) and (100) but the computation seems
oddly out of order. So I guess I must go back and try to understand
again why the result is a DirectProduct in your example.

Why is there no automatic coercion when R = Polynomial(Complex
Integer))?  Is this some limitation of Fraction?

Regards,
Bill Page.

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