On 06/10/2010 11:55 PM, Bill Page wrote:
> Ralf,
>
> In another thread Gaby observed that for a Field F SquareMatrix(n,F)
> should satisfy VectorSpace(F), but unfortunately at present it does
> not:
>
> (1) -> SquareMatrix(2,Fraction Integer) has VectorSpace(Fraction Integer)
>
> (1) false
It probably could if it somebody adds VectorSpace(R) into
SquareMatrixCategory(ndim,R,Row,Col): Category == Definition where
...
Definition ==>
...
if R has Field then
VectorSpace(R)
...
So why hesitate?
> Or perhaps even better if every SquareMatrix(n,R) satisfied Module(R).
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.
> 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.
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.
Ralf
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