Ralf Hemmecke <[EMAIL PROTECTED]> writes:
> > One can hardly say that these two domains differ only in the representation
> > of
> > their elements.
>
> Well, what about Dom1, Dom2, and DomS on
> http://axiom-wiki.newsynthesis.org/SandboxIsomorphic ?
Oh dear, it seems difficult to explain what I'm thinking of. All I want is:
> > Somehow, it might be nice to have the possibility to say
>
> > with CoercibleTo B where B has SomeCategory
Of course, this only makes sense for some very special Categories. But then it
makes a lot of sense. For example, for categories, that provide a common
interface to different *representations* of univariate polynomials - sparse or
dense, or matrices, sparse or dense, etc.
> define IsIsomorphicTo(C: Category, T: C): Category == with {
> coerce: % -> T
> }
> But I somehow believe that even if it were possible, it wouldn't help you in
> what you are thinking about. Can you be even more explicit. I am asking for
> it, because besides the categories one also has to think of how one actually
> could implement the respective coercion functions.
I don't see how this would help. As I said, I can have
UPOLYCoerce(A: UPOLYC, B: UPOLYC): with
coerce: A -> B
add
coerce a ==
resta := a
res: B := 0
while not zero? resta repeat
res := res + leadingCoefficient resta * leadingMonomial resta
resta := reductum resta
res
and this will provide a coercion function from any A to any B in UPOLYC, but I
cannot state that for any A and any B in UPOLYC
A has CoercibleTo B
(of course, I want to *state* it, I do *not* want the language to deduce it by
some magic.)
Martin
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