[Aldor-l] coercion problem

[Martin Rubey]

I'd like to report on a curious problem I have with SPAD/Aldor, which Python
does not seem to have.

In Axiom, we currently have the (mostly unused) Categories

CoercibleTo S, RetractableTo S and ConvertibleTo S that provide

coerce: % -> S, coerce: S -> % and retract: % -> S

respectively.  One can then ask

(4) -> SquareMatrix(2, INT) has CoercibleTo Matrix INT

   (4)  true
                                                                Type: Boolean

Very unfortunately, currently in almost all cases the query "has CoercibleTo
Something" will return false, because the coerce function is not inherited by
the category.

Now, I would like that for domains of the same category, say
UnivariatePolynomialCategory, that differ only in the representation of their
elements, say sparse or dense, we would have

A has CoercibleTo B and B has CoercibleTo A

Eg., we could have a package

UPOLYCoerce(A: UPOLYC, B: UPOLYC)

that implements coerce: A -> B generically, using only operations from the
category UPOLYC.

But it seems that we cannot teach Aldor/SPAD, that for all domains A and B of
UPOLYC we have

A has CoercibleTo B and B has CoercibleTo A

In Sage/python, this seems possible, although I'm not quite sure about it.
There, people implement a general coerce method in UPOLYC, that checks whether
it's argument is of the right type.  I admit, I do not know whether we can then
ask for two given types whether we can do the coercion.  Sorry for being very
vague here, I simple do not know the details.



Martin