Robert Bradshaw <[EMAIL PROTECTED]> writes:
> In Sage, we use the term "coercion" to denote a canonical (using the
> term a bit loosely), implicit map between Parents (or objects of a
> concrete category). E.g. from ZZ to F5 would be a "coercion," but
> there is a "conversion" and not a "coercion" the other direction.
> Coercions are invoked to do arithmetic, but conversions are not.
Just for the record, this is *exactly* the same definition as in FriCAS.
(in case you wonder, the notation "Object::SomeType" is syntactic sugar for
"coerce(Object)@SomeType", where @ is a language builtin, that selects the
function according to return type.
Unfortunately, the contributors to NAG Axiom were sometimes a bit sloppy about
which coercions to implement.
There was one idea, which I personally like a lot, to provide to "Categories"
(in the FriCAS/Axiom sense)
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. (I have a suspicion for the reason, but that's not important
here.)
However, I think in principle the design is *very* good. I think the design in
Sage is not so different (I did not check thoroughly, though), which comes as
confirmation.
Martin
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