Map question (coercion)

[thofma]

To all lovers of maps, there are some questions that came up during @ThomasBreuer recent cleanup of the julia <-> GAP conversions. Suppose that f is a Map with proper domain and codomain. I will only talk about image(f, x), but the same questions arise for preimage(f, y).

Should image(f, x) only work for parent(x) === domain(f) or should image(f, x) also work where we have "canonical" coercions in place?*

More concretely, if I have a map f : QQ[x] -> QQ[x], should f(1//2) or f(QQ(1//2)) also work?

Pro:

• Users will be happy.
• In the future we might want to extend a morphism f : QQ[x] -> QQ[x] to be automatically applicable also to an ideal I of QQ[x] via f(I). It think it would be surprising that f(I) would work but not f(1//2). Of course this point is moot if we do not intend to also allow f(I).

Con:

• Makes it a bit more complicated to reason about code. Sometimes it is not clear what a canonical coercion is and what not.

*: By canonical coercions I mean here the coercion that is already taken place for binary operations. For example, one can add an element of QQ and QQ[x] or an element of ZZ and any other (unitary) ring.

CC: @ThomasBreuer @fingolfin @fieker

[ThomasBreuer]

I think that such extended functionality is nice as long as the documented underlying rules are easy to understand.

For example, if image(f, obj) is defined as image(f, coerce_to(domain(f), obj)) whenever parent(obj) != domain(f) holds then the situation is clear for both users and developers.

If we want to support image(f, set) for subsets set of domain(f), as in the example of an ideal in domain(f), the rule becomes already more complicated. And then the natural question arises whether set may also be something that can be coerced to a subset of domain(f).