Looking for a good name...

[Florent Hivert]

Dear all,

I'm looking for a good name for the following concept:

In several place in Sage, we need to build a set (ie a parent) which will
generated some objects whose parents are actually a different set. Some
examples:

- I want to model the enumerated set of non negative integer or prime numbers,
but I'd rather the element generated by this set to be plain sage Integers
with parent Integer Ring.
- More generally, I'm building a subset of a certain set and I want the
element to be generated as element for the larger set.
- I'm building the union of different sets...

Of course a different way to do it is to set up coercion to automatically
convert element, but I'd rather to leave this choice to the user.

In MuPAD such a parent (= domain in MuPAD's terminology) was called a "facade
domain". I'm not sure this name of facade is very meaning full for the average
sage user. So I'm looking for suggestions. By the way, maybe this concept is
already used somewhere else in Sage. If so, please give me some pointers.

Thanks for your help,

Cheers,

Florent