Heloooooooooooo !!

> Well, the question should be whether Sage supports Cartesian products.

Then perhaps it should be named "set_cartesian_product" until this is fixed
?

> This comes from CategoryObject and there's a TODO to refactor it out into
> the proper category, but that would need everything (with a base ring) to
be
> a new-style parent.

It is good to know that there is a todo somewhere.

Now, permutation groups should have no base ring. Can it be fixed ?

> As mentioned Erik, these are because AG is an enumerated set.

Then I believe enumerated sets should not have methods named
first/next/last, for the methods of enumerated sets are inherited by
absolutely everything, and if it may sound a good idea to have a
first/next/last method in enumerated set it does not sound nice to have the
same in everything which contains something finite.

There is already .an_element() plus an __iter__ if I make no mistake...

>    The gens_dict* should also be refactored out like base_ring IMO (manly
to
> ParentWithGens once we get those to new-style parents). We do want to try
> and get away from the sometimes ambiguous gens() to explicit_generators()
> (and have them return a Family object so we can better index them and for
> consistency with the infinitely generated objects), but we can make gens()
> return a tuple of explicit_generators(), which will fix j_classes. The
last
> one returns the tuple (object, the unique generator) and I have no idea
what
> it is for.
>
> Want me to create the ticket?

Yes please. I have no idea how to fix that myself.

Nathann

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