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

   It does return a Cartesian product, but not without carrying as much 
structure as you might expect. It doesn't make sense to me to rename this 
-- as with other things in Sage, if it's not implemented, then you can 
request it or go ahead and do so yourself. I don't believe in making a more 
complicated situation when we want the current setup at the end of the day.

>
> It is good to know that there is a todo somewhere.
>
> Now, permutation groups should have no base ring. Can it be fixed ?
>

IDK off hand how difficult this would be. It depends upon how many 
old-style parents in Sage currently need that method. My guess is 
polynomial rings and free modules (http://trac.sagemath.org/ticket/10513 
handles the modules case). Fundamentally it's an easy fix: remove the 
method and let it be inherited from the category. However everything needs 
to use categories correctly.

> 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...
>

We need to append "finite" for the last method. However first() and next() 
are good to keep and differ from an_element(), which is recommended to 
return a non-trivial element and first() is usually trivial, and 
__iter__(), which doesn't get the next element in the numeration after a 
particular element.

Yes please. I have no idea how to fix that myself.
>
> This is now http://trac.sagemath.org/ticket/16718. I'll try to write a fix 
shortly.

Best,
Travis

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