Perhaps something towards (2) rather than (5), I believe the general 
principle is to have any method that a "standard" user will encounter to 
return a Sage Integer. The reasoning is exactly as you mentioned to avoid 
surprises to the user (e.g., why does "_.factor()" work for "foo" but not 
for "bar"?).

Best,
Travis


On Monday, July 12, 2021 at 1:44:05 AM UTC+10 Nils Bruin wrote:

> I'd expect it's (1). A more nuanced version might be:
>
> (5) As a rule, an Integer should probably be returned if the code is 
> probably going to interact with other sage code, but if you have good 
> (efficiency) reasons to prefer a python integer or if the primary function 
> is to be compatible with other python code (such as "len" methods) then 
> returning a python integer should be fine.
>
> The reality is that the "python integer" type interwoven with the language 
> and sage cannot avoid it.
>
>

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