On Wednesday, April 22, 2015 at 9:06:16 AM UTC-7, Peter Mueller wrote:
>
> without telling what the method is supposed to be. Trying 
> R.base_extend(GF(25,"dummy")) raises an error, so it doesn't seem to be a 
> base ring extension. Also, for some time I believed that it is not possible 
> to change the term order of a polynomial ring, until I learned (from a 
> recent answer in this forum) that, despite its misleading name, 
> .change_ring does that. I believe that a major weakness of the sage 
> documentation is that there are no ``see also''s at the end of a doc entry. 
> For instance, R.term_order? should point to R.change_ring. 
>

It seems it's something completely generic and I'm not so sure it should be 
there in the first place. If you want to call the routine on R and not get 
an error you can try

sage: R.base_extend(GF(25,"dummy")['a','b'])
Multivariate Polynomial Ring in a, b over Finite Field in dummy of size 5^2

Are you aware that with "??" you'll get the code (if sage can find it)? For 
such simple routines that's often more informative than the docstring (and 
the simplicity of the routine is probably what put the original author off 
writing a useful docstring in the first place). Indeed:

sage: parent((a^2+b^2).base_extend(GF(25,"dummy")['a','b']))
Multivariate Polynomial Ring in a, b over Finite Field in dummy of size 5^2

so it's just coercion for this case.

It seems that the standard "base_extend" method encountered here (coming 
from sage.rings.ring!) only considers the ring as an algebra over itself, 
which of course is inconsistent with

sage: R.base_ring()
Finite Field of size 5

so it seems base_extend should be overridden, perhaps already on 
ParentWithBase. After all, at least in this case the coercion framework can 
figure out how to make the extension:

sage: parent(a+GF(25,'t')(1))
Multivariate Polynomial Ring in a, b over Finite Field in t of size 5^2

If you just start browsing the methods on sage object you can quickly make 
it to dark and forgotten corners...

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