There are two confusing things about the code posted.  In the first
line, x is defined to be an element of k=GF(101^5) which generates
that field over the prime field.  In the next line, x is redefined to
be the generator of a polynomial ring over that field.  The first
meaning of x is not used in the input (it could not be) but might
appear in output of field elements, which would be confusing.

Secondly, as this is a curve of genus 2 defined over GF(105), the
number of points over GF(105^d) is completely determined by the
numbers for d=1 and d=2.  And the number of points will be about the
field size, i.e. about 10^10, so the original posted may not really
have wanted to see them all.

Having said all that, the code to find all the points seems very naive
and certainly has various bugs in it (I got a different one).

John

On Apr 15, 11:57 pm, "D. S. McNeil" <[email protected]> wrote:
> >> TypeError: list indices must be integers, not
> >> FiniteField_ext_pariElement
>
> > I see this problem on Mac OS X, so it's not specific to one type of system. 
> >  It may be due to a change in the way finite fields are handled as the size 
> > grows, but I'm not familiar with that code.
>
> > Can anyone hazard a guess?
>
> I think there are two issues:
>
> (1) _points_cache_sqrt, which is called if the order of the base ring
> is >= zech_log_bound=65536, requires the element to have an __index__
> method.  This is what's giving the error message.  If I replace the
> list with a dict and check for membership (or, I guess, the same
> try/except KeyError approach as in _points_fast_sqrt) so __index__ is
> unnecessary, everything seems to work.
>
> The duplication in _points_fast_sqrt/_points_cache_sqrt suggests it
> could do with a refactor.
>
> .. but (2) Isn't this going to have an *extremely* large number of
> points and take at least a month to compute?  IOW, even if we fix what
> I think is the problem, I'm not sure if it's going to be very good at
> doing what the OP wants it to.  I could easily be wrong, though, I'm
> just naively extrapolating..
>
> Doug

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