#9457: power series equality fails when trailing coefficients are zero
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Reporter: niles | Owner: malb
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.2
Component: commutative | Resolution:
algebra | Merged in:
Keywords: | Reviewers:
Authors: niles | Work issues: resolve problems with
Report Upstream: N/A | sha_tate.py
Branch: | Commit:
u/niles/ticket/9457 | e2219602a9d360f465ad79b098e4f923765ab791
Dependencies: | Stopgaps: #15748
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Comment (by niles):
Replying to [comment:29 wuthrich]:
> I try to remember what happened 4 years ago.
Thanks for putting this together :)
>
> So let's make a list - as there are several overlapping tickets and
issues:
>
> * (see #4656) is_zero is broken for power series. This causes your
{{{QpT( O(5^-1))}}} to print as zero. It remembers that it is not, if you
have .list you see its first coefficient is still {{{O(5^-1)}}}. We should
change {{{__nonzero__}}} in power_series_poly.pyx
>
#5075 addresses this too -- the patch there introduces 3 concepts of zero:
exact zero (infinite precision), maximally zero (zero to maximal precision
allowed by parent ring), and inexact zero (zero to precision less than
maximal precision). These are used to define some functions that are
equal to degree for polynomials over exact rings, but more subtle over
inexact rings, and these functions, in turn, are used to fix other
functions . . .
In short, that ticket seems to me like a good place to start.
> * (see #4656, too) power series compare wrongly. Your suggestion to use
padded_list above is better than what I tried to do in the other ticket.
That is cmp in power_series_ring_element.pyx
`padded_list` works, but is substantially slower. In the latest commit
here, I have a more direct fix. The patch at #5075 also has a fix that
looks similar to mine, but I didn't compare them closely.
>
> * (see #4656) power series also print wrongly. You would expect the
inexact coefficients of the form {{{O(p^2)}}} to print, too. I tried to
change that in the other ticket. That is {{{_repr_}}} in
power_series_ring_element.pyx
>
#5075 may address this too, at least judging by how some of the new
doctests appear.
> * (see #8198) Matrix multiplication on p-adics looses precision. I
believe that is the heart of the problem for getting the right answer for
this Dp_series. If I understand correctly you have spotted the same thing
above.
This might be right . . . in my calculation above, the input to the
vector*matrix multiplication is wrong, so I can't tell whether the matrix
multiplication would also go wrong or not.
>
> * There is also #5075 which I have never looked at myself.
I think we should go there :)
>
> We could take the out the doc-string in sha-tate out for now, so that
this and #4656 can be closed. Then reintroduce it if we can fix #8198.
Hmmm . . . that doctest is holding up some pretty reasonable fixes, but
it's also the only reason that we noticed these padic problems in the
first place so I'm extremely reluctant to take it out. I think it is
especially bad to take it out before we fully understand where the
problems are coming from.
--
Ticket URL: <http://trac.sagemath.org/ticket/9457#comment:30>
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