#9457: power series comparison should use padded_list
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Reporter: niles
| Owner: malb
Type: defect
| Status: needs_work
Priority: minor
| Milestone: sage-4.5.2
Component: commutative algebra
| Keywords:
Author: niles
| Upstream: N/A
Reviewer:
| Merged:
Work_issues: Fix bug in sage.schemes.elliptic_curves.sha_tate.Sha.an_padic;
mention ticket number in commit messages. |
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Comment(by niles):
Replying to [comment:12 niles]:
> So the {{{O(T^2)}}} in {{{lpv[1]}}} should really be {{{O(5^2) +
O(5^-1)*T + O(T^2)}}}, and this explains why {{{lpv*M}}} really should be
{{{(0, O(T^2))}}} (when M has a 5 in the upper-right entry).
oops, {{{lpv[1]}}} is {{{(-R(p)) * H}}}, so I guess it should be {{{O(5^3)
+ O(5^0)*T + O(T^2)}}}
and the arithmetic is:
{{{
(O(5^3) + (2*5^-1 + O(5^0))*T + O(T^2), O(5^3) + O(5^0)*T + O(T^2))*
[ 5/9 25/18]
[-5/18 5/9]
}}}
should be
{{{
(O(5^4) + (3 + O(5))*T + O(T^2), O(5^4) + O(5)*T + O(T^2))
}}}
which will cause {{{an_padic}}} to still throw the error :(
In any case, computing with a higher precision does give the right answer
with or without the patch. I noticed there is an optional argument for
this:
{{{
sage: set_verbose(1)
sage: EllipticCurve('53a1').sha().an_padic(5, prec=5)
...
verbose 1 (316: sha_tate.py, an_padic) the algebraic leading terms : (3 +
5 + 2*5^3 + 3*5^4 + 3*5^6 + 4*5^7 + 2*5^8 + 5^10 + 4*5^11 + 4*5^12 + 5^13
+ 3*5^15 + 4*5^16 + 4*5^17 + 3*5^18 + 4*5^19 + O(5^20), 5 + 5^2 + 3*5^3 +
4*5^4 + 5^5 + 2*5^6 + 3*5^7 + 2*5^8 + 4*5^9 + 2*5^10 + 4*5^12 + 3*5^13 +
3*5^14 + 4*5^15 + 3*5^16 + 2*5^17 + 3*5^18 + 5^19 + O(5^20))
verbose 1 (316: sha_tate.py, an_padic) ...computing the p-adic L-series
verbose 1 (316: sha_tate.py, an_padic) r = 1
verbose 1 (881: padic_lseries.py, series) using p-adic precision of 5
verbose 1 (881: padic_lseries.py, series) Now iterating over 2500 summands
verbose 1 (316: sha_tate.py, an_padic) the leading terms : [3 + O(5), 5 +
O(5^2)]
verbose 1 (316: sha_tate.py, an_padic) ...putting things together
verbose 1 (316: sha_tate.py, an_padic) the two values for Sha : [1 + O(5),
1 + O(5)]
1 + O(5)
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9457#comment:13>
Sage <http://www.sagemath.org>
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