#11936: image_type of galois_representation of EllipticCurve hangs on first call
-------------------------------+--------------------------------------------
Reporter: dkrenn | Owner: cremona
Type: defect | Status: new
Priority: minor | Milestone: sage-4.7.3
Component: elliptic curves | Keywords: ellipitc curve,
galois_representation, image_type, kash
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by wuthrich):
Thanks. The reason it hangs for you and not for me is that I don't have
the optional package KASH installed. For me it raises the
{{{NotImplemented}}} error and it passes to the except.
So this is not a problem of galois representations, but of how Galois
groups are calculated, I fear. Here is the command that is called:
{{{
R.<x> = QQ[]
f = x^36 + 232*x^35 - 1409590*x^34 - 208771080*x^33 + 542002034595*x^32 +
36849258927684*x^31 - 28701669009468742*x^30 - 1696654153633045980*x^29 +
733820474374957876065*x^28 + 40734331558473487809840*x^27 -
11465777486812349057484526*x^26 - 644250813449703542918356892*x^25 +
125177336158984809052605425600*x^24 + 7693565456991227136062966261700*x^23
- 1116530121510329941650665203053550*x^22 -
72071805573472538906636525663956020*x^21 +
9247213638567012639899553190096543060*x^20 +
489070230674343941519687717200037034600*x^19 -
63821424089313130077462129567772086334300*x^18 -
2076960734134142012731684732329794421249300*x^17 +
262061131595952754895901016203359127399833635*x^16 +
5147227487591445981717637850998628590176666520*x^15 -
185570840529826733080990829035096852217828321100*x^14 -
14878238968057089923405449092346290005791654017200*x^13 -
1547964860908179062293039197523670128542795694054325*x^12 +
34667825973614327709199311382710180266142624053184472*x^11 -
7770857837470021854621559660984035253823067605233925446*x^10 +
332496595306827138498694624156463235069407086237978206720*x^9 +
50515743005409091880315980155729585601028981868957828356515*x^8 -
1488439010064063165131003688799387682254808807901674208959260*x^7 +
11989258410297219585803474836805748253128362834002738889049838*x^6 +
11756542465546263464703460049021530422982958442853357231814356*x^5 +
113628831616635393026353283720453609974562180685019518331117688690*x^4 -
1493996526282733423722228420360775582764552584088512647233847040320*x^3 +
26598660230348604947516388314265739137380307179828340819884014361980*x^2 -
201214061751046506338009477533304151375139639284039242526562543549292*x +
40745133036885593180393722044782759619921619610745354128620011908847961
K.<t> = NumberField(f)
K.galois_group()
}}}
I won't be able to chase if this is a problem in KASH or if the
computation is just extremely difficult with KASH. Magma gives me the
answer
{{{
Permutation group acting on a set of cardinality 36
Order = 36 = 2^2 * 3^2
(1, 3, 14, 19, 21, 32)(2, 4, 13, 20, 22, 31)(5, 15, 35, 23, 34, 17)(6,
16,
36, 24, 33, 18)(7, 10, 11, 26, 27, 30)(8, 9, 12, 25, 28, 29)
(1, 17, 9, 2, 18, 10)(3, 31, 12, 7, 6, 34)(4, 32, 11, 8, 5, 33)(13,
29, 26,
24, 15, 21)(14, 30, 25, 23, 16, 22)(19, 35, 28, 20, 36, 27)
...
}}}
relatively quickly.
If it is a bug somewhere else it has to be fixed there. If instead the
computation is not feasable when having KASH installed, then we best take
this example out of the testing.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11936#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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