Opened 6 years ago
Closed 6 years ago
#18831 closed defect (fixed)
Hyperelliptic point counting various methods disagree
Reported by:  katestange  Owned by:  

Priority:  critical  Milestone:  sage6.8 
Component:  number theory  Keywords:  hyperelliptic curves, point counting 
Cc:  jpflori, defeo, jdemeyer  Merged in:  
Authors:  JeanPierre Flori  Reviewers:  Frédéric Chapoton 
Report Upstream:  N/A  Work issues:  
Branch:  55674c1 (Commits, GitHub, GitLab)  Commit:  55674c116c974d8a03762124646f4b9a173cb4a1 
Dependencies:  Stopgaps: 
Description
Various methods of point counts on a hyperelliptic curve produce a result but disagree.
R.<t> = PolynomialRing(GF(11)) H = HyperellipticCurve(t^5 t + 1) print H.count_points() print H.count_points_exhaustive() print H.count_points_frobenius_polynomial() print H.count_points_matrix_traces()
Output:
[8] [19] [19] [8]
This is reproducible in the single cell sage server and sagecloud.
Change History (13)
comment:1 Changed 6 years ago by
 Cc jpflori added
comment:2 Changed 6 years ago by
 Priority changed from minor to major
comment:3 followup: ↓ 4 Changed 6 years ago by
comment:4 in reply to: ↑ 3 Changed 6 years ago by
(ZZ(4*g).exact_log(p) + n//2).floor() + 1The
4*g
part does not look so good.
Actually it makes senses, it comes from expressing the trace of the frobenius on an extension as a sum of powers of the eigenvalues.
So maybe the //
is the problem.
comment:5 Changed 6 years ago by
 Branch set to u/jpflori/ticket/18831
 Commit set to b7b7f9a14bde497ebc0f65b6ba8589161713da9a
 Priority changed from major to critical
 Status changed from new to needs_review
Should be ok now.
I've also cleaned up the Sphinx doc a little bit.
New commits:
b7b7f9a  Use correct bound for traces of the Frobenius matrix of an hec.

comment:6 Changed 6 years ago by
 Cc defeo jdemeyer added
comment:7 Changed 6 years ago by
typo `a_g``
at beginning of the diff
otherwise, looks good to me.
comment:8 Changed 6 years ago by
 Commit changed from b7b7f9a14bde497ebc0f65b6ba8589161713da9a to 55674c116c974d8a03762124646f4b9a173cb4a1
Branch pushed to git repo; I updated commit sha1. New commits:
55674c1  Small typo in the doc.

comment:9 Changed 6 years ago by
Fixed!
comment:10 Changed 6 years ago by
 Status changed from needs_review to positive_review
Thanks, let's go.
comment:11 Changed 6 years ago by
By the way, what do you think of the new proposal for patchbot icons ? (click on top right roundel of this page to see some of them)
comment:12 Changed 6 years ago by
 Reviewers set to Frédéric Chapoton
It seems to me the new icons make more sense than the previous ones.
comment:13 Changed 6 years ago by
 Branch changed from u/jpflori/ticket/18831 to 55674c116c974d8a03762124646f4b9a173cb4a1
 Resolution set to fixed
 Status changed from positive_review to closed
I guess there is a problem with the padic precision used. The formula used should be checked. It currently reads:
The
4*g
part does not look so good.