Opened 5 years ago

Closed 5 years ago

#18831 closed defect (fixed)

Hyperelliptic point counting various methods disagree

Reported by: katestange Owned by:
Priority: critical Milestone: sage-6.8
Component: number theory Keywords: hyperelliptic curves, point counting
Cc: jpflori, defeo, jdemeyer Merged in:
Authors: Jean-Pierre Flori Reviewers: Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: 55674c1 (Commits) 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 5 years ago by jpflori

  • Cc jpflori added

comment:2 Changed 5 years ago by katestange

  • Priority changed from minor to major

comment:3 follow-up: Changed 5 years ago by jpflori

I guess there is a problem with the p-adic precision used. The formula used should be checked. It currently reads:

(ZZ(4*g).exact_log(p) + n//2).floor() + 1

The 4*g part does not look so good.

comment:4 in reply to: ↑ 3 Changed 5 years ago by jpflori

(ZZ(4*g).exact_log(p) + n//2).floor() + 1

The 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 5 years ago by jpflori

  • Authors set to Jean-Pierre Flori
  • 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:

b7b7f9aUse correct bound for traces of the Frobenius matrix of an hec.

comment:6 Changed 5 years ago by jpflori

  • Cc defeo jdemeyer added

comment:7 Changed 5 years ago by chapoton

typo `a_g`` at beginning of the diff

otherwise, looks good to me.

comment:8 Changed 5 years ago by git

  • Commit changed from b7b7f9a14bde497ebc0f65b6ba8589161713da9a to 55674c116c974d8a03762124646f4b9a173cb4a1

Branch pushed to git repo; I updated commit sha1. New commits:

55674c1Small typo in the doc.

comment:9 Changed 5 years ago by jpflori

Fixed!

comment:10 Changed 5 years ago by chapoton

  • Status changed from needs_review to positive_review

Thanks, let's go.

comment:11 Changed 5 years ago by chapoton

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 5 years ago by jpflori

  • Reviewers set to Frédéric Chapoton

It seems to me the new icons make more sense than the previous ones.

comment:13 Changed 5 years ago by vbraun

  • Branch changed from u/jpflori/ticket/18831 to 55674c116c974d8a03762124646f4b9a173cb4a1
  • Resolution set to fixed
  • Status changed from positive_review to closed
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