Opened 6 years ago

Closed 6 years ago

# Hyperelliptic point counting various methods disagree

Reported by: Owned by: katestange critical sage-6.8 number theory hyperelliptic curves, point counting jpflori, defeo, jdemeyer Jean-Pierre Flori Frédéric Chapoton N/A 55674c1 55674c116c974d8a03762124646f4b9a173cb4a1

### 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.

### comment:2 Changed 6 years ago by katestange

• Priority changed from minor to major

### comment:3 follow-up: ↓ 4 Changed 6 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 6 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 6 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:

 ​b7b7f9a `Use correct bound for traces of the Frobenius matrix of an hec.`

### comment:7 Changed 6 years ago by chapoton

typo ``a_g``` at beginning of the diff

otherwise, looks good to me.

### comment:8 Changed 6 years ago by git

• Commit changed from b7b7f9a14bde497ebc0f65b6ba8589161713da9a to 55674c116c974d8a03762124646f4b9a173cb4a1

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

 ​55674c1 `Small typo in the doc.`

Fixed!

### comment:10 Changed 6 years ago by chapoton

• Status changed from needs_review to positive_review

Thanks, let's go.

### comment:11 Changed 6 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 6 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 6 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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