Zeta functions of hyperelliptic curves giving wrong answers

[kedlaya]

Example from 9.0.beta5:

sage: P.<x> = PolynomialRing(GF(3))
sage: u = x^10 + x^9 + x^8 + x
sage: C = HyperellipticCurve(u)
sage: C.frobenius_polynomial()
x^8 + 731*x^7 + 6*x^6 - 720*x^5 + 18*x^4 - 2160*x^3 + 54*x^2 + 19737*x + 81

This is being computed using Pari, but actually gp gives the correct answer:

? u = Mod(1,3)*(x^10 + x^9 + x^8 + x)
? hyperellcharpoly(u)
%1 = x^8 + 2*x^7 + 6*x^6 + 9*x^5 + 18*x^4 + 27*x^3 + 54*x^2 + 54*x + 81

Since the x^7 term is off by 3^6, this is presumably an issue with not enough p-adic precision in the Frobenius matrix we are getting from Pari.

Depends on #28840

Upstream: Fixed upstream, in a later stable release.

CC: @roed314

Component: algebraic geometry

Keywords: hyperelliptic curves, zeta functions

Author: Kiran Kedlaya

Branch: 7eb3cd1

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/28789

[kedlaya]

comment:1

It looks like this was a bug which was just fixed upstream: I can reproduce the bug in gp version 2.11.1, but I get the correct answer in 2.11.2 (which is what I originally tried). So a simple Pari update should suffice.

[kedlaya]

Upstream: Fixed upstream, in a later stable release.

[kedlaya]

comment:2

See #28424 for a Pari upgrade ticket that would resolve this issue.

[kiwifb]

comment:3

#28424 is somewhat exploratory to check for broken stuff. Of course we have gone on the pari git branch in the past when Jeroen was after new features.

But #28424 shouldn't prevent you from making this ticket an upgrade to 2.11.2 to fix your issue. If that make fell you better most sage-on-distros are probably already using 2.11.2 without reported side effects (apart from getting the right answer in the problem pointed out by this ticket - I know I do in sage-on-gentoo).

[kedlaya]

comment:4

OK, so let's make this a ticket to upgrade Pari to 2.11.2. Unfortunately, updating an spkg falls outside of my expertise; but it should be trivial for someone more familiar with the build system.

[fchapoton]

comment:5

I have made #28840 for the upgrade to pari 2.11.2

[slel]

comment:6

Now that #28840 is in, it would be nice to add the example from this ticket
as a doctest in Sage's documentation. Something like:

Check that :trac:`28789` is fixed::

    sage: P.<x> = PolynomialRing(GF(3))
    sage: u = x^10 + x^9 + x^8 + x
    sage: C = HyperellipticCurve(u)
    sage: C.frobenius_polynomial()
    x^8 + 2*x^7 + 6*x^6 + 9*x^5 + 18*x^4 + 27*x^3 + 54*x^2 + 54*x + 81

[kedlaya]

Branch: u/kedlaya/zeta_functions_of_hyperelliptic_curves_giving_wrong_answers

[kedlaya]

Commit: 7eb3cd1

[kedlaya]

Dependencies: 28840

[kedlaya]

Author: Kiran Kedlaya

[kedlaya]

Changed keywords from none to hyperelliptic curves, zeta functions

[kedlaya]

comment:8

Agreed! I doctested both frobenius_polynomial and frobenius_polynomial_pari.

---

New commits:

7eb3cd1

Add doctests re 28789

[fchapoton]

comment:9

ok, good to go. Thanks

[fchapoton]

Reviewer: Frédéric Chapoton

[vbraun]

Changed branch from u/kedlaya/zeta_functions_of_hyperelliptic_curves_giving_wrong_answers to 7eb3cd1

[slel]

comment:11

Possibly related problem reported on sage-support with Sage 9.0:

• https://groups.google.com/d/topic/sage-support/JpbRY1HLEE8/discussion

[slel]

Changed commit from 7eb3cd1 to none

[slel]

Changed dependencies from 28840 to #28840