Opened 7 years ago

Closed 7 years ago

#15754 closed defect (duplicate)

Frobenius polynomial of hyperelliptic curve does not account for base field

Reported by: kedlaya Owned by:
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: number theory Keywords: hyperelliptic curve, Frobenius polynomial, base change
Cc: jpflori Merged in:
Authors: Reviewers: Jean-Pierre Flori
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

When one defines a hyperelliptic curve over a prime field and then changes the base ring to an extension field, the Frobenius polynomial should change accordingly. Currently it does not:

sage: P.<x> = PolynomialRing(GF(37))
sage: u = x^5 + 2*x + 1
sage: H = HyperellipticCurve(u)
sage: H.frobenius_polynomial()
x^4 - 2*x^3 + 48*x^2 - 74*x + 1369
sage: F.<a> = GF(37^2)
sage: HF = H.change_ring(F)
sage: HF.frobenius_polynomial()
x^4 - 2*x^3 + 48*x^2 - 74*x + 1369

Change History (8)

comment:1 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:2 Changed 7 years ago by jpflori

  • Cc jpflori added

comment:3 Changed 7 years ago by jpflori

  • Reviewers set to Jean-Pierre Flori
  • Status changed from new to needs_review

Fixed by #15148.

comment:4 Changed 7 years ago by jpflori

Note that the second test in the ticket description would take a very long time (as it's done by computing naively the number of points on the curve).

We hsould though include an example showing that the base ring is taken into account on a manageable example.

comment:5 Changed 7 years ago by jpflori

  • Status changed from needs_review to needs_work

comment:6 Changed 7 years ago by jpflori

  • Status changed from needs_work to positive_review

In fact there are already a bunch of tests from #15148 showing that hypellfrob is only used on prime fields and is correclty done with the naive method in other cases and that it is very slow and so on. So let's close this one as won't fix.

comment:7 Changed 7 years ago by jpflori

  • Milestone changed from sage-6.2 to sage-duplicate/invalid/wontfix

comment:8 Changed 7 years ago by vbraun

  • Resolution set to duplicate
  • Status changed from positive_review to closed
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