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: | |
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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: |
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
- Milestone changed from sage-6.1 to sage-6.2
comment:2 Changed 7 years ago by
- Cc jpflori added
comment:3 Changed 7 years ago by
- Reviewers set to Jean-Pierre Flori
- Status changed from new to needs_review
comment:4 Changed 7 years ago by
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
- Status changed from needs_review to needs_work
comment:6 Changed 7 years ago by
- 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
- Milestone changed from sage-6.2 to sage-duplicate/invalid/wontfix
comment:8 Changed 7 years ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
Fixed by #15148.