#6341: implement Mestre's algorithm for constructing genus 2 hyperelliptic
curves
-------------------------------------------------+-------------------------
Reporter: ncalexan | Owner: was
Type: enhancement | Status:
Priority: major | needs_review
Component: number theory | Milestone: sage-
Keywords: mestre algorithm genus 2 | feature
hyperelliptic curves sd35 sd51 | Resolution:
Authors: Florian Bouyer, Marco Streng | Merged in:
Report Upstream: N/A | Reviewers: Marco
Branch: | Streng
Stopgaps: | Work issues: see
| [comment:14]
| Dependencies:
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Changes (by florian):
* status: needs_work => needs_review
Old description:
> An implementation of Mestre's algorithm for reconstructing genus 2
> hyperelliptic curves from their invariants.
>
> This is limited to fields of characteristic not 2, 3, 5 and to curves
> with automorphism group generated by the hyperelliptic involution. Curve
> equations are not reduced, hence are unusably large over QQ, but see
> below.
>
> That's it. Various other tickets deal with extensions:
>
> * #14755 reduces the discriminant of the hyperelliptic curve (essential
> for getting usable models over number fields)
> * #14756 reduces the hyperelliptic curve equation once the discriminant
> is minimal (also essential for getting usable models over number fields).
> * #12199 treats the case of larger automorphism groups
> * #12200 is about characteristic 2, 3, 5
>
> Apply:
> * [attachment:6341-mestre-only.patch]
> * [attachment:trac_6341-mestre-only_cleanup.patch]
New description:
An implementation of Mestre's algorithm for reconstructing genus 2
hyperelliptic curves from their invariants.
This is limited to fields of characteristic not 2, 3, 5 and to curves with
automorphism group generated by the hyperelliptic involution. Curve
equations are not reduced, hence are unusably large over QQ, but see
below.
That's it. Various other tickets deal with extensions:
* #14755 reduces the discriminant of the hyperelliptic curve (essential
for getting usable models over number fields)
* #14756 reduces the hyperelliptic curve equation once the discriminant is
minimal (also essential for getting usable models over number fields).
* #12199 treats the case of larger automorphism groups
* #12200 is about characteristic 2, 3, 5
Apply:
* [attachment:6341-mestre-only.patch]
* [attachment:trac_6341-mestre-only_cleanup.patch]
* [attachment:trac_6341_correcttions.patch]
--
--
Ticket URL: <http://trac.sagemath.org/ticket/6341#comment:24>
Sage <http://www.sagemath.org>
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