#11930: function to check if hyperelliptic curve is singular in the sense of
hyperelliptic curves
------------------------------------------------------------+---------------
Reporter: dkrenn | Owner:
cremona
Type: enhancement | Status:
needs_work
Priority: minor | Milestone:
sage-4.8
Component: elliptic curves | Keywords:
hyperelliptic curve, singular, sd35
Work_issues: make resultants work for more general fields | Upstream:
N/A
Reviewer: Marco Streng, Damiano Testa | Author:
Daniel Krenn, Marco Streng, Damiano Testa
Merged: | Dependencies:
------------------------------------------------------------+---------------
Changes (by mstreng):
* work_issues: add singular examples to the documentation of the
constructor, do some tests => make
resultants work for more general fields
Old description:
> We have
> {{{
> sage: R.<x> = PolynomialRing(GF(3))
> sage: H=HyperellipticCurve(x^5+1)
> sage: H.is_singular()
> True
> }}}
> but `H` is a non-singular hyperelliptic curve.
>
> Hyperelliptic curves are smooth curves mathematically. In Sage, they are
> implemented as plane curves with a singularity at infinity, but that
> singularity can always be resolved.
>
> Apply
>
> * [attachment:11930_singular_hyperelliptic.patch]
> * [attachment:11930_is_singular.patch]
New description:
We have
{{{
sage: R.<x> = PolynomialRing(GF(3))
sage: H=HyperellipticCurve(x^5+1)
sage: H.is_singular()
True
}}}
but `H` is a non-singular hyperelliptic curve.
Hyperelliptic curves are smooth curves mathematically. In Sage, they are
implemented as plane curves with a singularity at infinity, but that
singularity can always be resolved.
Apply
* [attachment:11930b.patch]
* [attachment:11930_is_singular.patch]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11930#comment:10>
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