#11930: disallow non-smooth hyperelliptic curves, and let hyperelliptic curves
know
they are not singular
-------------------------------------------+--------------------------------
Reporter: dkrenn | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.8
Component: elliptic curves | Keywords: hyperelliptic
curve, singular, sd35
Work_issues: | Upstream: N/A
Reviewer: Marco Streng, Damiano Testa | Author: Daniel Krenn,
Marco Streng, Damiano Testa
Merged: | Dependencies:
-------------------------------------------+--------------------------------
Changes (by mstreng):
* status: needs_work => needs_review
* priority: minor => major
* type: enhancement => defect
* work_issues: make resultants work for more general fields or (better)
implement gcd for polynomial rings over
fields and use that =>
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:11930b.patch]
> * [attachment:11930_is_singular.patch]
New description:
Hyperelliptic curves are smooth curves mathematically. These patches add a
check for this to the constructor and implement {{{is_singular}}} to
always return {{{False}}}
Example
{{{
sage: R.<x> = PolynomialRing(GF(3))
sage: H=HyperellipticCurve(x^5+1)
sage: H.is_singular()
# used to return True, now returns False
sage: H=HyperellipticCurve(x^5)
# used to return a curve y^2 = x^5, now raises an error
}}}
Apply
* [attachment:11930c.patch]
* [attachment:11930_is_singular.patch]
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11930#comment:16>
Sage <http://www.sagemath.org>
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