#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-5.1
Component: elliptic curves | Resolution:
Keywords: hyperelliptic curve singular smooth sd35 | Work issues:
Report Upstream: N/A | Reviewers:
Marco Streng, Damiano Testa, David Eklund
Authors: Daniel Krenn, Marco Streng, Damiano Testa | Merged in:
Dependencies: | Stopgaps:
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Comment (by davideklund):
This all looks good. If the other reviewers agree, we can change the
status to positive review.
I only have two small comments on the patches:
About the example beginning with "A hyperelliptic curve should not be
given by polynomials of degree greater than `2g+2`, where `g` is the
genus." I'm not sure I understand what this means. The genus of what? It
is slightly unclear since I gather that in this example there is no
hyperelliptic curve whose genus we could be referring to. Is it the genus
of the desingularization of the corresponding plane curve? The way I view
this, the equation {{{y^2+hy=f}}}, where {{{h=x^100}}} and
{{{f=x^6+1-h^2/4}}} (appropriately homogenized with {{{z}}}) defines a
curve in weighted projected space {{{P(1,100,1)}}} but that curve is
singular at the point {{{(x,y,z)=(1,-1/2,0)}}}.
About the example beginning "Input with integer coefficients creates
objects with the integers as base ring, but only checks smoothness over
`QQ`, not `ZZ`". Is this to be interpreted as saying that the example
provided is not smooth as a scheme over {{{Spec(ZZ)}}}?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11930#comment:35>
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