#13084: Weierstrass form for toric elliptic curves
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.1
Component: algebraic geometry | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Volker Braun | Merged in:
Dependencies: #12553 | Stopgaps:
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Changes (by vbraun):
* cc: novoselt (added)
* status: new => needs_review
* dependencies: => #12553
Old description:
> This ticket implements the Weierstrass form for anticanonical
> hypersurfaces in toric surfaces defined by reflexive polygons:
> {{{
> sage: from sage.schemes.toric.weierstrass import WeierstrassForm
> sage: R.<x,y> = QQ[]
> sage: cubic = x^3 + y^3 + 1
> sage: WeierstrassForm(cubic) # cubic in P^2
> (0, -27/4)
> sage: WeierstrassForm(x^4 + y^2 + 1) # in P^2[112]
> (-4, 0)
> sage: WeierstrassForm(x^2*y^2 + x^2 + y^2 + 1) # in P^1xP^1
> (-16/3, 128/27)
> }}}
New description:
This ticket implements the Weierstrass form (of the Jacobian) of
anticanonical hypersurfaces in toric surfaces defined by reflexive
polygons:
{{{
sage: from sage.schemes.toric.weierstrass import WeierstrassForm
sage: R.<x,y> = QQ[]
sage: cubic = x^3 + y^3 + 1
sage: WeierstrassForm(cubic) # cubic in P^2
(0, -27/4)
sage: WeierstrassForm(x^4 + y^2 + 1) # in P^2[112]
(-4, 0)
sage: WeierstrassForm(x^2*y^2 + x^2 + y^2 + 1) # in P^1xP^1
(-16/3, 128/27)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13084#comment:1>
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