#12766: Better plotting for elliptic curves
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Reporter: roed | Owner: cremona
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.0
Component: elliptic curves | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Description changed by roed:
Old description:
> The plot for `EllipticCurve('448c6') looks like a vertical line. The
> reason is that `plot` contains
> {{{
> d = 4*x**3 + (a1**2 + 4*a2)*x**2 + (2*a3*a1 + 4*a4)*x + (a3**2 +
> 4*a6)
> r = d.roots(multiplicities=False)
> r.sort()
> if xmax is None:
> xmax = r[-1] + 2
> xmax = max(xmax, r[-1]+2)
> if xmin is None:
> xmin = r[0] - 2
> xmin = min(xmin, r[0]-2)
> }}}
>
> When `d` has only one real root, this approach doesn't work that well.
> One suggestion would be to also require that the plot contains the flex
> points, which can be found from the 3-division polynomial.
New description:
The plot for `EllipticCurve('448c6')` looks like a vertical line. The
reason is that `plot` contains
{{{
d = 4*x**3 + (a1**2 + 4*a2)*x**2 + (2*a3*a1 + 4*a4)*x + (a3**2 + 4*a6)
r = d.roots(multiplicities=False)
r.sort()
if xmax is None:
xmax = r[-1] + 2
xmax = max(xmax, r[-1]+2)
if xmin is None:
xmin = r[0] - 2
xmin = min(xmin, r[0]-2)
}}}
When `d` has only one real root, this approach doesn't work that well.
One suggestion would be to also require that the plot contains the flex
points, which can be found from the 3-division polynomial.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12766#comment:1>
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