#3416: Weierstrass form for cubics
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Reporter: moretti |
Owner: was
Type: enhancement |
Status: needs_work
Priority: major |
Milestone: sage-5.6
Component: elliptic curves |
Resolution:
Keywords: nagell, weierstrass, cubic, elliptic curves, editor_wstein |
Work issues:
Report Upstream: N/A |
Reviewers: John Cremona, Marco Streng, Nils Bruin
Authors: Niels Duif |
Merged in:
Dependencies: |
Stopgaps:
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Comment (by vbraun):
I think Maple does the same as #13458: it returns a rational multi-
covering. This you can also get without a point.
Currently I don't like the way the transformation is returned in this
ticket. A bunch of text, really? Can't we return concatenated maps or
something that can be accessed programmatically? Or, failing that, a
custom python object that can be queried for the defining polynomials.
The good news is that we seem to have all relevant algorithms implemented,
we just need to settle on an interface. My suggestion would be
A constructor function EllipticCurve_from_curve(equation, point=None,
proof=False)
If proof=False then just the Weierstrass form is returned using whatever
algorithm is fastest (probably ignoring the given point).
If proof=True and no point is given, a pair (E,f) of elliptic curve and
rational covering map from the curve to the Weierstrass form is returned.
If proof=True and a point is given, then a pair (E,f) is returned such
that f is an isomorphism.
Make EllipticCurve_from_cubic an alias for EllipticCurve_from_curve. The
latter will also handle e.g. y^2=quartic(x) e.g., so it shouldn't mention
cubic.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3416#comment:40>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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