#5856: elliptic curves over Z/pZ are treated totally differently than elliptic
curves over GF(p)
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Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.2
Component: number theory | Keywords:
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Changes (by AlexGhitza):
* cc: cremona (added)
Comment:
I see two options:
1. Change the {{{EllipticCurve}}} constructor so that if it is given
{{{Zmod(p)}}} for a prime number {{{p}}}, it actually returns the
corresponding elliptic curve over {{{GF(p)}}}. This would probably only
take a couple of minutes to do. However, this means that creating a curve
over {{{Zmod(5)}}} would return a different type than creating a curve
over {{{Zmod(4)}}}.
2. We keep creating the curve over {{{Zmod(p)}}} as before but we attach
to it the corresponding curve over {{{GF(p)}}} (cached). We put in the
headers of all the methods from {{{GF(p)}}} and have them call the
corresponding methods from {{{GF(p)}}} to do all the work. This is a
somewhat ugly.
Right now I like the first option better than the second. But maybe there
are better ideas out there, or convincing arguments in favour of one thing
or the other.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5856#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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