#5976: [with patch; needs review] Add an Elliptic Curve Isogeny object
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Reporter: shumow | Owner: shumow
Type: enhancement | Status: assigned
Priority: major | Milestone:
Component: number theory | Keywords: Elliptic Curves
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Changes (by cremona):
* cc: kohel (added)
Comment:
I am changing the tag on this from "needs work" to "needs review", since
that's the way to get people to look at it and review it! Which I now
intend to do.
At a first read through this looks really excellent and useful. One
question: why do you allow as input the list of coefficients of the
kernel poly but not a suitable kernel poly itself? For example, I would
expect to compute a 3-isogeny (for example) by forming the 3-division
polynomial, factoring it and passing any degree 1 factors to your code.
Second minor point: it would be sufficient for the two allowed values of
the algorithm parameter to be "velu" and "kohel" rather than the longer
forms you use. (Do you check that the supplied value is one of the two
allowed values and raise an error if not?)
Lastly, one of the things to do next is to insert member functions into
either ell_generic or ell_field to allow computation of an isogeny from a
given curve. i.e. if E is the curve and (say) poly is a suitable kernel
poly then I would like to be able to do E.isogeny(poly) which would return
your isogeny class object. There are more things one would do after that.
This is an excellent contribution to Sage. I will finish the review when
I have finished building 3.4.2 and can test it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5976#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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