#4964: [with patch, with positive review] Add Weil pairing to Sage
-------------------------------------+--------------------------------------
Reporter: dmhansen | Owner: mollerhansen
Type: enhancement | Status: reopened
Priority: minor | Milestone: sage-3.3
Component: algebraic geometry | Resolution:
Keywords: pairing, elliptic curve |
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Changes (by cremona):
* summary: [with patch, needs review] Add Weil pairing to Sage => [with
patch, with positive review] Add Weil pairing
to Sage
* milestone: sage-3.4.1 => sage-3.3
Comment:
The revised patch fixes the bug. I have taken the liberty of adding my
patch trac_4964a.patch (to be applied after trac_4964.patch) which does
the following:
1. Adds a doctest to show that the bug I reported is fixed.
2. Moves the functions to the class EllipticCurvePoint_field, as I
originally suggested, since this works perfectly well!
3. Illustrate my point in 2 by adding a docest computing a 5th order
Weil pairing over the 5th cyclotomic field.
4. Edited the documentation about the implementation only applying when
both points have the same order n, since in fact the only condition is
that n*P=n*Q=0, i.e. that they are both in E[n], so the function could be
applied to any two torsion points provided that n is a common multiple of
their orders.
If dmhansen is happy with these adjustments then I am happy with the
(combined) patch, so I am optimistically giving it a positive review.
Ideally, a 3rd party would take a look too.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4964#comment:17>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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