#4964: [with patch, with positive review] Add Weil pairing to Sage
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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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Comment (by dmhansen):
> 1. Adds a doctest to show that the bug I reported is fixed.
- Great! I also made a similar doc test using your example to test the
_miller_ unction implementation, so now we should be covered.
> 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.
- This is really good. Thank you a lot, really cool that it just
generalizes without any problems.
> 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.
- I agree. That's an important point to include.
> 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.
I am very happy with the changes and yes it would be nice to get a 3rd
party review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4964#comment:18>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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