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elliptic curves -- implement P.divide(n) for P a point on an elliptic curve and n an integer #3109
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comment:2
Attachment: sage-3109-part1.patch.gz {{{{
Something like that is next on my list. Maybe instead of P.divide(m), |
this adds lots of docs and fixes bugs. finishes implementing full_division_polynomial and multiplication by n. |
Attachment: sage-3109-part2.patch.gz |
comment:3
Attachment: sage-3109-part3.patch.gz |
comment:4
Review under way. |
comment:5
I applied the 3 patches in succession with no problems, and all the doctests in sage/schemes/elliptic_curves pass. All very well written and commented and documented with excellent doctests. I do have two issues, one more important than the other:
I really really think that we should implement this more general version for division polynomials now, even though your code for P.division_points() cleverly gets around it. To end on a more positive note: this is very well written and a model for others to follow! |
comment:6
Regarding the referee's report:
|
Attachment: sage-3019-part4.patch.gz some slight refactoring in ell_point.py |
comment:7
Comments on the comments:
Go for it! |
comment:8
John said:
I just want to point out that there were no typos in Silverman in that case. What is true Regarding your comments on my comments: |
comment:9
Merged all four patches in Sage 3.0.2.alpha0 |
Implement P.divide(n) for P a point on an elliptic curve and n an integer. This will:
ValueError
.Also, implement P.is_divisible_by(n) trivially in terms of the above, and document
the connection between the two functions. Also, have both implemented in terms of
a third function that just finds the polynomial whose root is x(Q), so we
can implement is_divisible_by more efficiently.
An algorithm to do this is described at the end of section 3 of
http://wstein.org/papers/kolyconj/
If you see this ticket and think of doing this, please immediately contact me (wstein@gmail.com) before, since I'm planning on doing this very soon.
Component: number theory
Issue created by migration from https://trac.sagemath.org/ticket/3109
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