ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 04 Feb 2024 20:26:50 +0100Get a half point of a point on elliptic curve.https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/Let $E$ be an elliptic cuve on finite field, $P\in E$ be a rational point.
Then, I want to get one of point $Q\in E$ such that $2Q=P$.
What shoud I do?Fri, 02 Feb 2024 23:02:25 +0100https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/Comment by Max Alekseyev for <p>Let $E$ be an elliptic cuve on finite field, $P\in E$ be a rational point.
Then, I want to get one of point $Q\in E$ such that $2Q=P$.</p>
<p>What shoud I do?</p>
https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/?comment=75769#post-id-75769Find the order $N$ of $E$ and compute $\frac{N+1}2P$ ?Sat, 03 Feb 2024 05:38:47 +0100https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/?comment=75769#post-id-75769Answer by Luca for <p>Let $E$ be an elliptic cuve on finite field, $P\in E$ be a rational point.
Then, I want to get one of point $Q\in E$ such that $2Q=P$.</p>
<p>What shoud I do?</p>
https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/?answer=75802#post-id-75802The method `P.division_points(n)` gives the list of all rational points Q such that nQ = P. It works for any base field.
sage: E = EllipticCurve([1,0])
sage: P = E(0)
sage: P.division_points(2)
[(0 : 0 : 1), (0 : 1 : 0)]
Sun, 04 Feb 2024 20:26:50 +0100https://ask.sagemath.org/question/75759/get-a-half-point-of-a-point-on-elliptic-curve/?answer=75802#post-id-75802