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.Mon, 20 Jul 2020 05:18:20 +0200elliptic curve scalar multiplicationhttps://ask.sagemath.org/question/52572/elliptic-curve-scalar-multiplication/ anyone know how to implement sagemath for the following:
i work on algo 1 & 2 (kanayama 2014 - Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials)leaMon, 20 Jul 2020 05:18:20 +0200https://ask.sagemath.org/question/52572/Get point coordinates of curve over number fieldhttps://ask.sagemath.org/question/51672/get-point-coordinates-of-curve-over-number-field/Suppose I have equation of curve `C`:
curve
# => y^2 + (x^2 + x)*y + x
curve.parent()
# => Univariate Polynomial Ring in y over Rational function field in x over Rational Field
and I know that there is a point with `x` value is a root of another equation (i.e. element of corresponding Number Field):
equation
# => x^3 + x^2 - 2*x - 9/2
equation.parent()
# => Univariate Polynomial Ring in x over Rational Field
is x-coordinate of some point of `C`.
How to properly get y-coordinate of `C` in `x`?
It is not as easy as it seems because of conversion problems.
My workaround is as following:
FF.<z> = NumberField(equation)
P.<x,y> = QQ[]
u = P(curve).subs(x=z)
P.<y> = FF[]
return z, P(u).roots()[0][0]
and it doesn't seem right.
Are there more elegant way of doing it?
P.S. `curve` is constructed as follows:
F = FunctionField(QQ, 'x')
x = F.gen()
R.<y> = F[]
curve = y^2 + (x^2 + x)*y + x;
But it was done in another place so I have no direct access to `x` and `y` from above code.petRUShkaMon, 01 Jun 2020 14:56:20 +0200https://ask.sagemath.org/question/51672/