Python complex numbers are entered as eg
1 + 3j
To avoid preparsing in sage, enter them as
1r + 3jr
Example:
sage: 1r+3jr
(1+3j)
sage: type(1r+3jr)
<type 'complex'>
Le jeudi 2 octobre 2014 15:08:19 UTC+2, John Cremona a écrit :
>
> What is j?
>
>
> On 2 October 2014 11:07, 'Padmanabhan Tr' via sage-support
> <[email protected] <javascript:>> wrote:
> > 1. I am using SAGE-6.2-x-86_64-Linux
> > 2. From Documentation I understand that the points are chosen randomly &
> may
> > differ at each entry.
> > 3. I wrote the code with [0,1] as coefficient set & tried first. Since I
> did
> > not get the points on the curve I made the change to [0+0j,1+0j]
> consciously
> > & tried.
> > 4. I wrote a Python program to get the points on the EC - extended field
> &
> > checked.; these points are not on the EC.
> > 5. With Python I have the following algebra for the 'point' [9+3j,
> 1+5j].
> >
> > y2 = (1+5j)**2
> >>>> y2
> > (-24+10j)
> >>>> x3 = 1+(9+3j)**3
> >>>> x3
> > (487+702j)
> >>>> a=487%11
> >>>> a
> > 3
> >>>> b = -24%11
> >>>> b
> > 9
> >>>> 702%11
> > 9
> > Mr Cremona, please see this.
> >
> >
> > On Wednesday, October 1, 2014 12:46:57 PM UTC+5:30, Padmanabhan Tr
> wrote:
> >>
> >> I am working with Elliptic curve in extended field. I tried to get
> points
> >> / order in the group. I have copied a small code set & results from
> >> notebook. The points obtained are not in the EC; I have checked it
> using a
> >> Python program I coded for this. Is it a bug / wrong use of codes by
> me?
> >>
> >> F.<f> = GF(11^2,'f')
> >> ff2 = EllipticCurve([0+f*0,1+f*0])
> >> ff2
> >> Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in f of size
> >> 11^2
> >> fg =ff2.gens()
> >> fg
> >> [(8*f : 6*f + 6 : 1), (5*f + 8 : 3*f + 6 : 1)]
> >
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