On 2 October 2014 19:32, slelievre <[email protected]> wrote: > Python complex numbers are entered as eg > > 1 + 3j
I did know that of course. The original poster was trying to do arithmetic in GF(11^2) using j which is problematic, especially as the generator chosen by Sage is not a root of x^2+1: sage: GF(11^2,'a').gen().minimal_polynomial() x^2 + 7*x + 2 I pointed this out in a reply to his original post but he persists in thinking that Sage cannot compute correctly. John Cremona > > 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]> 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)] >> > >> > -- >> > You received this message because you are subscribed to a topic in the >> > Google Groups "sage-support" group. >> > To unsubscribe from this topic, visit >> > https://groups.google.com/d/topic/sage-support/10kYPIEKnGw/unsubscribe. >> > To unsubscribe from this group and all its topics, send an email to >> > [email protected]. >> > To post to this group, send email to [email protected]. >> > Visit this group at http://groups.google.com/group/sage-support. >> > For more options, visit https://groups.google.com/d/optout. > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-support" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-support/10kYPIEKnGw/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
