Vasily Golyshev on Mon, 14 Oct 2002 00:33:08 +0400 (MSD)


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ellisoncurve() and ellpointtoz()


Hi,
here is an irregularity in ellisoncurve():

? C=ellinit([0,0,0,0,1])
%1 = [0, 0, 0, 0, 1, 0, 0, 4, 0, 0, -864, -432, 0,
[-1.000000000000000000000000000, 0.5000000000000000000000000000 -
0.8660254037844386467637231707*I, 0.5000000000000000000000000000 +
0.8660254037844386467637231707*I]~, 4.206546315976362783525057237,
-2.103273157988181391762528618 + 1.214325323943790805909970844*I,
-1.293554779614895267476757512 + 1.44309482 E-29*I,
0.6467773898074476337383787562 - 1.120251300333280219655206320*I,
5.108115717832556535122194506]


? ellisoncurve(C,[Mod(t,t^2-t+1),0])
%2 = 1
? ellisoncurve(C,[1/2-sqrt(3)/2*I,0])
%3 = 0

Now, what I actually need for my purposes is to find
(up to a sign) ellpointtoz() of a point, given only its abscissa,
but it appears that I have to do

 ellpointtoz(C,[p[1],ellordinate(C,p[1])[1]])

first, which fails in this case.