% edwards-conic2.tex
%
% Group law on an Edwards curve
%
% Author: Michael Naehrig
% Public domain

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\psplot[plotstyle=curve]{-3}{-1}{1 x x mul sub 1 -2 x mul x mul add div sqrt neg}
\psplot[plotstyle=curve]{1}{3}{1 x x mul sub 1 -2 x mul x mul add div sqrt}
\psplot[plotstyle=curve]{1}{3}{1 x x mul sub 1 -2 x mul x mul add div sqrt neg}
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\psplot[plotstyle=curve]{-0.685}{0.685}{1 x x mul sub 1 -2 x mul x mul add div sqrt neg}
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\uput[0](-1.1,0.385){$P_1$}
\uput[-90](1.2,-0.484){$P_2$}
\uput[-45](-3,-0.10){$C$}
\uput[0](2,1){$E_{2}$}
\uput[-45](0,1){$\mathcal{O}$}
\uput[135](0,-1){$\mathcal{O}'$}
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{-1.146210 -0.585416 x mul add 1.146210 2.229316 x mul add div}
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\uput[-45](0.666,2.228){$P_3$}
\uput[-135](-0.666,2.228){$-P_3$}
\uput[-45](2,2.228){$L_{1,P_3}$}
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