% ecdouble.tex
%
% Graphical representation of point doubling on the elliptic curve 
% E: y^2 = x^3 - x over the real numbers
%
% Author: Peter Schwabe
% Public domain


\psset{unit=1.2cm} 
\begin{pspicture}(-2,-2.5)(2,2.5) 
\psaxes{->}(0,0)(-2,-2.5)(2,2.5)  

\psplot[plotstyle=curve]{1}{2.0}{x x mul x mul x sub sqrt neg}
\psplot[plotstyle=curve]{-1}{0}{x x mul x mul x sub sqrt neg}
\psplot[plotstyle=curve]{1}{2.0}{x x mul x mul x sub sqrt}
\psplot[plotstyle=curve]{-1}{0}{x x mul x mul x sub sqrt}

\psplot[plotstyle=curve]{-2}{2}{x 0.3933 mul 0.8728 add}

\rput(-0.7,0.5975){{\color{red} $\bullet$}}
\rput(-0.7,0.7975){$P$}

\rput(1.55469,1.4843){{\color{red} $\bullet$}}

\psline[linestyle=dashed,dash=5pt 5pt](1.55469,1.4843)(1.55469,-1.4843)
\rput(1.55469,-1.4843){{\color{red} $\bullet$}}
\rput(1.75469,-1.4843){$R$}
\end{pspicture}