% ecadd.tex
%
% Graphical representation of point addition 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 0.9102 mul 0.4057 add}

\rput(-0.1,0.3146){{\color{red} $\bullet$}}
\rput(0.15,0.25){$Q$}
\rput(-0.9,-0.4135){{\color{red} $\bullet$}}
\rput(-0.67,-0.4135){$P$}

\rput(1.82812,2.0697){{\color{red} $\bullet$}}

\psline[linestyle=dashed,dash=5pt 5pt](1.82812,2.0697)(1.82812,-2.0697)
\rput(1.82812,-2.0697){{\color{red} $\bullet$}}
\rput(2.02812,-2.0697){$R$}

\end{pspicture}