\documentclass{article}

%% Created with wxMaxima 11.08.0

\setlength{\parskip}{\medskipamount}
\setlength{\parindent}{0pt}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{color}
\usepackage{amsmath}

\definecolor{labelcolor}{RGB}{100,0,0}

\begin{document}

\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i1) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
kill(all);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o0) }
done
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i1) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
load(ctensor);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o1) }
/usr/share/maxima/5.24.0/share/tensor/ctensor.mac
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i2) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
ct_coords:[r,theta,phi,t];
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o2) }
[r,\theta,\phi,t]
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i3) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
depends([%nu,%lambda],[t,r]);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o3) }
[\nu\left( t,r\right) ,\lambda\left( t,r\right) ]
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i4) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
lg:matrix([-exp(%lambda),0,0,0],[0,-r^2,0,0],[0,0,-r^2*(sin(theta))^2,0],[0,0,0,exp(%nu)]);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o4) }
\begin{pmatrix}-{e}^{\lambda} & 0 & 0 & 0\cr 0 & -{r}^{2} & 0 & 0\cr 0 & 0 & -{r}^{2}\,{\mathrm{sin}\left( \theta\right) }^{2} & 0\cr 0 & 0 & 0 & {e}^{\nu}\end{pmatrix}
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i5) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
cmetric(true);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
Do you wish to see the metric inverse?y;
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t5) }
\begin{pmatrix}-{e}^{-\lambda} & 0 & 0 & 0\cr 0 & -\frac{1}{{r}^{2}} & 0 & 0\cr 0 & 0 & -\frac{1}{{r}^{2}\,{\mathrm{sin}\left( \theta\right) }^{2}} & 0\cr 0 & 0 & 0 & {e}^{-\nu}\end{pmatrix}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o5) }
done
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i6) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
/* last index is up in Gamma */
christof(mcs);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t6) }
{mcs}_{1,1,1}=\frac{\frac{d}{d\,r}\,\lambda}{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t7) }
{mcs}_{1,1,4}=\frac{\left( \frac{d}{d\,t}\,\lambda\right) \,{e}^{\lambda-\nu}}{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t8) }
{mcs}_{1,2,2}=\frac{1}{r}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t9) }
{mcs}_{1,3,3}=\frac{1}{r}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t10) }
{mcs}_{1,4,1}=\frac{\frac{d}{d\,t}\,\lambda}{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t11) }
{mcs}_{1,4,4}=\frac{\frac{d}{d\,r}\,\nu}{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t12) }
{mcs}_{2,2,1}=-{e}^{-\lambda}\,r
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t13) }
{mcs}_{2,3,3}=\frac{\mathrm{cos}\left( \theta\right) }{\mathrm{sin}\left( \theta\right) }
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t14) }
{mcs}_{3,3,1}=-{e}^{-\lambda}\,r\,{\mathrm{sin}\left( \theta\right) }^{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t15) }
{mcs}_{3,3,2}=-\mathrm{cos}\left( \theta\right) \,\mathrm{sin}\left( \theta\right) 
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t16) }
{mcs}_{4,4,1}=\frac{{e}^{\nu-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) }{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t17) }
{mcs}_{4,4,4}=\frac{\frac{d}{d\,t}\,\nu}{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o17) }
done
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i18) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
ricci(true);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t18) }
{ric}_{1,1}=\frac{\frac{d}{d\,r}\,\lambda}{r}+\frac{\left( \frac{d}{d\,t}\,\lambda\right) \,{e}^{\lambda-\nu}\,\left( \frac{d}{d\,t}\,\nu\right) }{4}+\frac{\left( \frac{d}{d\,t}\,\lambda\right) \,{e}^{\lambda-\nu}\,\left( \frac{d}{d\,t}\,\lambda-\frac{d}{d\,t}\,\nu\right) }{2}-\frac{\frac{{d}^{2}}{d\,{r}^{2}}\,\nu}{2}-\frac{{\left( \frac{d}{d\,r}\,\nu\right) }^{2}}{4}+\frac{\left( \frac{d}{d\,r}\,\lambda\right) \,\left( \frac{d}{d\,r}\,\nu\right) }{4}+\frac{\left( \frac{{d}^{2}}{d\,{t}^{2}}\,\lambda\right) \,{e}^{\lambda-\nu}}{2}-\frac{{\left( \frac{d}{d\,t}\,\lambda\right) }^{2}\,{e}^{\lambda-\nu}}{4}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t19) }
{ric}_{1,4}=\frac{\frac{d}{d\,t}\,\lambda}{r}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t20) }
{ric}_{2,2}=-\frac{{e}^{-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) \,r}{2}+\frac{{e}^{-\lambda}\,\left( \frac{d}{d\,r}\,\lambda\right) \,r}{2}-{e}^{-\lambda}+1
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t21) }
{ric}_{3,3}=-\frac{{e}^{-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) \,r\,{\mathrm{sin}\left( \theta\right) }^{2}}{2}+\frac{{e}^{-\lambda}\,\left( \frac{d}{d\,r}\,\lambda\right) \,r\,{\mathrm{sin}\left( \theta\right) }^{2}}{2}-{e}^{-\lambda}\,{\mathrm{sin}\left( \theta\right) }^{2}+{\mathrm{sin}\left( \theta\right) }^{2}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t22) }
{ric}_{4,4}=\frac{{e}^{\nu-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) }{r}+\frac{\left( \frac{d}{d\,t}\,\lambda\right) \,\left( \frac{d}{d\,t}\,\nu\right) }{4}+\frac{{e}^{\nu-\lambda}\,\left( \frac{{d}^{2}}{d\,{r}^{2}}\,\nu\right) }{2}-\frac{{e}^{\nu-\lambda}\,{\left( \frac{d}{d\,r}\,\nu\right) }^{2}}{4}+\frac{{e}^{\nu-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) \,\left( \frac{d}{d\,r}\,\nu-\frac{d}{d\,r}\,\lambda\right) }{2}+\frac{\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu-\lambda}\,\left( \frac{d}{d\,r}\,\nu\right) }{4}-\frac{\frac{{d}^{2}}{d\,{t}^{2}}\,\lambda}{2}-\frac{{\left( \frac{d}{d\,t}\,\lambda\right) }^{2}}{4}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o22) }
done
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i23) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
leinstein(true);
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t23) }
{lein}_{1,1}=\frac{\left( \frac{d}{d\,r}\,\nu\right) \,r-{e}^{\lambda}+1}{{r}^{2}}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t24) }
{lein}_{2,2}=\frac{{e}^{-\nu-\lambda}\,r\,\left( \left( {e}^{\lambda}\,\left( \frac{d}{d\,t}\,\lambda\right) \,\left( \frac{d}{d\,t}\,\nu\right) +2\,{e}^{\nu}\,\left( \frac{{d}^{2}}{d\,{r}^{2}}\,\nu\right) +{e}^{\nu}\,{\left( \frac{d}{d\,r}\,\nu\right) }^{2}-\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -2\,{e}^{\lambda}\,\left( \frac{{d}^{2}}{d\,{t}^{2}}\,\lambda\right) -{e}^{\lambda}\,{\left( \frac{d}{d\,t}\,\lambda\right) }^{2}\right) \,r+2\,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -2\,\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\right) }{4}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t25) }
{lein}_{3,3}=\frac{{e}^{-\nu-\lambda}\,r\,\left( \left( {e}^{\lambda}\,\left( \frac{d}{d\,t}\,\lambda\right) \,\left( \frac{d}{d\,t}\,\nu\right) +2\,{e}^{\nu}\,\left( \frac{{d}^{2}}{d\,{r}^{2}}\,\nu\right) +{e}^{\nu}\,{\left( \frac{d}{d\,r}\,\nu\right) }^{2}-\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -2\,{e}^{\lambda}\,\left( \frac{{d}^{2}}{d\,{t}^{2}}\,\lambda\right) -{e}^{\lambda}\,{\left( \frac{d}{d\,t}\,\lambda\right) }^{2}\right) \,r+2\,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -2\,\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\right) \,{\mathrm{sin}\left( \theta\right) }^{2}}{4}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t26) }
{lein}_{4,1}=\frac{\frac{d}{d\,t}\,\lambda}{r}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%t27) }
{lein}_{4,4}=\frac{{e}^{\nu-\lambda}\,\left( \left( \frac{d}{d\,r}\,\lambda\right) \,r+{e}^{\lambda}-1\right) }{{r}^{2}}
\end{math}

\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o27) }
done
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i28) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
scurvature();
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o28) }
({e}^{-\nu-\lambda}\,(\left( {e}^{\lambda}\,\left( \frac{d}{d\,t}\,\lambda\right) \,\left( \frac{d}{d\,t}\,\nu\right) +2\,{e}^{\nu}\,\left( \frac{{d}^{2}}{d\,{r}^{2}}\,\nu\right) +{e}^{\nu}\,{\left( \frac{d}{d\,r}\,\nu\right) }^{2}-\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -2\,{e}^{\lambda}\,\left( \frac{{d}^{2}}{d\,{t}^{2}}\,\lambda\right) -{e}^{\lambda}\,{\left( \frac{d}{d\,t}\,\lambda\right) }^{2}\right) \,{r}^{2}+\left( 4\,{e}^{\nu}\,\left( \frac{d}{d\,r}\,\nu\right) -4\,\left( \frac{d}{d\,r}\,\lambda\right) \,{e}^{\nu}\right) \,r+\left( 4-4\,{e}^{\lambda}\right) \,{e}^{\nu}))/(2\,{r}^{2})
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i29) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
mu;
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o29) }
\mu
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i30) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
%alpha;
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o30) }
\alpha
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i31) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
%lambda;
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o31) }
\lambda
\end{math}
%%%%%%%%%%%%%%%


\noindent
%%%%%%%%%%%%%%%
%%% INPUT:
\begin{minipage}[t]{8ex}{\color{red}\bf
\begin{verbatim}
(%i32) 
\end{verbatim}}
\end{minipage}
\begin{minipage}[t]{\textwidth}{\color{blue}
\begin{verbatim}
%mu;
\end{verbatim}}
\end{minipage}
%%% OUTPUT:
\begin{math}\displaystyle
\parbox{8ex}{\color{labelcolor}(\%o32) }
\mu
\end{math}
%%%%%%%%%%%%%%%

\end{document}
