# No subject

Saleh Al-harbi alharbi at ma.man.ac.uk
Sun Mar 29 13:10:32 CEST 1998

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Dear    LATEX user
I try to do some Rooted trees (graph theory)
as J.D. Lambert did in his book [ Numerical Methods for Ordinary
Differential Systems PP. 164 ( below tex file) 1993],
but I couldn't .
Could you please explane to me who to do it .

Thank you , and best regard.

-- S. Alharbi.

\documentclass[12pt]{report}
%\documentclass[16pt,PhD]{mythesis}
\usepackage {pstricks,pst-node,pst-tree}
\usepackage {rotating}
\begin{document}
%\pstree{\Tdot}
%{
%\Tdot
%\pstree{\Tdot}
%{
%\pstree{\Tdot}
%{\Tdot \Tdot \Tdot}
%\Tdot
%}
\begin{table}[h]
\begin{center}
\begin{tabular}{|l||r|c|c|c|c|c|c|}\hline
Order&Tree& t&$F(t)$ & $r(t)$ & $\sigma(t)$& $\gamma(t)$ &
$\alpha(t)$\\\hline
1& \Tc*{2pt} & $\tau$ &  $f$   & 1& 1 & 1 & 1 \\\hline
2&
\newsavebox{\foo}
\savebox{\foo}{\parbox{1in}{
\pstree{\Tdot}
{\Tdot}
}}%
\begin{turn}{-45}\usebox{\foo}\end{turn}
& $[\tau]$&   $\{f\}$&
2 & 1 & 2 & 1 \\\hline
3&
\TC*  \TC*}
%\newsavebox{\f1}
%\savebox{\f1}{\parbox{1in}{
%\pstree{\Tdot}i
%{\Tdot  \Tdot  }
%}}%
%\begin{turn}{90}\usebox{\f1}\end{turn}
&
$[\tau^2]$ & $\{f^2\}$ &3& 2&3&1 \\
\TC*  \TC*}
& $[[\tau]]$ & $\{_2f \}_2$ &3 & 1& 6 & 1 \\\hline
4    &
\TC*  \TC* \TC*}
&$[\tau^3]$ &$\{f^3 \}$&4&6&4&1 \\
\TC*  \TC* \TC*}
& $[\tau[\tau]]$ & $\{f \{f \}_2$ &4& 1&8& 3 \\
\TC*  \TC* \TC*}
& $[[\tau^2]]$ & $\{_2f^2 \}_2$ &4 & 2 &12 &1 \\
\TC*  \TC* \TC*}
& $[[[\tau]]]$ & $\{_3f \}_3$ &4& 1& 24 &1\\\hline
\end{tabular}
\caption{\label{tb2.4.1} Coefficients, trees, and elementary differentials of
order up to 4. }
\end{center}
\end{table}

\end{document}

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