\section{Computational Appendices}

We believe in implementing as much as possible. Actually, we hardly believe ourselves unless we implement.

All code in these appendices is written in {\sl Mathematica}~\cite{Wolfram:Mathematica}.

\subsection{Computational Verification of Theorem~\ref{thm:GDO},~(i)} \label{app:GDOCompositions}

\input GDOCompositions.tex
