main.tex

cyclically as we consider successive possible values for $q$.
Calculating the maximums over all values of $q$ yields
$\sage{max(theorem2_bounds)}$ for theorem \ref{thm:rmax_with_uniform_eps}, and
$\sage{max(theorem3_bounds)}$ for theorem \ref{thm:rmax_with_eps1}.
\end{example}

\egroup % end scope where beta redefined to beta_{-}

\subsubsection{All Semistabilizers Giving Sufficiently Large Circular Walls Left
of Vertical Wall}


Goals:
\begin{itemize}
	\item refresher on strategy
	\item point out no need for rational beta
	\item calculate intersection of bounds?
\end{itemize}

\subsection{Irrational $\beta_{-}$}

Goals:
\begin{itemize}
	\item Point out if only looking for sufficiently large wall, look at above
		subsubsection
	\item Relate to Pell's equation through coordinate change?
	\item Relate to numerical condition described by Yanagida/Yoshioka
\end{itemize}

\newpage
\printbibliography

\newpage
\section{Appendix - SageMath code}

\usemintedstyle{tango}

\begin{footnotesize}
\inputminted[
	obeytabs=true,
	tabsize=2,
	breaklines=true,
	breakbefore=./
]{python}{filtered_sage.txt}
\end{footnotesize}

\end{document}