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equations_output_integer_linear.tex
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\begin{alignat}{2}
\label{eq:scalarFlux_0}
& \phi = \\
& + \l[ I + \frac{1}{3} \opL_r + \frac{1}{5} \opL_r^{2} + \frac{1}{7} \opL_r^{3} \r] \l[ F - \ATL \r] \nonumber \\
& + \l[ I + \frac{3}{5} \opL_r + \frac{3}{7} \opL_r^{2} \r] \axaziTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:isoATL_0}
& \ATL = \\
& - \l[ \frac{1}{3} \opL_z + \frac{1}{5} \opL_z^{2} + \frac{1}{7} \opL_z^{3} \r] \l[ F - \RTL \r] \nonumber \\
& - \l[ I + \frac{3}{5} \opL_z + \frac{3}{7} \opL_z^{2} \r] \halfLZ \radpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linradpolTL_0}
& \radpolTL = \\
& + \l[ \frac{1}{5} \opL_r + \frac{3}{35} \opL_r^{2} + \frac{1}{21} \opL_r^{3} \r] \axpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linaxpolTL_0}
& \axpolTL = \\
& + \l[ \frac{1}{3} I + \frac{1}{5} \opL_z + \frac{1}{7} \opL_z^{2} \r] \halfLZ \l[ F - \RTL \r] \nonumber \\
& + \l[ \frac{3}{5} \opL_z + \frac{3}{7} \opL_z^{2} + \frac{1}{3} \opL_z^{3} \r] \radpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linradpolTL_1}
& \radpolTL = \\
& + \l[ \frac{1}{5} \opL_r + \frac{3}{35} \opL_r^{2} + \frac{1}{21} \opL_r^{3} \r] \axpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linaxpolTL_1}
& \axpolTL = \\
& + \l[ \frac{1}{3} I + \frac{1}{5} \opL_z + \frac{1}{7} \opL_z^{2} \r] \halfLZ \l[ F - \RTL \r] \nonumber \\
& + \l[ \frac{3}{5} \opL_z + \frac{3}{7} \opL_z^{2} + \frac{1}{3} \opL_z^{3} \r] \radpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linradpolTL_2}
& \radpolTL = \\
& + \l[ \frac{1}{15} \opL_r + \frac{1}{35} \opL_r^{2} + \frac{1}{25} \opL_r \opL_z \r] \halfLZ \l[ F - \RTL \r] \nonumber \\
& + \l[ \frac{3}{25} \opL_r \opL_z + \frac{9}{175} \opL_r^{2} \opL_z + \frac{3}{35} \opL_r \opL_z^{2} \r] \radpolTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linradpolTL_3}
& \radpolTL = \\
& + \l[ \frac{1}{15} \opL_r + \frac{1}{35} \opL_r^{2} + \frac{1}{25} \opL_r \opL_z \r] \halfLZ \l[ F - \RTL \r] \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:isoATL_1}
& \ATL = \\
& - \l[ \frac{1}{3} \opL_z + \frac{1}{5} \opL_z^{2} + \frac{1}{7} \opL_z^{3} + \frac{1}{15} \opL_r \opL_z + \frac{1}{35} \opL_r^{2} \opL_z + \frac{2}{25} \opL_r \opL_z^{2} \r] \l[ F - \RTL \r] \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:isoATL_2}
& \ATL = \\
& - \l[ \frac{1}{3} \opL_z + \frac{1}{5} \opL_z^{2} + \frac{1}{7} \opL_z^{3} + \frac{1}{15} \opL_r \opL_z + \frac{1}{35} \opL_r^{2} \opL_z + \frac{2}{25} \opL_r \opL_z^{2} \r] \phi \nonumber \\
& - \l[ \frac{1}{3} \opL_z + \frac{1}{5} \opL_z^{2} + \frac{1}{7} \opL_z^{3} + \frac{1}{15} \opL_r \opL_z + \frac{1}{35} \opL_r^{2} \opL_z + \frac{2}{25} \opL_r \opL_z^{2} \r] \ATL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linaxaziTL_0}
& \axaziTL = \\
& + \l[ \frac{1}{5} \opL_z + \frac{3}{35} \opL_z^{2} + \frac{1}{21} \opL_z^{3} \r] \radaziTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linradaziTL_0}
& \radaziTL = \\
& + \l[ \frac{1}{3} \opL_r + \frac{1}{5} \opL_r^{2} + \frac{1}{7} \opL_r^{3} \r] \l[ F - \ATL \r] \nonumber \\
& + \l[ \frac{3}{5} \opL_r + \frac{3}{7} \opL_r^{2} \r] \axaziTL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:linaxaziTL_1}
& \axaziTL = \\
& + \l[ \frac{1}{15} \opL_r \opL_z + \frac{1}{25} \opL_r^{2} \opL_z + \frac{1}{35} \opL_r \opL_z^{2} \r] \l[ F - \ATL \r] \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:scalarFlux_1}
& \phi = \\
& + \l[ I + \frac{1}{3} \opL_r + \frac{1}{5} \opL_r^{2} + \frac{1}{7} \opL_r^{3} + \frac{1}{15} \opL_r \opL_z + \frac{2}{25} \opL_r^{2} \opL_z + \frac{1}{35} \opL_r \opL_z^{2} \r] \l[ F - \ATL \r] \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:scalarFlux_2}
& \phi = \\
& + \l[ I + \frac{1}{3} \opL_r + \frac{1}{5} \opL_r^{2} + \frac{1}{7} \opL_r^{3} + \frac{1}{15} \opL_r \opL_z + \frac{2}{25} \opL_r^{2} \opL_z + \frac{1}{35} \opL_r \opL_z^{2} \r] F \nonumber \\
& - \l[ I + \frac{1}{3} \opL_r + \frac{1}{5} \opL_r^{2} + \frac{1}{7} \opL_r^{3} + \frac{1}{15} \opL_r \opL_z + \frac{2}{25} \opL_r^{2} \opL_z + \frac{1}{35} \opL_r \opL_z^{2} \r] \ATL \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:isoATL_3}
& \ATL = \\
& - \l[ \frac{1}{3} \opL_z + \frac{4}{45} \opL_z^{2} + \frac{1}{15} \opL_r \opL_z + \frac{1}{35} \opL_r^{2} \opL_z + \frac{44}{945} \opL_z^{3} + \frac{8}{225} \opL_r \opL_z^{2} \r] \phi \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:scalarFlux_3}
& \phi = \\
& + \l[ I + \frac{1}{3} \opL_r + \frac{1}{3} \opL_z + \frac{1}{5} \opL_r^{2} + \frac{1}{5} \opL_z^{2} + \frac{16}{45} \opL_r \opL_z + \frac{1}{7} \opL_r^{3} + \frac{1}{7} \opL_z^{3} + \frac{1528}{4725} \opL_r^{2} \opL_z + \frac{1528}{4725} \opL_r \opL_z^{2} \r] F \nonumber \\
\end{alignat}
\begin{alignat}{2}
\label{eq:transport3D_0}
& F = \\
& + \l[ I - \frac{1}{3} \opL_r - \frac{1}{3} \opL_z - \frac{4}{45} \opL_r^{2} - \frac{4}{45} \opL_z^{2} - \frac{2}{15} \opL_r \opL_z - \frac{44}{945} \opL_r^{3} - \frac{44}{945} \opL_z^{3} - \frac{101}{1575} \opL_r^{2} \opL_z - \frac{101}{1575} \opL_r \opL_z^{2} \r] \phi \nonumber \\
\end{alignat}