update: auto commit

report.tex

@@ -828,7 +828,7 @@ $}
     {\color{red} \textbf{Unfortunately, this naive system is not even weakly hyperbolic!}}
     \vspace{0.2cm}
 
-    We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues.
+    We have to add some constraint terms that contribute to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues.
 
     Available terms to add:
     \[
@@ -842,6 +842,17 @@ $}
     \]
   \end{frame}
 
+  \begin{frame}{Searching for a first order Z4c}{Introducing Mathematica into workflow}
+    To speed up the process and reduce the chance of making mistakes, I wrote a Mathematica notebook using a package \texttt{MathGR}.
+
+    \texttt{MathGR} can do symbolic tensor calculations, and render tensor equations in a readable way:
+    \begin{figure}
+      \centering
+      \includegraphics[width=0.8\textwidth]{imgs/mathGR1.png}
+      \caption{A simple example of using \texttt{MathGR} to write tensor equations.}
+    \end{figure}
+  \end{frame}
+
   \begin{frame}{References}
     \printbibliography
   \end{frame}