update: auto commit

report.tex

@@ -827,7 +827,16 @@ $}
     {\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. This is the most tricky part, and we have to do it by hand, which is very time consuming and error prone.
+    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.
+  \end{frame}
+
+  \begin{frame}{Searching for a first order Z4c}{old workflow: by hand}
+    Available terms to add:
+    \begin{gather*}
+      \constraintA{_i} \qc \constraintB{^i_j} \qc \constraintC*{_i} \qc \constraintD*{_i_j_k},\\
+      \Partial{_{[i}} \constraintA{_{j]}} = \Partial{_{[i}} \dlapse{_{j]}} \qc \Partial{_{[i}} \constraintB{^j_{k]}} = \Partial{_{[i}} \dshift{^j_{k]}} \qc \Partial{_{[i}} \constraintC*{_{j]}} = \Partial{_{[i}} \dchi*{_{j]}} \qc \Partial{_{[i}} \constraintD*{_{j]kl}} = \Partial{_{[i}} \dsmetric*{_{j]kl}},\\
+      \Partial{_i} \left( \smetric*{^j^k} \Ktf*{_j_k} \right) \qc \Partial{_i} \left( \smetric*{^k^l} \dsmetric*{_j_k_l} \right)
+    \end{gather*}
   \end{frame}
 
   \begin{frame}{References}