update: auto commit

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wyj committed 2026-04-10 02:01:20 -04:00
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commit c08927672f
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@@ -831,11 +831,15 @@ $}
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 equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues.
Available terms to add: Available terms to add:
\begin{gather*} \[
\scalebox{0.8}{$\displaystyle
\begin{aligned}
\constraintA{_i} \qc \constraintB{^i_j} \qc \constraintC*{_i} \qc \constraintD*{_i_j_k},\\ \constraintA{_i} \qc \constraintB{^i_j} \qc \constraintC*{_i} \qc \constraintD*{_i_j_k},\\
\Partial{_{[i}} \constraintA{_{j]}} = \Partial{_{[i}} \dlapse{_{j]}} \qc \Partial{_{[i}} \constraintB{^j_{k]}} = \Partial{_{[i}} \dshift{^j_{k]}} \qc \Partial{_{[i}} \constraintC*{_{j]}} = \Partial{_{[i}} \dchi*{_{j]}} \qc \Partial{_{[i}} \constraintD*{_{j]kl}} = \Partial{_{[i}} \dsmetric*{_{j]kl}},\\ \Partial{_{[i}} \constraintA{_{j]}} = \Partial{_{[i}} \dlapse{_{j]}} \qc \Partial{_{[i}} \constraintB{^j_{k]}} = \Partial{_{[i}} \dshift{^j_{k]}} \qc \Partial{_{[i}} \constraintC*{_{j]}} = \Partial{_{[i}} \dchi*{_{j]}} \qc \Partial{_{[i}} \constraintD*{_{j]kl}} = \Partial{_{[i}} \dsmetric*{_{j]kl}},\\
\Partial{_i} \left( \smetric*{^j^k} \Ktf*{_j_k} \right) \qc \Partial{_i} \left( \smetric*{^k^l} \dsmetric*{_j_k_l} \right) \Partial{_i} \left( \smetric*{^j^k} \Ktf*{_j_k} \right) \qc \Partial{_i} \left( \smetric*{^k^l} \dsmetric*{_j_k_l} \right)
\end{gather*} \end{aligned}
$}
\]
\end{frame} \end{frame}
\begin{frame}{References} \begin{frame}{References}