From b660c825c6a8a3c5ec5daf86c7eef40ceff42a0e Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 20:22:44 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/report.tex b/report.tex
index 5d86363..6750939 100644
--- a/report.tex
+++ b/report.tex
@@ -277,6 +277,17 @@
     where $\tensor{e}{^i}$ is the standard column vector basis of $\setR^3$, while $\tensor{e}{_i}$ is the standard row vector basis of $(\setR^3)^*$.
   \end{frame}
 
+    \begin{frame}{Towards first order Z4c}{First order reduction}
+    The principal symbol matrix is
+    \begin{equation}
+      \tensor{P}{^I_J}(\xi) = \begin{pmatrix}
+        0 & 0 & 0 \\
+        0 & 0 & -\tensor{\xi}{_i} \\
+        0 & -\tensor{\xi}{^i} & 0
+      \end{pmatrix},
+    \end{equation}
+  \end{frame}
+
   \begin{frame}{Existing first order formulations}
     \subsection{Existing first order formulations}
     \begin{itemize}