update: auto commit

2026-04-10 01:18:27 -04:00
parent be2a7bc007
commit 68a93429a6
1 changed files with 8 additions and 6 deletions
@@ -702,12 +702,14 @@ $}

  \begin{frame}{Searching for a first order Z4c}{old workflow: by hand}
    We introduce the following auxiliary variables:
-    \begin{equation}
-      \dlapse{_i} \definedby \Partial{_i} \lapse \qc
-      \dshift{^i_j} \definedby \Partial{_j} \shift{^i} \qc
-      \dchi*{_i} \definedby \spaceD*{_i} \ln(\chi) \qc
-      \dsmetric*{_i_j_k} \definedby \Partial{_i} \smetric*{_j_k},
-    \end{equation}
+    \[
+    \scalebox{0.8}{$\displaystyle
+        \dlapse{_i} \definedby \Partial{_i} \lapse \qc
+          \dshift{^i_j} \definedby \Partial{_j} \shift{^i} \qc
+          \dchi*{_i} \definedby \spaceD*{_i} \ln(\chi) \qc
+          \dsmetric*{_i_j_k} \definedby \Partial{_i} \smetric*{_j_k},
+    $}
+    \]
    and replace all the spatical derivatives of the original variables with the new auxiliary variables, we got this
    \[
    \scalebox{0.6}{$\displaystyle