From 14863952f0209423a2fa2d5938179c5f3d0a0a28 Mon Sep 17 00:00:00 2001
From: Thomas Guillermo Albers Raviola <thomas@thomaslabs.org>
Date: Mon, 3 Aug 2026 21:30:38 +0200
Subject: Compute q_mcs

---
 setup.mac | 34 ++++++++++++++++++++++------------
 1 file changed, 22 insertions(+), 12 deletions(-)

diff --git a/setup.mac b/setup.mac
index 96d0b31..1c4483a 100644
--- a/setup.mac
+++ b/setup.mac
@@ -78,18 +78,6 @@ uh_AB[4,4] : exp(2*γ)*sin(θ)^-2$
 uh_AB[3,4] : 0$
 uh_AB[4,3] : 0$
 
-/* 2-sphere metric */
-q_AB[3,3] : 1$
-q_AB[4,4] : sin(θ)^2$
-q_AB[3,4] : 0$
-q_AB[4,3] : 0$
-
-/* 2-sphere inverse metric */
-uq_AB[3,3] : 1$
-uq_AB[4,4] : sin(θ)^-2$
-uq_AB[3,4] : 0$
-uq_AB[4,3] : 0$
-
 /* Christoffel symbols of 2-sphere */
 for i : 3 thru 4 do for j : 3 thru 4 do for k : 3 thru 4 do (
   h_mcs[i, j, k] : sum(uh_AB[k,C]*(
@@ -111,4 +99,26 @@ for i : 3 thru 4 do for j : 3 thru 4 do (
 /* Ricci scalar of 2-sphere */
 h_ric_s : expand(sum(sum(uh_AB[i,j]*h_ric[i,j], i, 3, 4), j, 3, 4));
 
+
+/* 2-sphere */
+
+/* 2-sphere metric */
+q_AB[3,3] : 1$
+q_AB[4,4] : sin(θ)^2$
+q_AB[3,4] : 0$
+q_AB[4,3] : 0$
+
+/* 2-sphere inverse metric */
+uq_AB[3,3] : 1$
+uq_AB[4,4] : sin(θ)^-2$
+uq_AB[3,4] : 0$
+uq_AB[4,3] : 0$
+
+/* Christoffel symbols of 2-sphere */
+for i : 3 thru 4 do for j : 3 thru 4 do for k : 3 thru 4 do (
+  q_mcs[i, j, k] : sum(uq_AB[k,C]*(
+      cdiff(q_AB[j, C], i)
+      + cdiff(q_AB[i, C], j)
+      + cdiff(q_AB[i, j], C))/2, C, 3, 4));
+
 print("Setup done!");
-- 
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