From e6cee1630795b118414070d52606b7be1813a328 Mon Sep 17 00:00:00 2001
From: Thomas Albers Raviola <thomas@thomaslabs.org>
Date: Sun, 4 Aug 2024 16:12:44 +0200
Subject: 2024-08-04

---
 sphere.mac | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 sphere.mac

(limited to 'sphere.mac')

diff --git a/sphere.mac b/sphere.mac
new file mode 100644
index 0000000..b58cd57
--- /dev/null
+++ b/sphere.mac
@@ -0,0 +1,57 @@
+/* 1920x1080 - HD screen */
+linel: 230;
+/* 3840x1600 - Ultrawide screen */
+linel: 470;
+/* 1366x768 - Poor man's thinkpad */
+linel: 150;
+
+derivabbrev: true;
+
+load("ctensor");
+
+dim: 2;
+cframe_flag: false;
+ct_coords: [θ, ϕ];
+
+lg : zeromatrix(2, 2);
+/* dθ dθ */
+lg[1, 1] : 1;
+
+/* dϕ dϕ */
+lg[2, 2] : sin(θ)^2;
+
+/* Load metric and compute inverse */
+cmetric();
+
+/* mcs[i, j, k]: Christoffel symbols of the second kind (one upper index - k) */
+christof(false);
+
+
+depends(c, [u, θ]);
+
+Ndown: zeromatrix(2, 2);
+Ndown[1, 1] : 2*diff(c, u);
+Ndown[2, 2] : -2*diff(c, u)*sin(θ)^2;
+
+f(m, n) := sum(ug[m, a] * sum(ug[n, b] * Ndown[a, b], b, 1, 2), a, 1, 2);
+
+
+Nup: zeromatrix(2, 2);
+for i: 1 thru 2 do for j: 1 thru 2 do Nup[i, j]: f(i, j);
+
+
+
+
+
+X: sum(sum(Nup[A,B]*Ndown[A,B], A, 1, 2), B, 1, 2);
+
+Q: zeromatrix(2, 1);
+for i: 1 thru 2 do Q[i]: sum(diff(Nup[i,B], θ)
+  + sum(mcs[B, D, i] * Nup[D, B], D, 1, 2)
+  + sum(mcs[B, D, B] * Nup[i, D], D, 1, 2), B, 1, 2);
+
+Y: diff(Q[1], θ) + sum(sum(mcs[A, B, A], A, 1, 2) * Q[B], B, 1, 2),expand;
+
+
+/* M_u */
+- (1/8)*X + (1/4)*Y,expand;
-- 
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