From d2c601834a96a04cadcd75dc1ce9690ccae75f46 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Mon, 7 Aug 2023 20:46:45 +0200
Subject: [PATCH] nil Christoffel formulas in model

---
 nonisotropic.cpp | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/nonisotropic.cpp b/nonisotropic.cpp
index f233f350..bd6b25b0 100644
--- a/nonisotropic.cpp
+++ b/nonisotropic.cpp
@@ -787,6 +787,32 @@ EX namespace nilv {
 
   hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported, ld model = model_used) {
     /* to do: write these formulas in model */
+    if(model == nmSym) {
+      hyperpoint c; c[3] = 0;
+      ld x = Position[0]; ld y = Position[1]; ld diag = (y*y-x*x)/8;
+      c[ 0 ] = 0
+       + Velocity[ 0 ] * Transported[ 1 ] * ( -y/4 )
+       + Velocity[ 1 ] * Transported[ 0 ] * ( -y/4 )
+       + Velocity[ 1 ] * Transported[ 1 ] * ( x/2 )
+       + Velocity[ 1 ] * Transported[ 2 ] * ( -1/2. )
+       + Velocity[ 2 ] * Transported[ 1 ] * ( -1/2. );
+      c[ 1 ] = 0
+       + Velocity[ 0 ] * Transported[ 0 ] * ( y/2 )
+       + Velocity[ 0 ] * Transported[ 1 ] * ( -x/4 )
+       + Velocity[ 0 ] * Transported[ 2 ] * ( 1/2. )
+       + Velocity[ 1 ] * Transported[ 0 ] * ( -x/4 )
+       + Velocity[ 2 ] * Transported[ 0 ] * ( 1/2. );
+      c[ 2 ] = 0
+       + Velocity[ 0 ] * Transported[ 0 ] * ( x*y/4 )
+       + Velocity[ 0 ] * Transported[ 1 ] * diag
+       + Velocity[ 0 ] * Transported[ 2 ] * ( x/4 )
+       + Velocity[ 1 ] * Transported[ 0 ] * diag
+       + Velocity[ 1 ] * Transported[ 1 ] * ( -x*y/4 )
+       + Velocity[ 1 ] * Transported[ 2 ] * ( y/4 )
+       + Velocity[ 2 ] * Transported[ 0 ] * ( x/4 )
+       + Velocity[ 2 ] * Transported[ 1 ] * ( y/4 );
+      return c;
+      }
     if(model == nmHeis) {
       ld x = Position[0];
       return point3(