From f2000e5731f52e2583d15619738acbd86c7c7974 Mon Sep 17 00:00:00 2001
From: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Date: Thu, 15 Feb 2024 16:25:09 -0800
Subject: [PATCH] Test different sign patterns for cosines

It seems like there are real solutions if and only if the product of the
cosines is positive.
---
 engine-proto/Engine.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/engine-proto/Engine.jl b/engine-proto/Engine.jl
index e92eed4..a517117 100644
--- a/engine-proto/Engine.jl
+++ b/engine-proto/Engine.jl
@@ -44,7 +44,7 @@ tangencies = [
   Engine.AlignsWithBy{CoeffType}(
     spheres[n],
     spheres[mod1(n+1, length(spheres))],
-    CoeffType(-1)^n
+    CoeffType([1, 1, 1][n])
   )
   for n in 1:3
 ]
@@ -90,7 +90,7 @@ vbls = Variable.(symbols(coordring))
 system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
 norm2 = vec -> real(dot(conj.(vec), vec))
 rng = MersenneTwister(6071)
-n_planes = 3
+n_planes = 36
 samples = []
 for _ in 1:n_planes
   real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))