From 1f92d1af9c4b0a38f6f2084708cfa05fb7f30120 Mon Sep 17 00:00:00 2001
From: Florian Stecker <mail@florianstecker.de>
Date: Mon, 25 Apr 2022 14:08:11 -0500
Subject: [PATCH] add reducible reps to barbot.plt

---
 barbot.plt | 38 ++++++++++++++++++++++++++++++++++++--
 1 file changed, 36 insertions(+), 2 deletions(-)

diff --git a/barbot.plt b/barbot.plt
index b04a566..370589a 100644
--- a/barbot.plt
+++ b/barbot.plt
@@ -1,11 +1,45 @@
+set size ratio 1.3
 set grid
 set xrange [0:2.5]
 set yrange [0:5]
+set samples 1000
+set parametric
+
+# set terminal pngcairo size 1000, 1200
+# set output "barbot.png"
+
+# solves the equation rho(s)q^2 - (s+1)q + 1 = 0
+# (s^2 + cs + 1)q^2 - (s+1)q + 1 = q^2 s^2 + (cq - 1)qs + (q^2 - q + 1)
+c = 2*cos(4*pi/5)
+rho(s) = s**2 + c*s + 1
+qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
+qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
+d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
+sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
+sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
+
+#  = sqrt(s**2 + 2*cos(4*pi/5) + 1)
+# solplus(x) = x/2 + sqrt((x/2)**2 - 1)
+# solminus(x) = x/2 + sqrt((x/2)**2 - 1)
+# Tplus(s) = solplus((s+1)/rho(s))
+# Tminus(s) = solminus((s+1)/rho(s))
+# qinvp(s) = 0.5*(s+1+sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
+# qinvm(s) = 0.5*(s+1-sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
+# set trange [0:5]
+
+# sp(q) = (1-2*q*cos(2*pi/5)+sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)
+# sm(q) = (1-2*q*cos(2*pi/5)-sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)
 
 plot "output/barbot_map_5000_frequencies" \
-	 using ($1/100.0):($2/100.0):(($3==0||$3>6)?1/0:$4) w p pt 7 ps 1 lc palette t '', \
+	 using ($1/100.0):($2/100.0):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
 	 "output/barbot_map_500000"	\
-	 using ($1/10.0) :($2/10.0) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t ''
+	 using ($1/10.0) :($2/10.0) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
+	 sm(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
+	 sp(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
+	 t, qm(t) w l lw 2 lc 7 t "", \
+	 t, qp(t) w l lw 2 lc 7 t ""
+
+# plot "output/barbot_map_50000_zoom_b" using ($1/1000.0):($2/5000):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t ''
 
 pause mouse keypress
 reread