From 5450d623ec7e9b897f28e5fc0bde1a1a07e73f30 Mon Sep 17 00:00:00 2001
From: Ricardo Fabbri <rfabbri@gmail.com>
Date: Fri, 14 Jun 2024 04:23:50 -0700
Subject: [PATCH] merging chicago.m2 with eval_monodromy_demo.m2

---
 tutorial/README.md   | 14 ++++++++++++++
 tutorial/ex-start.m2 | 23 ++++++++++++++++++++---
 2 files changed, 34 insertions(+), 3 deletions(-)

diff --git a/tutorial/README.md b/tutorial/README.md
index b8d331c..db560b8 100644
--- a/tutorial/README.md
+++ b/tutorial/README.md
@@ -10,4 +10,18 @@ C = {
     makeSLProgram(matrix{cameraParams},P3)
   }
 
+## Evaluate to check equation
+- How can we evaluate the the equations on the system?
+evaluate(F,x0||p0) only for F gatematrix, but we ony have gateSystem in Ex, not
+gatematrix.
 
+Usually one creates gateSystem from Gatematrix:
+GS = gateSystem(GS)
+
+
+(p,x)=fabricateChicago CC
+evaluate(F,x||p)
+
+(p0,x0) = fabricateChicago(CC)
+evaluate(F,x0||p0)
+    
diff --git a/tutorial/ex-start.m2 b/tutorial/ex-start.m2
index 7446bde..a49d368 100644
--- a/tutorial/ex-start.m2
+++ b/tutorial/ex-start.m2
@@ -1,10 +1,18 @@
+-- Ex and Pro marked bellow mean Example (simple) and Pro (fast)
+
+
 -- code for generating various evaluators 
 restart
 needsPackage "SLPexpressions"
 needsPackage "MonodromySolver"
 -- "gateSystem" exists only in M2 v 1.14
+
+-- Ex---------------------------------------------------------------------------
+-- Pro doesn't use declareVariable
 variables = declareVariable \ {x,y}
 params = declareVariable \ {a,b,c,d,e,f}
+
+-- Ex and Pro ------------------------------------------------------------------
 GS = gateSystem(
     matrix{params},
     matrix{variables},
@@ -13,10 +21,17 @@ GS = gateSystem(
 	    d*x+e*y+f}
 	}
     )
+-------------------------------------------------------------------------------
 
+-- Ex and Pro ------------------------------------------------------------------
 cameraVars = flatten entries vars GS
 PH = parametricSegmentHomotopy GS
 
+-- Pro only --------------------------------------------------------------------
+-- setDefault(CorrectorTolerance=>1e-8)
+
+-------------------------------------------------------------------------------
+
 -- HxHt
 h=cCode(
     transpose(PH.GateHomotopy#"Hx"|PH.GateHomotopy#"Ht"),
@@ -26,6 +41,9 @@ h=cCode(
 -- HxH
 h=cCode(transpose(PH.GateHomotopy#"Hx"|PH.GateHomotopy#"H"),gateMatrix{cameraVars|{PH.GateHomotopy#"T"}|flatten entries PH#Parameters})
 
+-- Maybe useful
+-- cCode PH
+
 -- Ex 1 --------------------------------------------------------------------------
 -- monodromy needs an initial pair of parameter, solution
 -- the command below won't work for most use cases
@@ -57,10 +75,9 @@ h=cCode(transpose(PH.GateHomotopy#"Hx"|PH.GateHomotopy#"H"),gateMatrix{cameraVar
 
 -- Ex 3 -------------------------------------------------------------------
 -- parameter point
--- V.BasePoint
+V.BasePoint
 -- corresponding solutions
--- points V.PartialSols
--------------------------------------------------------------------------------
+points V.PartialSols
 
 -- Pro 3 --------------------------------------------------------------
 -- quality check