Tutorial: Readme with step-by-step instructions

tutorial/README.md

@@ -1,19 +1,73 @@
 # CVPR 204 fast Homotopy Continuation tutorial
 
+A new polynomial systems can be solved in a number of ways within our framework,
+ranging from an initial Macaulay prototype, to a more advanced Macaulay
+prototype to a fast C++ version. From the initial prototype to the final C++
+code, there are a number of intermediate steps to follow. 
 
+## Running the example Macaulay2 template
 
+The example is called linecircle and computes the intersection of a line and a
+circle.
 
-# Developer Internal Notes
+The equations are stored in: `equations-linecircle.m2`
 
-## Starting files
-The tutorial started from Chicago trifocal problem code
+### Solve the start solutions
 
-mostly 
+In a terminal, type:
+```bash
+m2
+```
 
-Completely integrated
-minus/m2/chicago/formulation-minors-original-in-minus/t
-minus/scripts/eval_monodromy_demo.m2
+Then
+
+```
+load("start-linecircle.m2")
+```
+
+This will run monodromy to compute the solutions in your file.
+It will write out the following files into the current folder:
+
+- `startSys` : the start solution and corresponding base point (parameters).
+  This is a text file in Macaulay format. It can be used both for your fast C++ solver,
+  and for prototyping the fast online solution in the next step.
+
+- `HxHt.cxx`, `HxH.cxx`: C++ evaluators for writing your optimized solver later on
+
+
+## Solving your own system
+
+Give your new problem a name, say `problem1`
+
+
+### Type your equations
+
+Copy the template over:
+
+```
+cp equations-linecircle.m2 equations-problem1.m2
+```
+
+Edit the file typing your variables, parameters and equations, foloowing the
+template as an example.
+
+
+### Compute start stystems
+
+First, copy over the solution template:
+```
+load("start-linecircle.m2")
+```
+
+In a terminal, type:
+```bash
+m2
+```
+
+Then
+
+```
+load("start-linecircle.m2")
+```
 
-and the code after "end" in  (XXX)
-/Users/rfabbri/cprg/vxlprg/lemsvpe/minus/M2/chicago/formulation-minors-original-in-minus/chicago.m2
 

tutorial/TODO.md

@@ -0,0 +1,14 @@
+# Developer Internal Notes
+
+## Starting files
+The tutorial started from Chicago trifocal problem code
+
+mostly 
+
+Completely integrated
+minus/m2/chicago/formulation-minors-original-in-minus/t
+minus/scripts/eval_monodromy_demo.m2
+
+and the code after "end" in  (XXX)
+/Users/rfabbri/cprg/vxlprg/lemsvpe/minus/M2/chicago/formulation-minors-original-in-minus/chicago.m2
+

tutorial/start-linecircle.m2

@@ -96,7 +96,7 @@ PH = parametricSegmentHomotopy GS
 
 -- HxHt
 symbols = flatten entries vars GS
-h=cCode(--"HxHt.cxx",
+h=cCode("HxHt.cxx",
         transpose(PH.GateHomotopy#"Hx"|PH.GateHomotopy#"Ht"),
         gateMatrix{symbols|{PH.GateHomotopy#"T"}|flatten entries PH#Parameters})