update to do list

checklist.md

@@ -35,4 +35,30 @@ If $f(x)=x + x^3$, there is no solution for (3) with polynomial unit.
 
 # To do
 
-- Check if Pfistetr's and Hiroshi's algorithms can handle examples that we can.
+- Check if Pfistetr's and Hiroshi's algorithms can handle examples that we can. - Done
+
+- List of mappings vs algorithms and check if they work
+	- Failing examples
+	- Failing examples that can be converted into working examples
+	- Other nice working examples
+
+- Positive characteristic
+	- Find finite determinacy criteria
+	
+- Algorithm modulo a submodule of O_n^p (usually the one generated by a power of the maximal ideal)
+	- Submodule in source or in target??
+	- Let this sumbodule to be the zero module (this is just the usual algorithm)
+	- It always converges up to a maximal ideal power, can we find which?
+		- If it is not too expensive: search and use a power of the maximal ideal for which it converges
+		- If it is too expensive: let the user choose if they want to search for this maximal ideal power
+		
+- Finite determinacy criteria (modulo a submodule)  -- Guillermo
+
+- Implement complete transversal algorithm
+
+- Stopping criteria for the algorithm
+
+- Verify that if the local-global basis is the same then the algorithm:
+	1. Finishes
+	2. It finishes correctly
+	3. If it does not, it gives an upper bound