This folder contains the MATLAB code used for the paper:
     "A proof of Jones' conjecture" by J. Jaquette.
The codes require installing and starting the interval arithmetic package INTLAB.

The file "AP_Bounding_Functions.m" requires the code library "Floquet-Wright" from:
    ``Stability and uniqueness of SOPS to Wright's equation'' (2017)
    J. Jaquette, J.-P. Lessard, and K. Mischaikow.
 
	To run this code with the improvement from Proposition 5.6, 
	the file "Prune.m" from the code library "Floquet-Wright" should be replaced with 
	the file "Prune.m" from the subfolder "Floquet-Wright-Modification". 
	This new version of the file has added new code in lines 147-160.



To run the code which proves Theorem 1.1, first run "AP_Bounding_Functions.m" with the following inputs: 
   i=1 ===>  alpha = [pi/2 , 1.6]
   i=2 ===>  alpha = [ 1.6 , 1.7]
   i=3 ===>  alpha = [ 1.7 , 1.8]
   i=4 ===>  alpha = [ 1.8 , 1.9]
Then run "parallel.m".


The files (left) correspond to the parts of the papers (right).

AP_Bounding_Functions   From paper [10], Algorithm 5.1
BranchNBound            Algorithm 6.1
FourierProjection       Algorithm 5.1
Initial Prep            Algorithm 5.7
PostVerify              Algorithm 6.3
X2Y                     Algorithm 5.7 Steps 2&3
parallel                Theorem 1.1
	

In the folder "Cube" is a matlab class definition. 
The files (left) correspond to the parts of the papers (right).

Branch                  Algorithm 6.1 Step 9
Cube                    Definition 2.7
DFeval                  Definition 3.1 & Proposition 2.6
FTail                   Definition 2.11 (a) -Also- Eq. (21)
Feval                   Eq. (9) and Eq. (16a). 
Krawczyk                Definition 3.2
Prune                   Algorithm 4.1
gInfty                  Definition 3.2 - Also - Definition 2.11
gM                      Definition 3.2 - Also - Definition 2.11
PhaseCondition          Algorithm 5.3
