The MATLAB code contained is this directory, together with the data files at the web page 

http://archimede.mat.ulaval.ca/jplessard/galepu/

has been used to run the computations that led to Theorems 5.6 and 5.8 of 

"Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions", Marcio Gameiro, Jean-Philippe Lessard and Alessandro Pugliese, 2013.

Here is an example of how to run these computations in MATLAB

load data_Example_5.5.mat
for k=1:500
   distrVerification(node,simplex,k,500)
end

Output data will be saved to the files output_file_001of500.mat to output_file_500of500.mat.

The above output files contain the verification flags for all the simplices in the database imported from data_Example_5.5.mat.
The computation is intended to be run on an HPC computing environment, i.e. each instance inside the "for cycle" is intended to be executed by its own computing unit. The code relies on the presence of one copy of INTLAB for each one of the subdirectories ./job001/ to ./job500/.