Simplex Algorithm

[ftneek]

Uploaded latest changes which returns "∅" instead of ∅ for infeasible model and switches pivoting rule to Bland's rule when a repeated basis is detected.

Appendix B: An example of cycling / test18()
> simplex([[1,0,0,1/4,-8,-1,9,0],[0,1,0,1/2,-12,-1/2,3,0],[0,0,1,0,0,1,0,1],[0,0,0,-3/4,20,-1/2,6,0]],-3)

[-5/4,..., transpose([3/4,0,0,1,0,1,0,0,0,0])]

I tried to verify the solution using other solvers (xcas lpsolve, Wolfram alpha..) but had no luck so far. One thing I noticed is that the appendix says the repeated basis is detected on the 6th iteration, but according to the P counter it was detected on the 8th pivot1 call (see the commented out return on line 185), 2 tableaus passed the initial tableau shown.

The hashin file uses the new program structure (part PPL and part python) to access the python hash function. The downside is that this causes the outdated connectivity kit on my main computer (mac) to crash upon trying to open the file, but it is simple enough it can probably be split up or included in the simplex file to still work on older software. Hopefully updates will come soon for outdated software, and the new program structure can actually be used.