This program implements the 
algorithm presented in the paper

``All Linear and Integer Programs
are Slim 3-way Transportation Programs''

By J. De Loera and S. Onn.

The input is a polyhedron in the
form P={x | Ax=b x>=0}. The output
are 

1) On the screen, the 2-margins of a
3-way transportation polytope. 

2) 2 files, one is a CPLEX LP readable
file with the transportation problem 
in question from those margins.

3) A PPRN encoding of the bi-transportation
problem associated.

To run the program you just need to type

./phase23 filename

If you know a bound U, for the largest
coordinate entry on the polytope P
you can feed it directly, else, the 
program give a ``generic'', but sufficient, 
bound.

for example 

[deloera@convex transportationencoding]$ ./phase23 t2.in 
Would you like to [c]alculate U or [g]ive the value?:

Since the problem has a bound of 1/3, we can answer g
and give 1/3. The output on screen will be the margins, that
is:


***TOP***
1 0 0 1 0 1 0 0 
0 1 0 1 0 0 1 0 
0 0 1 1 0 0 0 1 
0 1 0 0 1 1 0 0 
0 0 1 0 1 0 1 0 
1 0 0 0 1 0 0 1 
***LEFT***
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
***RIGHT***
1 1 0 
1 1 0 
1 1 0 
2 0 1 
1 0 2 
0 1 1 
0 1 1 
0 1 1 

