homology of the T(6,5)torus knot:
q \ t  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19 
78 
                   1 
76                    1  
74                   1  1  
72                  2  1  1 1 1  
70                1   2 1  2 1   
68              1   2  1  1 3  2   
66              2   1 3  4  1  1 1   
64            1   2 1  4  2  3 1  1    
62            1  2  2  5 1  1 1  1 1  1    
60          1  1  1  5  1  1 1 3  2      
58          1  4   3 2  3  1  1      
56         2  1  4 1  1  1 2  3        
54       1   3  1  1 2  3   1        
52       2   1 1  3  1  1          
50     1   1 1  2   3     

     
48     1  1  1  2   1     
      
46     1  2   1       
      
44    1   1         
      
42  1   1           
      
40  1             
      
38  1             
      
Computed in six minutes on an AMD Opteron, 2.2GHz, using 80MB of RAM.
Diagram drawn with the KnotTheory` package for Mathematica.
For details, see my paper foam homology calculations:
arxiv.org/abs/1212.2553.
Download
foamho1.1.tar.gz containing the source code and installation instructions in the README file.
To compile, you will need at least the MPIRlibrary, which
is used for rational and integral arbitrary precision arithmetic.
Optionally, the PARIlibrary is used to obtain smith normal forms
(not necessary if you only want to compute rational homology), and the PROCPSlibrary
to display memory consumption (on Linux only).
foamho.exe, a windows executable compiled using minGW running on Windows XP. No additional libraries necessary,
but it is not guaranteed to work on your system.
foamho, a linux executable. No additional libraries are necessary,
but it is not guaranteed to work on your system.
Old version (1.0): foamho1.0.tar.gz, foamho.exe, foamho.
Some results
Let us list all knots of twelve or less crossings for which the
 and
concordance invariants differ
(click on the knot to see his diagram on the Knot Atlas
or on KnotInfo).
In our normalisation, both invariants have a value of 2 for the righthanded trefoil knot.
