I am using Maple to compute the Smith normal form (SNF) of a $120 \times 120$ matrix and it seems that I will never get an answer back. I have checked my code for small cases and I believe that it is correct. When I try to compute the SNF for a $24 \times 24$ matrix, the real time and CPU time are about 0.1~0.2 seconds. I don't think it will take more than 3 hours for a $100 \times 100$ matrix. I have also tried it on several operating systems and the results are similar.
Anyway, what is the approximate time complexity of the computation time of SNF? Is there a limit for the matrix size in Maple to do SNF?
Thank you so much!