[GAP Forum] Algorithmic question

[Kasper Andersen]

Dear forum,

This is strictly speaking not a GAP question but hopefully someone on the 
list knows something about this....

Suppose A is a subgroup of Z^n. The M=A\cap N_0^n is a finitely generated 
monoid. How does one test effectively decide whether M is a free monoid?

One could of course first find a minimal generating set of M and check if 
this set is linearly independent -- however I dont know efficient 
algorithms for finding a minimal generating set.

Furthermore one could hope that one could decide freeness without 
computing a minimal generating set....

thanks in advance,

Kasper Andersen
University of Copenhagen