Definite maybe, if it is a system of polynomials. You can do
NSolve[a]
to get the code for NSolve
loaded. Then do
System
NSolveDumpdebugLevel=12;
With this set, you might get a spew of messages when you feed NSolve
your system. If you do, it means NSolve
at least used the eigensystem decomposition method in some part of the process. If not, then it did "other things" (apologies for such technical jargon).
Note that the variable being set is strictly for internal debugging purposes. You are using it at your own risk. I don't think it will bite. But bear in mind I'm the owner of this particular pet and it has never interacted with outsiders in my presence, so I can't really predict the outcome.