@acer 

Excellent, thanks! I did not know how this SolutionsMayBeLost flag worked, but I get it now!

@Alejandro Jakubi 

Excellent, thank you so much! I'll try it out!

@Alejandro Jakubi 

I'm not sure I understand. Does this mean that Maple cannot distinguish between those cases where it cannot find a solution from those where it can prove that no solution can exist (by contradiction)? Would this be indicated by different types of messages in the Warning when you increase the infolevel?

Hi guys,

First of all, thanks for you reply!

Sorry for posting such a hurried question, let me clarify. I won`t get into the details of the problem I`m trying to solve. Suffice to say that I have a problem in Quantum Mechanics where I have to decide whether a given quantum system is capable of performing a given transformation, and that reduces to a set of nonlinear polynomial equations on the free parameters of the system.

Now, as both answers said, Maple, as any other CAS, is not a theorem prover. However, if I only have a certain set of polynomial equations, there is an algorithm to decide whether they have a solution (via Grobner bases), right? And in principle, deciding this is just a matter of time. So presumably, Maple should be able to output one of three answers: (i) no solution was found; (ii) a solution was found, or (iii) the system has no solutions because it is inconsistent. Right? I mean, I'm not very experienced with Maple, and maybe there is a better way to do this. But in Mathematica, if I give it a set of polynomial equations and use the Reduce command, it will either give me a solution, or it will say "Mathematica was not able to find a solution using the tools available", or it will output "False" which, as far as I understand, means that it actually figured out that the system is inconsistent. So why is it that, in Alejandro's example, when you give the equations y-x=0 and y-x=1 - which clearly are incosistent and thus have no solution - doesn't Maple inform us precisely of that? Is there a different way to do this? I tried playing aroud with Grobner bases for a while, which I know that can be used to solve this problem, but my code is just too slow (much slower than simplying inputting the system to the built-in 'solve' command).

Thanks again for any help!