@acer ok, I understand now. I am a new member of Maple community, so thanks for clarifying.

I did find some answers of yours to questions related to multicore processing and parallel computing, but I could not find anything I could direclty implement to my script. Would you kindly look into it?

Thank you all for the continued support!

@acer 

Why was it removed? Rather than a follow-up, the problem I now have has changed and I thought (and still think) it deserves another question.

@Carl Love

After some simplifying assumptions about the parameters and manipulations (exclusion of redundancies), I re-wrote my nonlinear system as shown in the second last document block (the first solve() out of the two consecutive solve()) in the following:

newsystem.mw

The number of variables are still 6, but also the equations are now 6. While the system is not overdetermined anymore (thus not almost certainly inconsistent anymore), the execution of solve() still gets stuck. The equations are all algebraic but still quite complicated. I now wonder how I can leverage parallel computing on Maple to find an analytical solution (before trying numerical procedure through fsolve()).

My machine has 128 cores (256 threads) and over 1TB of RAM. GPU is an NVIDIA Tesla A100. What's the most effective way on Maple to maximise the usage of such computational power? How can I implement solve() with the best parallel computing procedure for my problem at hand?

Thank you for the continued support!

@Carl Love Thanks for trying it independently. I encounter the same issues.

I hope someone else can help me thinking of some alternative ways to check consistency and, if consistent, if any (even just a single) solution can be found. I can't vote you up because I don't have enough reputation.

@Carl Love thank you for the very detailed and clear answer. Much appreciated. 

However, I get stuck at step 3.: EqP:= eval(Eq, indets(EqN, name)=~ 1):

I get the error "Error, numeric exception: division by zero" regardless of the simple exact value I choose (1, 0 or anything else). What's a workaround for this? I tried to follow the instructions in the following:

division by zero - Maple Help (maplesoft.com)

and by redefining how to handle exceptions does not really help me: EqP's value ("View EqP" from the "Variables" palette) includes some undefined, which I think will corrupt the procedure to test whether my system is inconsistent.

Would you mind directly implementing your check procedure on my script and sending it back to me? I attach here my script (cleared of the massive outputs) with the Eq and V sets for you to execute.

systemhasolutions.mw

Thank you for your continued support.

@Carl Love are you implying that when Maple's solve() seems to get stuck is because the system has no solution?

I am new to Maple, I am just trying to understand if it's my system that is inconsistent or if there are alternatives to solve() that I can test on my problem at hand. Since the system is not linear in the lambdas, it's not straightforward to assess whether is inconsistent or not (what do you suggest?).

Did you check my script?

problemaple.mw

Thank you! (I am new to Maple)