I am confused. What precisely do you mean by "solutions"? Your worksheet consists of three functions of three variables. Do "solutions" refer to points (x,y,z) at which these three functions vanish simultaneously, as the answers by tomleslie and Kitonum suggest; or do you actually have something completely different in mind, perhaps fix points?

@wswilson3: Happy to hear that it was useful, although perhaps not user friendly :-).

@Fzen: Ah, I see. I had misunderstood what you want to achieve. I thought that you wanted to select the polynomials of degree <= n for some given set L of polynomials.

@lemelinm: That looks better :-).

@ecterrab: My question was related to the presence of Physics:-`^` in the above comment by lemelinm. Nothing deeper than that. I do understand the need for Physics:-`^` in general noncommutative settings.

@lemelinm: You are quite welcome. I am learning new stuff as well going along. For instance the smart way that you make a sequence of matrices of the Christoffel symbols of the second kind:

seq(Christoffel[j,mu,nu,matrix],j = [`~1`,`~2`,`~3`]);

Doing instead

seq(Christoffel[~j,mu,nu,matrix],j = 1..3);

does not work.

I have a question: Is the use of Physics:-`^` above, rather than `^`, due just to some copy-paste 'quirk', or is it really deliberate? If the latter, then why?

PS: By the way, you have an Einstein space, right, the Einstein tensor being proportional to the metric.

@Carl Love: I am having no doubt that you correct. But on these matters concerning levels of execution I am basically completely ignorant, although I would certainly like to be otherwise. Could you perhaps point me to some introductory material?

@tsunamiBTP: Why not use the command map to raise the components of some Matrix or Vector to some power?

M := Matrix([[2,3],[1,6]]):
V := Vector([2,4,-3]):
map(x -> x^3,M);
map(x -> x^5,V);

@Axel Vogt: That was also what I thought, and, of course, I agree with you on that.

@Axel Vogt: The original post of brian bovril had ID 220538. But perhaps I misunderstand you.

@brian bovril: That clears up matters.

Update: Just seen acer's post now.

@Carl Love. Thanks for that reassurance.

I have experienced censorship several times at a different internet ressource, more specifically in the threads of a newspaper, for comments that seemed to me not all that objectionable. But I may be personally biased, of course. Anyway, that is the reason why I feared censorship here because of my and your critical comments concerning missing replies from the MaplePrimes administrators.

PS: You have my blessing to convert this to a post :-), if you like so.

@Carl Love: From the example OP gives, I reckoned that the variables would take up little space each. You are right, of course, concerning the naming of a. The variables must be saved as a sequence of variables, as I also write, without, though, giving OP an explicit implementation/example of any such.

@Kitonum: Thanks for that feedback. I somewhat feared that some censoring had happened; happy to hear that that is not the case. I have located the post now. Why it has been changed to a post also puzzles me, though.

@Carl Love: I am aware of that, thanks anyway, though. My intention with my comment was just to second Christopher's idea to a potential improvement, from MapleSoft, to the interrupt button.