@fluff I take it that you want the option of doing 0, 1, or 2 switches, right? You can't get two switches by including the switch argument twice.You make switches take a value in {0, 1, 2} by specifying the parameters like this

MontyHall:= proc(N::posint, {switches::identical(0,1,2):= 0})

and then making the calls like this

MontyHall(100000);  MontyHall(100000, switches=1);

etc.

@Markiyan Hirnyk Note that the prime notation for derivatives, A'(t), only works with 2D input.

@Kitonum It's O(n^4) because inside the loop for choose(S,3) there is a seq that scans over the remaining vertices.

I agree with you on points (1) and (3).

Do you mean that you want to do a simulation of the situation, with random selection?

Do you want the contestant to choose to switch always?

@rwooduk The green arrow for file upload is the last (rightmost) item in the second row of the toolbar.

(But I was able to download your file from zippyshare.)

@jelmew None of the basic simplifying commands work with the non-commutative multiplication operator `.`. If you are working with tensors, you should probably load the Physics package, which has its own simplifiers. Outside of that, the expression at hand can be further simplified via

eval(%, `.`= `*`);

First, please format your code so that it is readable by a human. Something like this
printf("No           root                   x[i+1]                 abs(x[i+1]-x[i])\n");
for i to n do
     y[i] := evalf(x[i]+(-D1(x[i])+sqrt(D1(x[i])^2-2*f(x[i])*D2(x[i])))/D2(x[i]));
     x[i+1] := evalf(y[i]-f(y[i])/sqrt(D1(x[i])^2-2*f(x[i])*D2(x[i])));
     printf("%d         %10.10f     %10.10f       %10.10e \n",
             i+1,       x[i+1],    f(x[i+1]), abs(x[i+1]-x[i])
     );
     if abs(x[i+1]-x[i]) < tol then
          print("approximate solution" = x[i+1]);
          print("No of iterations" = i+1);
          break
     end if
end do;

What is y[i]? What are D1 and D2? Did you intend for n to represent the maximum allowed number of iterations? n and tol and f need to be specified. Your formula for x[i+1] looks weird---too complicated. What function are trying to find the root of?

This is the kind of error message that a programmer puts into code to indicate that a serious bug has occured. This error message in particular occurs in the short procedure DynamicSystems:-TF_Matrix.

@jelmew I tested this on the uploaded worksheet:

evalindets(combine(Mcross, symbolic), sqrt, expand);

Maybe there are no solutions. It would be nice to have some evidence that a solution exists (such as a plot) before fine tuning fsolve with options.

There are complex solutions that fsolve will find if you give it the option complex.

@Adri van der Meer Regarding your point (1): It is not necessary to declare the dimensions of an Array. See my Answer for an example of this.

@Preben Alsholm These links cover the univariate case only.

@john125 Can you post a worksheet with the actual equations, please?

@john125 Sorry, I meant

select(y-> is(y>0), [Sols]);

@toandhsp Cut and pate Kitonum's code directly from the Post.