@MaPal93 When simplify acts on some of your expressions containing names of type RandomVariable (here, appearing as _R, _R0, _R1, _R2) the results contain different versions of those names.

note: those names have attributes on them, one of which starts as a module or the name of one.

That might also mess up the solve, ie. it might see various _R0 names present in the Eqs as being distinct, etc, and not be able to work properly in consequence.

You might try the following: make all the preliminary calls to Mean & Variance, generate the unsimplified expressions, replace those problematic names without some innocuous names, then simplify, then assemble the Eqs and call solve, etc.

To show the nastiness, running the following in your code (right after the assignments to Exp_nu1_S & Exp_nu2_S):

foo:=Mean(nu[2]) + Sigma__vs[2] . MatrixInverse(Sigma__ss) . (S - Mean~(S)):
map(nm->print(nm,addressof(nm)),indets(foo,RandomVariable)):
"and...";
map(nm->print(nm,addressof(nm)),indets(simplify(foo),RandomVariable)):
"and...";
map(nm->print(nm,addressof(nm)),indets(simplify(foo),RandomVariable)):
                    _R, 36893627906852826684

                   _R0, 36893627906824461084

                   _R1, 36893627906689103900

                   _R2, 36893627906689104572

                            "and..."

                    _R, 36893627904561785564

                   _R0, 36893627904561779740

                   _R1, 36893627904561781532

                   _R2, 36893627904558314012

                            "and..."

                    _R, 36893627904773265372

                   _R0, 36893627904773259548

                   _R1, 36893627904773261340

                   _R2, 36893627904773263132

map(nm->print(nm,addressof(nm)),indets(add(S),RandomVariable)):
"and...";
map(nm->print(nm,addressof(nm)),indets(simplify(add(S)),RandomVariable)):
                    _R, 36893627906852826684

                   _R0, 36893627906824461084

                   _R1, 36893627906689103900

                   _R2, 36893627906689104572

                            "and..."

                    _R, 36893627904819602812

                   _R0, 36893627904819604540

                   _R1, 36893627904819598076

                   _R2, 36893627904819599804

@OtherAlloyMonkey Could explain in more detail -- or demonstrate, or explain explicitly -- why you think that the determinant of your Matrix AA , evaluated at omega=1, say, should not be zero?

Also, do you intend gamma to be just some name, or is it your intention to use it (as Maple does) as Euler's constant?

It's very difficult to provide best advice here since you haven't provided the actual example. You haven't even indicated how many unknowns you have.

You question, "Is there a limit to the matrix size on which the Determinant(A) can operate?" is not sensibly posed in the absence of some additional details. Useful answers depend on some of them.

@OliverB Something like this?

Adding to your prior code,

ff := proc(x, y)
  local res;
  if not [x, y]::list(numeric) then
    return 'procname'(_passed);
  end if;
  res := f(x, y);
  if not res::numeric then -1000; else res; end if;
end proc;

vlo, vhi := 100, 900;
ContPlotimpl := plots:-display(
  seq(plots:-implicitplot(ff(x, y) = v, x = -200 .. 200, y = -200 .. 200,
                          color = ColorTools:-Color("HSV", [0.667*(1 - (v - vlo)/(vhi - vlo)), 1, 1]),
                          legend = v), v = vlo .. vhi, 50));

plots:-display(ContPlotimpl, Tubeout, Tubein, Coreout);

ps. Workbooks are awkward to use here (and I find them awkward altogether). If possible, I'd much prefer to get a .mw file. (Thanks)

@ControlLaw Is there some special reason that you cannot show us your actual expression?

@OliverB Having the actual data would be useful.

@OliverB Yes, in Maple 2021 the contourplot command does not itself have any direct options for providing a rainbow of colors (eg. via colorscheme).

It could still be done by programmatically manipulating the resulting structure returned by your version's contourplot command. That's not terribly difficult, but I'm afraid that I don't have time to write that today.

One alternative might be to simply call implicitplot for each color and contour value pair that you want, and plots:-display the results together.

Another alternative might be to call densityplot instead of implicitplot (with a piecewise? that is undefined out of bounds, perhaps, or disabled extrapolation?, or a bounding hull?), with the desired color effect.

What do you mean by this?

   log/(x__3^(1/2)*x__4)

Are you trying to call the log command on something?

What do you mean by,

   F5 := 1/sqrt(x__3) = -2*log(2.51)/(F3*sqrt(x__3));

if you've already assigned an equation to F3, ie.

   F3 := 0.1*p*x__4/u = 0.1*p*x__4/u;

It doesn't make sense if you're making things with a form like,

   F5  :=  blah = blech*( foo = bar )

since that's an equation with another equation on its right-hand side. That's not just a problem for Maple; it doesn't make much sense mathematically.

I changed your Post into a Question.

In future, please submit your queries as Questions, rather than as Posts. Thank you.

Another alternative here is to use PolyhedralSets. That too produces a lightweight plot with cleanly rendered boundaires, but with less need for thinking about the inequalities and region.

We could optionally remove the sphere symbols at the vertices, adjust the view, etc.

Download polyhedral_ex.mw

@C_R You wrote about five inequalities (now adjusted). But four inequalities are sufficient, and are given by the OP. Ie,

   0<=x, x<=y, y<=z, z<=1

Please don't start wholly separate new Question threads for this problem.

@Christopher2222 What is the size of your actual Matrix?

If it's datatype=float[8] then is ImageTools:-Threshold fast enough?

Or is it so large (and not just floats), so that you really need parallelism?

Did you read the Help page for that command?

If so, then which specific parts of did you not understand?

Could you provide your complete example?