@nm I'd agree with you that odetest ought to use limit here.

(...and, better to have a duplicate report than none)

@KIRAN SAJJAN I asked how you wanted it laid out, with Gr taking multiple values. You have not answered that.

For example, you could have all the Cf columns together, and all the Nux columns together. Or you could have Cf,Nux in pairs, for each Gr.

@Andiguys 

You don't need the DirectSearch package to get the result I obtained in my previous Reply above. (I already gave you two separate URLs for obtaining it, btw). My use of that package merely confirmed -- even without substituting nu=sigma, etc -- the result I had already obtained without it, in the same worksheet: numerically using Minimize which my worksheet showed, and also symbolically which I didn't show.

Your previous attachment N1.mw contained plot3d call of something that doesn't contain I1 and I2, and the ranges you passed it were for I1 and I2. That doesn't make sense here.

If you have some formula for Q3 -- based on some other fixed parameter values and formulas for Q1,Q2 then why did you attempt to minimize TRC(sigma,nu,Q3) without using any such substitution for Q3?

If I take your formulas present elsewhere in the worksheet for Q1(sigma) and Q2(sigma), and the fixed parameter values present somewhere else in your worksheet, and then use those for a value for Q3, then Minimize succeeds with Digits:=30. In fact the results agree with what I had obtained in my previous worksheet, with Q3 allowed to vary (in a range I deduced from the constraints, with the lower bound the value I actually suspected).

The following attachment makes the various corrections (substituting appropriately for Q3, correcting variables in the plot3d call, use higher Digits): N1_11_acc.mw

Here is the 3D plot, including the TRC surface as well as transparent vertical surfaces for the 2D constraints.

ps. I believe that this would have been simpler if you had provided description of your methodology earlier.

@KIRAN SAJJAN You description is missing necessary important details.

You write that you want eta to go from 0 to 20 (in 1000 steps). You write that you want the results in table, and tried to use a Matrix.

Are you trying to create a Matrix that includes all four Gr values? What's the xi value(s)? How would that be laid out as columns in a Matrix, if either xi or Gr are to have multiple values?

@mmcdara The last time I checked, with utilizes an undocumented internal utility named bind, to rebind the export names. That makes the binding/unbinding of with/unwith work like a stack (FILO, First In Last Out).

@mmcdara 

If a name is an export of more than one loaded package then the effective binding for that name is that of the last one loaded.

Thanks for the color adjustment. I originally had it as you suggest, but later got lazy trying to save a little space... I've corrected the file. The key thing is that such colorings are quite easy.

@Axel Vogt Yes, it produces that form from Maple 16 to Maple 2022.2, but not in Maple 2023.2.1 and Maple 2024.0.

@Ronan You asked about improving the quality, and to my eye it's visually clear that the transformed 3D instance of your 2D plot collection has much better quality than the intersectplot 3D results. That was my main point, about transform.

I added an after-note, as a minor secondary consideration, is all. If you do it right then you can beat implicitplot (which is what I referred to as a hammer, not intersectplot) in terms of both computational time and memory to store the final result. If you end up animating, or manually rotating many larger objects in a GUI plot, then these things can make a difference in performance. That might not make any significant difference to your small example here; I mention it only as a potential going concern. If efficiency is not a concern in this then you can just ignore the whole commentary.

I wrote "line, or even plot with..." before. That does not mean that plot would be my first choice. With line you can construct a small structure quickly. Here's another:

with(plots):
# you might re-use either of these
L := rhs(isolate(-(13*x)/12 - (5*y)/8 + 71/96,y));
xrng := [-3,2];

# I personally don't find this next one too complicated.
# If you have many such L formulas then this could be
# done some with some simple added `seq` action.

pointplot([[xrng[1],eval(L,x=xrng[1])],
           [xrng[2],eval(L,x=xrng[2])]],
           style=line,color=red);

Of course you may well prefer shorter code at the expense of some time and memory. There's nothing wrong with that in your given example.

@Andiguys

I made corrections to your worksheet (and added a couple of plots you requested).

But the optimization approach was what you set up, not me.

Your overall goal is unclear. See my Reply above (May 30) to your original Question, which you still have not answered properly.

To me it seems that you use some names in contradictory ways.

Please put your followup and closely related queries on this here, or Branch from here (there's a button for that right below your Question), instead of spawning a wholly separate new Question thread for it.

A few notes:

Download eval_zero_power.mw

@vv I have reported it. Your last sentence seems to sum it up.

Another case to deal with,

evalc(0^n);
Error, (in type/complex) too many levels of recursion

@Ronan Thanks.

I added a couple of shorter ways to do your given example to the start of my Answer.

@Ronan The structure of my type-check was as follows:

  type(...,
            And(                            # it must pass all the following
                      name,                # it must be of type name
                      Not(constant)   # disallow Pi, gamma, etc
                      satisfies(mine)  # return true when mine is applied to it
                    )
         ) 

Here's some explanation of my use of type satisfies. This type allows you to utilize a custom procedure as the predicate of the type-check. That's very flexible and powerful.

Download type_satisfies.mw

@C_R Were you trying something like the following?

(evalc takes the unknown a as real)

(we can optionally simplify the signum(a)^3 to just signum(a), for a little extra clarity)

Download C_R_polar0.mw