@PinheiroRJ If you want each section to be self-contained, you can just put a restart at the beginning of each section.

@PinheiroRJ Sorry, I was confused by your use of "label" for equations, which in Maple are the numbers in parentheses on the right-hand side of the worksheet. a1 and a2 are variables in which results are stored. The statements such as a1:=x^2 are in "execution groups", which have the prompt ">" and a line like [ to the left. The calculation is done or "executed" by pressing "enter" in the execution group.

If I paste the new section in from another worksheet the a1:=3*x is not executed, but if the insert a new section and hit enter after entering a1:=3*x then it is executed and the earlier value of a1 is overwritten. You could go back to the line a1 := x^2 and hit enter to execute it, then skip down to the line a2 := 2*a1 and hit enter there (without hitting enter on a1 :=3*x) and you will get the result you want.

However, people tend to expect the result to be as in the sequance going down the page (and this is what you get executing the whole worksheet with the "!!!" icon), so it is less confusing if you just change a1 in the line a1 := 3*x to be something else, say b1. I don't know a way to do this automatically.
 

@WD0HHU This is on the plot3d help page: "If the first argument in any of the calling sequences is a set or list of surfaces, then the surfaces are plotted together. There is one exception to this: a list of three algebraic expressions or procedures is always interpreted as a parametric plot. To specify a list of three distinct plots, use the option plotlist=true (or simply plotlist)."

@acer I added back the negative sign in the last step, but combine would have been better. I'm always nervous about doing things by hand, and was hoping IntegrationTools:-Expand would put the integral inside the sum.

@one man Thanks. I first played round with it with various options in PolynomialSystems without much success. My past experience has been that the polynomial system doesn't have to be very large before it is intractable, but once @vv showed it could be done I wanted to pursue it a bit more.

Please provide some more details, including your Maple version, and preferably uploading some sample files (with the green up-arrow).

In Maple 2024.2, if I have two worksheets A and B open, and copy contents from A into the middle of B, the equation labels in B are automatically renumbered. Are you using some other method?

I agree; this is very frustrating. The vertices are pixellated because each plot is exported at lower resolution than if exported separately. This is for the elements that are bitmaps, the pdf export properly renders the lines and the fonts.

This is much more noticeable when exporting arrays of 3d plots of surfaces. I found that exporting to html and then printing to pdf (using Adobe print driver) from the html gives higher resolution for the bitmap elements but poorer resolution for the fonts and lines - it also doesn't respect the page breaks.

So my standard for publications is to export the individual plots to .eps and assemble the array of plots in another piece of software, e.g., CorelDraw.

@MaPal93 I wasn't suggesting the different results were pathological, rather that there was some minor error somewhere. A pathological case might occur for example if you want lim(a(x)*b(x),x=infinity). You evaluate lim(a(x),x= infinity and find it is infinity. Or you evaluate limit(b(x),x=infinity) and find it is zero. You cannot conclude anything from this, because we could have a=x^2 and b=1/x^2 and the true limit is 1. But if both limits are finite and non-zero, you should be OK.

I redid the calculation and simplification steps, checking numerically at each step. The result is different from above. To find out why, you could apply the same numerical checks to the other procedures to track done what is probably some small error in one step. (Edit: I see you figured this out.) But W4 is achieved without any limiting process, and is verifiably correct. If you rerun with gamma = 1e8, you see that W4 and the limiting values agree. So I am confident this version is correct.

limits.mw

@MaPal93 I wanted to check the limit for the RootOf, since there was some error with an earlier example that I submitted an SCR for, but at least for lambda it looks OK. You could pursue the sort of numerical tests I do here to resolve the discrepancy.

same3.mw

@MaPal93 I can imagine some pathological cases, but in general I would expect that the results should be the same. If I use limit(X[i], gamma = infinity) in generic_n-form_of_infinity_limit2_MaPal.mw I don't get the expression for X[i] in  n_from_2_to_6_-_not_coincide.mw so perhaps something is incorrectly entered, or perhaps I am not understanding what you are doing.

@MaPal93 I rewrote with as few summations as possible and was able to get the following simple result:

generic_n-form_of_infinity_limit2.mw

The _a indices arise when it would otherwise lead to a summation over i inside another summation over i, which is confusing since they are only dummy indices and not related. So Maple makes sure they have different names.

@MaPal93 I don't have any specific suggestions other than try to figure out the patterns.

Download patterns.mw

@MaPal93 Actually, I realized that if you use collect(W, gamma) (first method) you see W = (stuff1)*gamma+(stuff2), so the limit will be +infinity if stuff1 > 0 and -infinity if stuff1 < 0. So it seems correct that is infinite. (But now you have new X[i] etc.)

In general if you see something like signum(n*rho - rho + 1) you can just make some assumption like n*rho - rho + 1>0 to make it go away, assuming that such an assumption is valid.

@salim-barzani So if the input is 1/G(xi)*($$$$$$$$$$$$+diff(G(xi),xi)*(##########) what is the output you want?

I don't understand what you are trying to do, but this might be useful.

collect.mw