@dharr For instance, what about 

expr1 := a^3*b^3*(12*(a*b+a+b)-28*(a+b+1)^2)+4*a^2*b^2*(a+b+1)*(a^2+b^2+(a+1)*(b+1))*(13*(a+b+1)^2-8*(a*b+a+b))+a*b*(7*(a+b+1)^8-40*(a*b+a+b)*(a+b+1)^6+32*(a*b+a+b)^2*(a+b+1)^4+28*(a*b+a+b)^3*(a+b+1)^2-20*(a*b+a+b)^4)+(a+b+1)*(a*b+a+b)*((a+b+1)^4-6*(a*b+a+b)*(a+b+1)^2+6*(a*b+a+b)^2)^2: # %assuming nonnegative

and

expr2 := (a+b+1)^6-27*(a*b+a+b)*(a+b+1)^4+472*(a*b+a+b)^2*(a+b+1)^2+112*(a-1)*(b-1)*(a-b)*(a*b+a+b)*(a+b+1)-16*a*b*(2*(a+b+1)^2+3*(a*b+a+b))*(a+b+1)-1152*(a*b+a+b)^3: # %assuming real

? The former one is over nonnegative reals, and the latter one is over the real numbers.

Unexpectedly, Maple's solve (or RealDomain:-solve) is rather slow in solving expr₁＝0. (For the second equation, can Maple simplify or normalize the values?)

@C_R Sorry for the confusion. I don't signify there's a connection between these two questions. I just cite a worksheet that is not created by myself: The purport of it is to show that the problem is irrelevant to the worksheet (by me or by other users).

@C_R As Options Dialog - Export Tab - Maple Help (maplesoft.com) says, there are two different settings. However, this doesn't change the situation. Here is the worksheet: https://www.mapleprimes.com/questions/235749-Better-Way-To-Remove-Entries-In-Piecewise#answer292495.

Export using text for searchable text and smaller file size: remove_undefined１.pdf.
Export using shapes for greater fidelity: remove_undefined２.pdf.

E.g., confirmed.pdf

Download confirmed.mw

@Axel Vogt Well, this is hard to say, since I don't check the results (using other CAS’s). But I tend to believe that it's complete.

@Hullzie16 The key is that the domains of variables have been restricted.

Here is a simple example (just for fun): 

SolveTools:-SemiAlgebraic({36*a^2*b^2-9*a*b*((a+b)^2+7)+(a+b)*((a+b)*((a+b-5)*(a+b)+24)-5)+1=0}):

In the field of real numbers, how many possible solutions exist exactly? 
If you thought ∞, you’re wrong. (But this fact is, in effect, not easy to clarify.)

Can you give the values of k and w?

@acer Thanks. I find that the following codes are more or less convenient: 

[`$`](''parse(DocumentTools:-Tabulate([sprintf("%ld", i)], 'exterior' = 'none'), 'noeval', 'statement'), ifactors(2^i - 1)[-1]'', 'i' = 190 .. 200); DocumentTools:-Tabulate([[]]): 

@lcz SVG is an XML-based text format. So the connection between .svg and .xml is, in effect, closer.

In this question, @Carl Love posted an example of finding one shortest possible tour through several 3D points. His code only took he around four minutes, and just took @dharr about six minutes. Unexpectedly, executing it takes me nigh on 9 min! Well, these may be determined by one's computer. But how about Steam Deck's performance?
 

Download testTSP.mws (Sorry for a typo in it.) 

The selection works for sets as well.

@mmcdara For a small problem, minimizing the unsquared sum of actual distances (something like perpendicular offsets) remains possible in practice.

But it seems that Maple haven't collected this method yet, so one has to implement these by hand!

@lcz Replace "\n" and/or "\t" between term and datum with " ". For example, 

fontName	"Dialog"

is replaced by 

fontName "Dialog"

and 

LabelGraphics
		[

is replaced by 

LabelGraphics [

@acer Thanks again. It's what I want.

@sand15 Cheers. I believe the "smooth" means "antialiased", but I'm unfamiliar with these technical terms, and don't know how to define them.