@dharr Thanks. I'm astonished to see that the speed of your code beats that of mine (that is, manipulating text directly) instead, since a number of routines provided by the StringTools package essentially make use of and accordingly benefit from compiled libraries, while your code doesn't even call any external functions. (Anyway, I still don't know why the uncompiled Mathematica implementation runs quite fast. Maybe there'll be a dramatic speed-up in some future release. Let's look forward to seeing this.)

@Axel Vogt Hmm, this means that one has to change softwares (and ways of thinking) at each stage, which may retard (or even waste) productive computing in certain cases. The help page notes that "since the importing of NAG routines into Maple is an ongoing project, future releases will include the ability to handle a larger selection of input shapes and storage modes". This sentence is about the LinearAlgebra package, but I intend to know if future Maple releases will introduce more highly efficient optimization routines (because the add-on Global Optimization Toolbox cannot solve non-convex mixed-integer nonlinear problems as well). 

@Axel Vogt I read that "the Optimization package solvers rely on a built-in library of optimization routines provided by the Numerical Algorithms Group". And according to Optimization : NAG FL Interface, "mixed integer nonlinear programming" is supported in fact, but Maple's documentation simply writes that assume = integer is "only accepted by the Optimization:-LPSolve command". This is strange.

@vv Thanks. But the elapsed time is quite long; on my low-end computer, executing this code takes about six minutes. And it is strange that the returned values are not the optimum: 

Actually, the original problem (not posted here, since it is more expensive) asks for twenty variables (rather than nine variables). Is it possible to speed up the optimization processing (so that a medium-scale analogue can also be solved in an acceptable time)?

@Kitonum Thanks. This's justified (and faster). But if the problem has twenty variables, I'll have to write 20 do loops, which seems to be somewhat inadvisable. (Yes, the original problem asks for twenty variables instead of nine variables, but as this problem appears to be too expensive for a low-end computer, I just post a modified version here. (I choose "nine" because (-(-5)^3*(9-1))^(1/3) is simply a nice number.))

@vv I second that. I once wanted to use a more uncommon function in my question (to avoid certain non-essential "tricks"), but at last I gave up, as a simple function can achieve the desired effect as well.

@Axel Vogt Thanks. But it appears that this doesn't work for other functions.

Another potential workaround is: 

> m := Matrix([[1, 1, 3], [0, 1, 0], [0, I, 2]], datatype = complex(sfloat)):
> UseHardwareFloats := false:++Digits:
> add(residue~('z'/(exp('z') - 1)*LinearAlgebra:-MatrixInver\
> se('z'*LinearAlgebra:-IdentityMatrix(LinearAlgebra:-Dimens\
> ion(m)) - m), 'z' = lambda), lambda in ListTools:-MakeUniq\
> ue(LinearAlgebra:-Eigenvalues(m, output = list), 1, testfloat, 1));
                  [0.58197670686 + 0. I    -0.33869688735 + 0.20926639797 I    -0.80682426410 + 0. I]
                  [                                                                                 ]
                  [     0. + 0. I                0.58197670686 + 0. I                0. + 0. I      ]
                  [                                                                                 ]
                  [     0. + 0. I                0. - 0.26894142136 I          0.31303528550 + 0. I ]

Unfortunately, the default value of Digits is not enough here. (And I don't think that this is efficient (though not ineffective) for other functions.)

@dharr Thanks for your detailed analysis.
I read that "many LinearAlgebra package functions use NAG routines to carry out computations", while the LinearAlgebra['MatrixFunction'] does not make use of this external library. This is strange, since such routines are available (according to F01 (Matop) : matrix functions) in fact. 

@dharr Thanks. But I do not understand why the obsolete linalg:-matfunc (whose use is discouraged) performs better even with the default 10-digit precision. Equally, can't the built-in LinearAlgebra:-MatrixFunction go beyond the basics?

@Thomas Richard Actually, the OP's purpose is to display "x^2-2*x-3*x+6,x^2+3*x-7*x-21,x^2-9*x-10*x+90" instead of "x^2-5*x+6,x^2-4*x-21,x^2-19*x+90". For such a purpose, one may make use of InertForm:-Display(… have to be processed in advance …, inert = false). 

However, this is not very easy (though not impossible) to handle. In Mathematica, one can simply use: 

In[1]:= HoldForm[x^2-a*x-b*x+a*b]/.Distribute[{{a,b}}\[Rule]{{2,3},{-3,7},{9,10}},List,Rule,List,Rule/*Thread]

          2                     2                      2
Out[1]= {x  - 2 x - 3 x + 2 3, x  - -3 x - 7 x - 3 7, x  - 9 x - 10 x + 9 10}

There are also some other Hold* in Mma, yet I cannot find similar direct commands in Maple.

@Carl Love Many thanks. Surprisingly, I find that even if I don't compile it, the execution time of your implementation is still shorter than that of mine (well, tens of seconds faster).
Does loop-based code (instead of the so-called functional operation, which is used in my initial translation) typically provide better performance in similar cases?

To obtain some information about what the compiler is doing, you can set infolevel[Compiler] to a positive value (1 or 3). What can you find?

@dharr Many thanks. I believe that if GraphTheory:-AllPairsDistance (or networks:-allpairs) is fixed, this task will be more convenient to be finished.

@acer & @tomleslie Many thanks. I have just submitted a software change request.

@tomleslie According to updates,Maple2021,GraphTheory, GraphTheory['AllPairsDistance'] has had their efficiency improved. But somebody tells me that he cannot reproduce these in a "legacy" Maple. Can anyone compare the output from Maple 2020 and that from Maple2021 respectively?