@C_R I don't think this is an easy job.  
In different interfaces, the outputs are distinct: 

But the common point is that in 1-D math Maple considers the Unicode character “λ” to be different from the Greek symbol “lambda”! 

I find that searching for the Unicode letter “λ” (instead of “lambda”) is enough. Unfortunately, this trick does not work for subscripted variable names (for example, “λ₁” does not match the 2D output of “lambda__1”…). 

@dharr Thanks for exploring. 
Strangely, `eliminate` works fine when I set a (redundant) dummy variable _Y: 

> expr := `~`([a, b, c]^2 = 4*[y*z/((x+y)*(x+z)), z*x/((y+z)*(y+x)), x*y/((z+x)*(z+y))]):
> eliminate([expr[], x+y+z = _Y, _Y <> 0], [x, y, z])[-1];
   /  / 2        2            2\ / 2        2            2\\ 
  { a \a  - 4 + b  + a b c + c / \a  - 4 + b  - a b c + c / }
   \                                                       / 

But if I use “[expr[], x+y+z = 0]”, the result will remains empty. (Note that x＋y＋z can be zero, for instance, .) 

@Axel Vogt Thanks. Strangely, if I write something like “p += …” and “f mod= …”, Maple will raise an error.

@acer Many thanks. This is a useful trick! 

@acer Thanks. After some search, I found that “irem((j - 1)!^2, j)” is just OEIS A010051 (1 if n is prime, else 0), yet the equivalent “ifelse(isprime(j), 1, 0)” cannot be compiled. (Maybe there is a mechanism to indicate operations that should be directly evaluated in the Maple kernel rather than being compiled into low-level code?)

@Kitonum Strangely, the plot generated by MaplePrimes is correct instead: 

@romanrieme You can still use “V_D2[1]” as usual. 

@John May Many thanks! I hope that this kind of functionality will be added to the GraphTheory package in the future. 
(As a side note, there exist several questions and posts in MaplePrimes about enumerating all paths/cycles/cliques/… (like this, this, this and this), but regretably such functions never seems to have been considered for being built into the GraphTheory package. Perhaps this lack will be fixed in Maple 2025.)

@John May Thanks. I think that I have an extra problem. GraphTheory:-DijkstrasAlgorithm (as well as GraphTheory:-BellmanFordAlgorithm and GraphTheory:-ShortestPath) does give one shortest path, yet sometimes more are needed; is there a ready-to-use function that can find all (shortest) paths? 
For example, by some visual inspection, one may find three other optimal paths in this puzzle: 

I wonder if the GraphTheory package provides such a command?

This is amazing. But when I run your code, the rendered plot does not seem aesthetically compelling: 

Have you set any additional options? 
Besides, I notice that this page claims that 

while your spd₂ is 5036. Any typos? 

@dharr Actually,  assuming x>0 has no effect when Maple solves eq, since solve ignores assumptions on the variables for which it is solving. (The above equation is adapted from the fourth problem in this page.)

This must be a bug, since the returned value of “applyrule(x::anything^n::'nonunit'(anything) = f(n), 1);” is “f(`/n1`)”.
(“applyrule(x::'nonunit'(anything)^p::'nonunit'(anything) = f(p), 1 + x^2 + x^4);” works, but I believe that it is also a bug if it works like this.)

As a side note, the following code also works: 

convert(Xvector, `+`);

@acer Its source code can be found at http://www.mmrc.iss.ac.cn/~lzhi/Research/hybrid/SDPTools/.
@bathudaide There exists another problem: A slightly detailed explanation of several main functions is written in simplified Chinese. (That English paper does not seem to describe their calling format.)