@John Fredsted 

I guess sand15 wanted to write

S2 := map(u -> [ 2*rhs(u[1])-1, 2*rhs(u[2])+1], [S1]) ;

This seem to work well : 

S3 returns [[1, 3375], [3, 1125], [5, 675], [9, 375], [15, 225], [25, 135], [27, 125], [45, 75]] which seems to mean
the first sequence has only one element centered at 3375 ; the second 3 consecutive odd numbers centered at 1125 and so on.

I am awaiting confirmation

@acer I apologize, I read that the solution provided by Maple was [0, 0, 0] as it is just the verification rhs(..)=lhs(...).

SORRY AGAIN.

That'll teach me a lesson to watch the ITALY-BELGIUM football match and trying to do maths 

End of the day for me, I go to sleep. SORRY again

@acer  

With all due respect, I'm not the author of the question. I may have misled you by clicking on the "reply" button at the bottom of your own answer to candermix (?)
Saying that I'm just a third party in this discussion.

Fot the "2042"  value thr true one is 9*sqrt(2042) ; I have forgotten the 9 somewhere by thoughtlessness.

However, If I consider, as I think you did too in your answer to candermix, that each equation 

eq. := ......, N ;  has to be interpreted as  eq. := ...... =  N ; then your equations are analytical representations of 

spherical surfaces.

My purpose was not to complete squares (to be honnest I did this to obtain the values of the radii), but to draw a solution procedure based on geometrical analogies (so the spheres instead of the equations you sent me).

With the reasoning that I sketched, I found there could not be any (real) solution. This was a very different result than the one you provided. But drawing the three surfaces seems to confirm I'm right.

So the true point is : If I'm right, what is the meaning of this double [0,0,0] solution Maple returns  ?
All the more so that x=0, y=0, z=0 is not, obviously, a solution of any of the 3 equations (easier to verify with the original ones)


I won't take up your time, but I would appreciate an aswer,
Thank you in advance

@acer By simple computations :

eq1 represents a sphere S1 centered at (67, -400, 180) with radius sqrt(2042) 
eq2 represents a sphere S2 centered at (467, -450, 185) with radius sqrt(133027) 
eq3 represents a sphere S3 centered at (307, -675, 555) with radius sqrt(787948) 

the distance between the centers of balls S1 and S3 is 273850
the one between the centers of balls S and S3 is 213125

each of these distances is less than the sum of the radii of the coresponding spheres.

So the sphere 3 does not intersect any of the others (a simple reasoning shows that are located inside the biggest one)

The system then has no solution at all.

How is it that Maple finds one ?

Did I do some mistake ?

M := 1100: 
p1 := plots:-implicitplot3d(eq1,x=67-M..67+M,y=-400-M..-400+M,z=90-M..90+M,style=surface, color="Niagara Azure"):
p2 := plots:-implicitplot3d(eq2,x=67-M..67+M,y=-400-M..-400+M,z=90-M..90+M,style=surface, color="Gold"):
p3 := plots:-implicitplot3d(eq3,x=67-M..67+M,y=-400-M..-400+M,z=90-M..90+M,style=surface, color="Green"): plots:-display(p1,p2,p3);

@Carl Love  I use the version 2015.2 ; the operating system is OS X el Capitan 10.11

@Carl Love  

Option 1 (:-LinearAlgebra:-Transpose(A)) works perfectly.

Very useful are the variants of  with(...) you have given.

Option 2 : with(Maplets:-Examples, ({Maplets:-Examples:-_pexports()[]} minus {LinearAlgebra})[]);
used this way 

restart:
with(Maplets:-Examples, ({Maplets:-Examples:-_pexports()[]} minus {LinearAlgebra})[]);
A := Matrix(2,2,[1,2,3,4]):
LinearAlgebra:-Transpose(A)

still returns 

"Error, Transpose is not a command in the Maplets:-Examples:-LinearAlgebra package"

... probably something I didn't understand correctly  ?