@Joe Riel I think the depends is an elegant solution to the problem. Why do you say that it only partially solves the problem?

@Joe Riel To me, a dimension check in the body of the anonymous procedure is certainly nastier than using subs to create a check in the header.

@weirp Are the scalars a and b going to be specific numeric values at the time of execution, or will they be unspecified symbols? If the latter, then I'm afraid that your computation is not feasible. The size of A[k] grows by a factor of about 3 for each k, and A[16] is already 460 megabytes. Whereas with a and b as specific integers I've finished the computation up to k = 100 in a few seconds with no problems.

@pepegna90 I have the worksheet already! I need the matrix data. That's what I couldn't find on filedropper.

You've given the initial value for k. I think that it is also necessary to give initial values for i and j and also to specify their upper bounds.

@pepegna90 I can't find your file from the link on filedropper. The link just takes me to the fledropper main page.

@Joe Riel Can you please show this example done with objects? Would using objects avoid the "nastiness" of having to use subs?

@brian bovril The opposite of NextTo(a, b, V) is Rel(NotNextTo, a, b, V)).

Update: There's a problem with using NotNextTo: I decided not to make it an export of the module. It's been a very long time, so I can't remember why. So the above is the internal form of the negation of a NextTo constraint. Internally, I also have a way to express the negation of almost any constraint. So here's a way to negate a NextTo using accessible exports:

The negation of NextTo(a, b, V) is Rel(Separated, a, b, V, [1]),

i.e., a and b are separated by a distance of at least 1 when measured wrt V. Since Separated is an export of the dynamic module, this constraint needs to be specified after the with is executed.

I added "physics package" to the tags, in the hope that Edgardo would see.

@boris_m I can't reproduce it in any version of Maple that I have. That includes Maple 17.02/32-bit on Windows 8.1/64-bit.

The nature of the problem is that it is acting as if zip is an unknown function. Check if a regular zip command works for you at the top level. If it does, then try this

m:= module()
option package;
export
     `*`:= proc(a::list, b::list)
     option overload;
     local i, L:= zip(:-`*`, a, b);
          if L::function then
               print(L);
               error "No zip."
          end if;        
          add(i, i in L);
     end proc
;    
end module;

If that doesn't work, we can do it without zip like this:

m:= module()
option package;
export
     `*`:= proc(a::list, b::list)
     option overload;
          `+`(:-`*`~(a,b)[])
     end proc
;    
end module;

Please post your exact code.

@Ratch You claim that solve in Maple 16 did not work for you. Using Maple 16.02, I got nine solutions with solve. Eight are nonreal, and there's the real solution given by fsolve.

@Markiyan Hirnyk Nevermind. I made a typo transcribing the equations from the OP.

@Markiyan Hirnyk Using the first answer from DirectSearch:-SolveEquations, I get much higher residuals than what it reports.

@maple_leeon You need to load the procedure JoggedLine before you can use it. You need to cut-and-paste it into your Maple session from the post that I linked to.