I can't understand why this error Error, adding lists of different length show up only when removing a print statement!

Why would a print has anything to do with an error message showing up or not?

some context. I wanted to call map on expression, but wanted to collect the result of operating on each indent in a list as map goes through the expression on term after the other. The expression will be type `+`.

I did not know how to do it inside map. So I create separate proc which map call.

Inside this proc, I use list to append to (this will small list, few terms at most).  To be able to do this, I made the list I want to collect thing into a global variable outside the proc.  Everything was working OK, until I remove a print statement  I had inside the proc for debugging.

I am sure there is a better way to do this all (i.e. collect map output into a list) and I am trying to find better way. But my question is: Why would this error shows up only when I remove a print statement from the last line in the proc?

I also notice when removing the line variable declaration global L now both version work with no error, but get warning Warning, (in f) `L` is implicitly declared local which is why I added declaration global L in first place.

Maple 2021.2 on windows 10

Download why_error.mw

Thanks to everyone for the answers and information I did not know that map does process return value from a proc it calls. Good to know.

I looked at combinat package but it is too large and could not find what I want.

I'll explain with example to make it easy. Given n=2 I want to generate all possible arrangements of sets of length n where each element can be either +1 or -1. So it will be 2^n=4 possible arrangements

And for n=3 then want to generate all possible sets of length 3 where each element can be either +1 or -1 so it will be  2^n=2^3=8 possible sets

And for n=4 it will be 2^n=16 possible arrangements

And so on. I picked [+1,-1] in the above as an example.   

Is there a command to do this in Maple?  I can ofcourse program it using using loops and if's and so on. But thought there might be a command in Maple package which will generate all these possibles sets. Either as list of lists or Matrix or any other format. 

I'd like to get the simplest possible expression when using simplify. The problem is that this is all done in a program, without having the benifit of looking at the expression on the screen and trying things. So I need a method that works for large set of input all the time.

I noticed in this example that simplify did not do what I think it should have.

Given the expression -2*(x^3 + 2)/(x*(x + 1)*(sqrt(3)*I + 2*x - 1)*(sqrt(3)*I - 2*x + 1)) it can be simplified to (x^3 + 2)/(2*x^4 + 2*x) but  I had to go into many tries in order to get this final result.

Is there a better way to do this? I end up now   doing simplify(expand(numer(expr))/expand(denom(expr))) in the hope to get better simplification.  Here is an example

It would be nice if Maple simplify would just do it directly as follows in Mathematica. May be there is a an  option I am overlooking

Download simplify.mw

I read that abs(v) should find the magnitude of complex number. But I find cases where it does not.

Should one then use sqrt( Re(v)^2 + Im(v)^2 ) instead or is there different command to use?  Here is an example

Download complex.mw

Here is the same thing in Mathematica:

I searched help for modulus but could not find one.

Maple 2021.2

I am translating old Maple code to run on Maple 2021.2. This code from 1985. I think it was Maple 3 then. I'll put a link to the paper and page number.

It uses this syntax

Btw, the " above is meant to be % in new Maple. I do not know what w='@W' is supposed to translate to.

The paper is

A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

by  Carolyn J. Smith.

Here is the link

https://cs.uwaterloo.ca/research/tr/1984/CS-84-35.pdf

The above is at page 67. Near the end.  The code also uses some old functions, which are not given in the listing, I searched but could not find these.. One is called Lsolve (to solve linear equations, but I can replace this with solve) and  on page 77 it uses these 

           Functions required: scanmap, expcontract, lncontract, explnsimp

These are not given in the source code in the paper. I assume these are old Maple function which no longer exist?. But I can just use simplify for now in their place.

My question is on the use of `@W` and what it could mean? This syntax @ is used in many places in this old Maple code.