@dharr thanks! I did not know the name of this sequence.

I used subs command on the expression, so every radical on the polynomial showed as ν. When i undid the substitution simplify(...,radicals) worked just fine.

@dharr Thanks a lot guys! 🔥

@Carl Love that was surprisingly instructive! You are absolutely right: the third interpretation IS the one i needed to clarify in order to keep going with my research. Your answer was insightful, instructive, and precisely the one i needed. I realize now the difference between an operator-type procedure and a function. You are also rigth when you say that dharr's last answer is sufficient for the cases i'm interested in, but generalizing the code for operators migth be very helpful for me in the future. A billion thanks, i would lend you 5 likes if i could...😅😂😁🙏🏽

@tomleslie 

This one did the trick! So, i can map an expression to a function of itself! That was clever! 👏🏽🙏🏽

@dharr 

i understood better the _passed/_npassed relation...but my problem persists. You'll see, i'm trying to make an algorithm that takes simple functions (like f(x,y,z)=x+y+z), and then works with both input and output...maybe something like this:

F: (x, y, z) -> (r_x+r_y)r_z

G=proc(f::function/procedure,n::nonneginteger) local a,b;

a= {addition of arguments of f}
b= {division by two of the output of f}
(a+b)*n

end proc

G(F, 3)= (x+y+z+(r_x+r_y)r_z/2)*3

@Carl Love thanks! this one works perfectly for all types of subsets!

@acer great, that really worked! Also, thanks for the warning on maplesoft 18 release date! 👍🏽👍🏽

@nm zip is a binary operation! I need the sum to be over a large list (or set) of A_i's, if 'i' grows too large i would need to iterate one zip at a time, and would take too long!

@Carl Love, this procedure returned an exception! Both "add" commands need two arguments (maybe it's my version, Maplesoft 18)!

i tried "add(x[ ],x=S)" and i got a more satisfactory answer, though.

@dharr 

Ok, that totally worked! 
thank you! 👍🏽👍🏽👍🏽

@dharr 

no problem! 
Symbolic answers will suffice:

a common example would be this

lets say we have a set of cosets, like this one:

A={{a_0,b₀,c₀},{a₁,b₁,c₁},...,{a_n,b_n,c_n}}

and B={i,j,k}

my goal is to make this two sets into a vector space, by turning them into a sequence (or set, or list) of vectors of the form:

s(i)=A[i]*B=a_ii+b_ij+c_ik

The resulting sequence should have this form:

a₀i+b₀j+c₀k , a₁i+b₁j+c₁k , ... , a_ni+b_nj+c_nk

i hope that clarifies everything. I know how to get the secuence term-by-term, but that is practically imposible if n gets too large. Thanks for the help!