@Mac Dude  I try to limit my use of float evaluation for as many algebraIc steps as possible, and also there are a couple of situations where evalf will output spurious results when evaluating certain trancendental expressions (or having contained in it trancendental numbers) 

@Mac Dude  RE the rot13 yep i havent done it in a conventional manner as a prequisite for another functionality of the algorithm  i want to do for the next "project" i assign for myself for "cryptology 101" the problem with using evalf here is that  my code is entirely symbollic - in that it uses only set and list functions as well as maple's StringTools package.

@Mac Dude yea im trying to get into the process of storing source code inside a maple data structure and the maple engine only requires to complile and destroy an arbitary number of executables at some point throughout an algorithm's loop as per whatever requirement each particular executable is used however the processing requirements of this will be handled by the external programs as opposed to it being demanded entirely by that of the maple engine.

well at least thats the heuristic attempt to push me to greater efficiency levels like in as much as i am proud of some code i have written alot of others for what ever reason all have a common flaw in that they are all very sluggish. Last night i composed a ROT13 cipher/decryptor tool and if it were to be implemented in a say a 2 way instant messenger format or even a forum like this, the time taken by my patch of code to perform the encryption woud mean people would only be able to send a message once every 35 minutes or so for more that 8 characters!

@vv in case that is there anyway of internationally legislating the prohibition of its use in mental health sciences?

@vv  is there any chance of using a different word to replace pathological? or will i face too much opposition to this?

@acer 

this in particular i dont understand the underlying principle of amoungst the help page for SERIES

@acer sure ill definately take a look at dismantle seeings i have never used it before or even known of it, but on the whole am i basically left to my own wet ware as they say in regards to the debugging of in built functions?

@vv yes i think where i got confused is in assuming the O was protected rather than defined by series 

@acer so i did ask you reccomended, (using op without additional options on both) and yes i can see now how the series function results in differing output when calling inside of op(), what i still don't understand is why it returns the coeffiecent followed by the index of the oprand's factor of z. see the attached to see what i mean, i just dont understand why the code has been written this way to produce "pairs" of data for a SERIES data structure as opposed to just the oprands as is the case when the SUM structure. 
 

Download acer1.mw

@vv 

yes i know thats the entire purpose of my code, to test an potential approximation to the most accurate known, so the initial input is an accurate approximation to about 10 decimal places, and the "while" loop is simply making a progressively more accurate rational error term that is the difference. yes i'm aware its a dirty little trick, its just been helpful for me to do things this way.

@acer  ok thanks i should be able to sort out what im not getting from here

@gkokovidis 

ok im still not sure im understanding why yet still but anyway ill read the help page for op and see how i go.

@gkokovidis  ok so it is related some how to the order function but what i dont understand is why  it returns the value of 2 is returned when calling the line:

with(LinearAlgebra);
omega[0] := proc (n) options operator, arrow; proc (i, j) options operator, arrow; f(n, i, j) end proc end proc;
omega[1] := proc (m) options operator, arrow; proc (i, j) options operator, arrow; g(m, i, j) end proc end proc;
proc (N, M) options operator, arrow; {seq(seq(map(eval, piecewise(IsMatrixShape(Matrix(N, omega[1](i))-Matrix(N, omega[0](j)), zero) = true, [i, j], IsMatrixShape(Matrix(N, omega[1](i))-Matrix(N, omega[0](j)), zero) = false, 0), [n = i, m = j]), j = 1 .. M), i = 1 .. M)} end proc;
 

@Adam Ledger 

it does make perfect sense tho seeings what the "is" function does is check that the equality is true or false