@Preben Alsholm  yes i think this is why i got confused about the meaning of a global in that i had been regarding to be the same as _Z1,_Z2,_Z3 etc that are local to RootOf and or Solve, would there be any loss of generality if it were say replaced with what ever the symbol was assigned by the user in a similar fashion as you have done in the line R:=proc(pol,x) local _Z; rootof(subs(x=_Z,pol)) end proc;
?

@vv  i feel as if there is an inconsistency with your advice between users regarding how practical it is to determine divisors of large numbers :-\

@Rouben Rostamian sorry, my mistake, perhaps this isnt the meaning of global variable they were refering to, but it was from the help page that i was under the impression that _Z is a global variable, as specified in the extract from the RootOf help page attached:

@vv 

delta[P] := proc (n) options operator, arrow; piecewise(isprime(n) = true, 1, 0) end proc

delta[d] := proc (n, k) options operator, arrow; piecewise(`mod`(n, k) = 0, 1, 0) end proc

q := proc (n) options operator, arrow; n/(product(delta[d](n, k)*delta[P](k)*k+1-delta[d](n, k)*delta[P](k), k = 1 .. n)) end proc

EDIT: ok that is useless too returns a memory error fuck it this is why im unemployed im going to bed for a week

@vv  is that how it does it so fast? 

@vv yes that implies phi(n)=phi(p)phi(q). i still dont understand where this is going to help me see what i am asking but ok  i would say that would be something like :

proc (n) local i, R; global p, q; for i from 1 by 1 to n-1 do R := irem(n, n-i); if R = 0 then do p := n-i; q := n/p; end do; else NULL end if; end do; end proc;

werid wtf is with it putting a picture of the code? and it skips stuff too 

anyway that cant be right thats the slowest thing ive ever written

@vv  the method you described as using the Euler product formula uses the function factorset(n) which uses ifactors(n), which uses igcd(k,n), which is also used in the formula i posted in the image.

So given that both methods use igcd, which is inbuilt and therefore cannot be accessed using showstat, how were you able to determine their difference in computational efficiency?

@Kitonum oh ok i dont see why they even have it if the number theory package uses the Euler product formula i mean if it is more efficient it's clearly the better choice. They may as well just compile the number theory package into the physics package and go with what the number theorists have chosen for things i think 

@vv  oh great i had stopped working with show stat and began assuming everything i asked to see was in built

@Kitonum  i asked how it is calculated by maple i know what it is that is being calculated, i mean i wouldnt be able to write the formula above if i didnt.

@ganelon  They belong to R, why would you want to perform complex analysis?

@Mac Dude thanks yes i saw the part about java running out of space, i guess what i really want know is if it is the the quanity of data i am expecting maple to parse or the displaying of the plots, because yes, reducing the size of the plots but their entire purpose is for me to sit there staring at them and writing down basic observations when i am too sleep deprived to do actual work, so, ideally i want to find a way to keep the size of the plots.

Great so java expert to the rescue but also mac user i havent met many for a long while it was usually artists or musicians with mutual interests back in the day. which is not macs of course.

edit: can you reccomend me a bunch of IDE and debugging stuff to download for dealing in java please

@ganelon  sorry are referring to complex numbers with a non zero imaginary part?

It was my understanding that a polynomial interpolation can be determined for literally any finite sequence of rational numbers, the denominators and numerators having interpolations taken seperately in such a process then determining their gcd using the euclidean algorithm can also arrive at what maple refers to as a rational interpolation ie the most simplified ratio of two polynomials.

So i had been requiring any such interpolation to have further meaning that simply existence and consistency, like say for example they must belong to a common equivalence class, if i identify that they are all even polynomials then i will take further consideration.

But never for a stand alone sequence because there is no means of logical analysis one can perform, I guess what i am saying is that it only makes sense to begin with a binary relation of sorts for a set of sequences, in assertaining that these are infact the parition of a set, we can look to determine an equivalence relation it represents.

For people that are well what i can only aspire to at this stage they have been pretty tolerant or non vigilant to the extent they could be encryption wise regarding the authenticity of product registration.