how to shift shift(1,[x,y,z]) = [y,z,x]

shift(2,[x,y,z]) = [z,x,y]

shift(3,[x,y,z]) = [x,y,z]

is it possible?

i want to prove the injective of new custom operator based on custom logic table according to previous post

and want to see why new custom operator for integers are unordered or sometimes ordered

https://social.msdn.microsoft.com/Forums/vstudio/en-US/cc2a85ad-30ec-44ed-8c75-636ff71eade2/how-to-convert-integer-or-decimal-number-into-any-base-number?forum=csharpgeneral

1. for example how to convert decimal or integer number into base 3 number, base 5 number etc.

2.how to do logical operation with custom logic table for example,

120 special operator 235 

01111000

11101011

special operator according to logical table is

  01111000

  11101011

=00010100 = 20

how to derive poincare series from symmetric function in maple

use taylor function need to specify its limit

if we do not know its limit, 

how to know whether a function is finite in taylor expression

for example poincare series

1/((1+x)*(1+x^2))

how to display as taylor series without specify the limit of degree

because do not want to approximate poincare series with taylor 

want a complete taylor series

goal is to find the polynomials which degree are 1 and 2 in above example