incOrbit -- the increasing map orbit of an element

• Usage:

  O = incOrbit(f,n)

  O = incOrbit(F,n)

• Inputs:
  • f, a ring element, an element of a ring created by buildERing
  • F, a list, a list of ring elements
  • n, an integer, the index bound
• Optional inputs:
  • Symmetrize => ..., default value false
• Outputs:
  • O, a list, a list of all elements in the orbit of f or F

i1 : R = buildERing({symbol x}, {1}, QQ, 2);

i2 : O = incOrbit(x_0^2, 4)

       2   2   2   2
o2 = {x , x , x , x }
       0   1   2   3

o2 : List

i3 : P = incOrbit(x_0 + x_1^2, 3, Symmetrize=>true)

       2             2   2             2   2             2
o3 = {x  + x , x  + x , x  + x , x  + x , x  + x , x  + x }
       1    0   1    0   2    0   2    0   2    1   2    1

o3 : List