I'm working on coming up with prime forms. I've been using this calculator online to check my work.
My problem is that the prime form I compute for a certain PCS doesn't agree with the calculator, but I can't find my error. I need help figuring out where I'm going off the tracks, or if the online calculator is wrong (which seems unlikely).
I'm starting with the PCS: [8, 11, 10, 1, 0]
Showing my work, I enumerate these rotations:
[0, 1, 8, 10, 11]
[1, 8, 10, 11, 12]
[8, 10, 11, 12, 13]
[10, 11, 12, 13, 20]
[11, 12, 13, 20, 22]
I then choose as the normal form [8, 10, 11, 12, 13]
, because the distance between the first and last items (13 - 8 = 5) is the least of all of the other rotations.
I then transpose the normal form to [0, 2, 3, 4, 5]
(through the interval of 4)
So I get to a prime form of [0, 2, 3, 4, 5]
.
The online calculator (when I click on the buttons for [0 1 8 10 11]
) yields a different prime form of (0,1,2,3,5)
.
So to recap, my prime form is [0, 2, 3, 4, 5]
and the calculator says the correct prime form is [0, 1, 2, 3, 5]
.
What's going wrong here?