To invert a given pc set, you subtract each member of the set from 12, remembering to convert any number larger than 12 using mod 12 math.

For example: given the set {0,1,4,5}, subtracting each member from 12 would yield {0,11,8,7}. The normal order of this set would be {7,8,11,0}.

            12 12 12 12
             0  1  4  5
             0 11  8  7

To determine if two sets are related by inversion, follow this procedure. Add the normal order of one set to the reverse (or retrograde) of the normal order of the second set. If the sums of each pairing is the same, the sets are related by inversion (and transposition) at that level.

For example: consider the sets {10,11,2,3,4} and {1,2,3,6,7}. Reverse the second set ({7,6,3,2,1}) and add each member to the same member of the first set (10 and 7, 11 and 6, 2 and 3, etc.). Note that the sum is 5 in each case. Therefore, these two sets are related by inversion at transposition level 5 (IT5).

            10 11 2 3 4
             7  6 3 2 1
             5  5 5 5 5