on slices, negative indices, which are the equivalent procedures?

[Jach Feng]

> >>>>> s = "Jack Brandom" 
> >>>>> s[3 : -13 : -1] 
> >> 'kcaJ' 
> >> I have no idea how to replace that -13 with a positive index. Is it 
> >> possible at all? 
That's not possible because a positive index is relative to the leftmost item 0

Below is some rules of slice usage which I collected sometimes ago.
-----
slice s[i:j:k]
     The result is from start index i to stop index j (excluded) in step k (default is 1).  i, j, k can be positive or negative. For example:  s = [1,  2,  3,  4,  5]
1. Positive index is relative to the leftmost item (0), negative index is relative to the rightmost item (-1). Note: out-of-range index is valid.
       s[-4:5] == s[1:5] == [2,3,4,5]  # index 5 is out-of-range
       s[4:-6:-1] == [5,4,3,2,1]  # index -6 is out-of-range
2. The default index of i and j (When index is omitted) was decided by the sign of k. 
    For positive k, the start index is 0 (the leftmost item) and the stop index is the one after the rightmost item.
       s[:3] == s[0:3] == [1,2,3]
       s[1:] == s[1:5] == [2,3,4,5]
   For negative k, the start index is -1 (the rightmost item) and the stop index is one ahead of the leftmost item 
       s[:2:-1] == s[-1:2:-1] == [5,4]
       s[3::-1] == s[3:-6:-1] == [4,3,2,1]
3. The items pick-up order was decided by the sign of k. For positive k, the direction is toward the right. For negative k, it is toward the left.
    s[1:4] == [2,3,4]
    s[3:0:-1] == [4,3,2]
4. Invalid slice will return an empty []
    s[2:0] == []
-----

--Jach