Question

The extended indexing syntax is mentioned in python’s doc.

slice([start], stop[, step])

Slice objects are also generated when extended indexing syntax is used. For example: a[start:stop:step] or a[start:stop, i]. See itertools.islice() for an alternate version that returns an iterator.

a[start:stop:step] works as described. But what about the second one? How is it used?

Answer 1

a[start:stop,i] calls the method a.__getitem__((slice(start,stop,None), i)).

This raises a TypeError if a is a list, but it is valid and useful notation if a is a numpy array. In fact, I believe the developers of Numpy asked the developers of Python to extend valid Python slicing notation precisely so that numpy array slicing notation could be implemented more easily.

For example,

import numpy as np
arr=np.arange(12).reshape(4,3)
print(arr)
# [[ 0  1  2]
#  [ 3  4  5]
#  [ 6  7  8]
#  [ 9 10 11]]

1:3 selects rows 1 and 2, and the 2 selects the third column:

print(arr[1:3,2])
# [5 8]

PS. To experiment with what slice is getting sent to __getitem__, you can
play around with this toy code:

class Foo(list):
    def __getitem__(self,key):
        return repr(key)

foo=Foo(range(10))
print(foo[1:5,1,2])
# (slice(1, 5, None), 1, 2)