np.delete is not doing anything unique or special. It just returns a copy of the original array with some items missing. Most of the code just interprets the inputs in preparation to make this copy.
What you are asking about is the obj parameter
obj : slice, int or array of ints
In simple terms, np.s_ lets you supply a slice using the familiar : syntax. The x:y notation cannot be used as a function parameter.
Let's try your alternatives (you allude to these in results and errors, but they are buried in the text):
In [213]: x=np.arange(10)*2 # some distinctive values
In [214]: np.delete(x, np.s_[3:6])
Out[214]: array([ 0, 2, 4, 12, 14, 16, 18])
So delete with s_ removes a range of values, namely 6 8 10, the 3rd through 5th ones.
In [215]: np.delete(x, [3:6])
File "<ipython-input-215-0a5bf5cc05ba>", line 1
np.delete(x, [3:6])
^
SyntaxError: invalid syntax
Why the error? Because [3:4] is an indexing expression. np.delete is a function. Even s_[[3:4]] has problems. np.delete(x, 3:6) is also bad, because Python only accepts the : syntax in an indexing context, where it automatically translates it into a slice object. Note that is is a syntax error, something that the interpreter catches before doing any calculations or function calls.
In [216]: np.delete(x, slice(3,6))
Out[216]: array([ 0, 2, 4, 12, 14, 16, 18])
A slice works instead of s_; in fact that is what s_ produces
In [233]: np.delete(x, [3,4,5])
Out[233]: array([ 0, 2, 4, 12, 14, 16, 18])
A list also works, though it works in different way (see below).
In [217]: np.delete(x, x[3:6])
Out[217]: array([ 0, 2, 4, 6, 8, 10, 14, 18])
This works, but produces are different result, because x[3:6] is not the same as range(3,6). Also the np.delete does not work like the list delete. It deletes by index, not by matching value.
np.index_exp fails for the same reason that np.delete(x, (slice(3,6),)) does. 1, [1], (1,) are all valid and remove one item. Even '1', the string, works. delete parses this argument, and at this level, expects something that can be turned into an integer. obj.astype(intp). (slice(None),) is not a slice, it is a 1 item tuple. So it's handled in a different spot in the delete code. This is TypeError produced by something that delete calls, very different from the SyntaxError. In theory delete could extract the slice from the tuple and proceed as in the s_ case, but the developers did not choose to consider this variation.
A quick study of the code shows that np.delete uses 2 distinct copying methods - by slice and by boolean mask. If the obj is a slice, as in our example, it does (for 1d array):
out = np.empty(7)
out[0:3] = x[0:3]
out[3:7] = x[6:10]
But with [3,4,5] (instead of the slice) it does:
keep = np.ones((10,), dtype=bool)
keep[[3,4,5]] = False
return x[keep]
Same result, but with a different construction method. x[np.array([1,1,1,0,0,0,1,1,1,1],bool)] does the same thing.
In fact boolean indexing or masking like this is more common than np.delete, and generally just as powerful.
From the lib/index_tricks.py source file:
index_exp = IndexExpression(maketuple=True)
s_ = IndexExpression(maketuple=False)
They are slighly different versions of the same thing. And both are just convenience functions.
In [196]: np.s_[1:4]
Out[196]: slice(1, 4, None)
In [197]: np.index_exp[1:4]
Out[197]: (slice(1, 4, None),)
In [198]: np.s_[1:4, 5:10]
Out[198]: (slice(1, 4, None), slice(5, 10, None))
In [199]: np.index_exp[1:4, 5:10]
Out[199]: (slice(1, 4, None), slice(5, 10, None))
The maketuple business applies only when there is a single item, a slice or index.
