Speedup commonly used Sage functions?

edit

OK, that makes more sense. But for some purposes, xmrange is faster. Suppose you actually want the output of xmrange as a list. Then if you look at:

def test1(nx):
    return xmrange([nx]*3)

def test2(nx):
    answer = []
    for k1 in xrange(nx):
        for k2 in xrange(nx):
            for k3 in xrange(nx): answer.append([k1,k2,k3])
    return answer

the xmrange solution wins:

timeit('test1(10)')
    625 loops, best of 3: 28.5 µs per loop

timeit('test2(10)')
    625 loops, best of 3: 403 µs per loop

although I'm sure there are more efficient ways to use xrange for this.

Those two functions don't really do the same thing. They both return [0,0,0], so if that's all you want you could do:

def test3():
    return [0,0,0]

The function test1 is probably slower because it has to actually construct an object to iterate over those values, while test2 does not. It might be more fair to compare functions that return all the values.