py3: fix all doctests in schemes/product_projective

[fchapoton]

by adding a missing __len__ method.

plus some light code cleanup.

Component: python3

Author: Frédéric Chapoton

Branch/Commit: 9440e0a

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/27449

[fchapoton]

Branch: u/chapoton/27449

[fchapoton]

Commit: 9440e0a

[fchapoton]

New commits:

9440e0a

py3: fix all doctests in schemes/product_projective/*

[fchapoton]

comment:2

green bot, please review

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:3

It turns out that it is actually faster to do a yield statement in Python2 than give a generator object back for a single list:

sage: def gen(n):
....:     return (x for x in range(n))
sage: def it(n):
....:     for x in range(n):
....:         yield x
sage: %timeit len(list(gen(5)))
1000000 loops, best of 3: 1.15 µs per loop
sage: %timeit len(list(it(5)))
1000000 loops, best of 3: 1.05 µs per loop

sage: %timeit len(list(gen(100)))
100000 loops, best of 3: 5.18 µs per loop
sage: %timeit len(list(it(100)))
100000 loops, best of 3: 4.64 µs per loop

sage: %timeit len(list(gen(10000)))
1000 loops, best of 3: 402 µs per loop
sage: %timeit len(list(it(10000)))
1000 loops, best of 3: 385 µs per loop

For a double, there ends up being not much noticable difference:

sage: def gen(n):
....:     return (x*y for x in range(n) for y in range(n))
sage: def it(n):
....:     for x in range(n):
....:         for y in range(n):
....:             yield x*y
sage: %timeit len(list(gen(5)))
100000 loops, best of 3: 3.56 µs per loop
sage: %timeit len(list(it(5)))
100000 loops, best of 3: 3.41 µs per loop
sage: %timeit len(list(gen(100)))
1000 loops, best of 3: 530 µs per loop
sage: %timeit len(list(it(100)))
1000 loops, best of 3: 534 µs per loop

I am not saying that anything needs to be changed (I actually like the simplicity of returning the generator), just pointing out some timings (this probably does not need to be super optimized anyways).

So LGTM.

[vbraun]

Changed branch from u/chapoton/27449 to 9440e0a