Add __len__ and cardinality to cartesian_product_iterator and CartesianProduct

[roed314]

If cartesian_product_iterator has a __len__ method we can use it in random.sample.

We also fix a bug that yields an infinite loop:

sage: for a in cartesian_product_iterator([ZZ,[]]):
....:     print "hello world"
<INFINITE LOOP>

---

Apply:

1. attachment: 14285.patch
2. attachment: trac_14285_review.patch

CC: @hivert

Component: combinatorics

Author: David Roe

Reviewer: Julian Rueth

Merged: sage-5.9.beta1

Issue created by migration from https://trac.sagemath.org/ticket/14285

[roed314]

Author: David Roe

[saraedum]

comment:4

Minor issue: The description of the patch has no trac ticket number.

[saraedum]

comment:5

I'm happy with it if the patchbot is.

[saraedum]

Reviewer: Julian Rueth

[roed314]

comment:7

I'm also happy with it once the patchbot approves.

[roed314]

comment:8

Updated to fix doctest failures...

[jdemeyer]

comment:10

On 32-bit systems:

sage -t --long devel/sage/sage/misc/mrange.py
**********************************************************************
File "devel/sage/sage/misc/mrange.py", line 62, in sage.misc.mrange._is_finite
Failed example:
    _is_finite(xrange(10^10))
Exception raised:
    Traceback (most recent call last):
      File "/var/lib/buildbot/build/sage/arando-1/arando_full/build/sage-5.9.beta1/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 459, in _run
        self.execute(example, compiled, test.globs)
      File "/var/lib/buildbot/build/sage/arando-1/arando_full/build/sage-5.9.beta1/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 815, in execute
        exec compiled in globs
      File "<doctest sage.misc.mrange._is_finite[4]>", line 1, in <module>
        _is_finite(xrange(Integer(10)**Integer(10)))
    OverflowError: Python int too large to convert to C long
**********************************************************************

[roed314]

Attachment: 14285.patch.gz

[roed314]

Attachment: trac_14285_review.patch.gz

review patch

[roed314]

comment:11

Fixed.

[jdemeyer]

Merged: sage-5.9.beta1