Binomial coefficients are not expanded by default

[prasoon2211]

Initial fix for issue 3544. Now,

>>> b = binomial(n, 8)

>>> print b
>>> binomial(n, 8)

>>> b.expand(func=True)
>>> n**8/40320 - n**7/1440 + 23*n**6/2880 - 7*n**5/144 + 967*n**4/5760 - 469*n**3/1440 + 363*n**2/1120 - n/8

>>> expand_func(b)
>>> n*(n - 7)*(n - 6)*(n - 5)*(n - 4)*(n - 3)*(n - 2)*(n - 1)/40320

Let me know if more changes are required.
I expect many tests to fail because of this change. I'll update them later.

[prasoon2211]

It seems I'll have to do a lot of changes throughout the code so that binomial(n, r) is replaced with expand_func(binomial(n, r)). Same thing I'll have to do in the tests.

[asmeurer]

binomial(-1, 1) should still auto-evaluate.

[asmeurer]

And it looks like many of the other failures are similar. For example, binomial(S(1)/2, 1) should still auto-evaluate too.

[prasoon2211]

Yes. You're right. I was checking for binomial(1/2, 1) but not binomial(S(1)/2, 1). The former does evaluate. In any case, I'll correct the errors.

[asmeurer]

1/2 gives 0 in Python, because of integer division. That's why you have to use S(1)/2, to force it into a SymPy Rational.

[asmeurer]

Also, please add tests.

[prasoon2211]

I'll do that as soon as I can fix this.

[prasoon2211]

I've made some fixes. I believe there shouldn't be any more failed tests. If there aren't, then I'll add some tests of my own. Otherwise, it'll require more fixing.

[prasoon2211]

Fixed few errors in the doctest and added some documentation. Also, added some tests and doctests. I think things should work now.

[prasoon2211]

Good to merge? Or changes required?

[asmeurer]

Tests like this do nothing. What you should do is test that binomial(n, 3) is still an instance of binomial. The best way to do this is assert binomial(n, 3).func == binomial.

[asmeurer]

Just those comments. Also, my bot will eventually test this, though just Travis is fine too.

[asmeurer]

SymPy Bot Summary: 🔴 Failed after merging prasoon2211/binomial-iss3544 (10fb4a5) into master (485b303).
@prasoon2211: Please fix the test failures.
✳️ Python 2.5.0-final-0: pass
✳️ Python 2.6.6-final-0: pass
✳️ Python 2.7.2-final-0: pass
✳️ Python 2.6.8-final-0: pass
✳️ Python 2.7.3-final-0: pass
✳️ PyPy 2.0.0-beta-1; 2.7.3-final-42: pass
✳️ Python 3.2.2-final-0: pass
✳️ Python 3.3.0-final-0: pass
✳️ Python 3.2.3-final-0: pass
✳️ Python 3.3.0-final-0: pass
🔴 Python 3.3.0-final-0: fail
✳️ Sphinx 1.1.3: pass

[prasoon2211]

Tests are failing on 3.3 because one of them took too long.

[prasoon2211]

@asmeurer I think this PR is good to merge. I has been lying around for some time now. Not trying to pester or anything .. just checking.

[asmeurer]

SymPy Bot Summary: 🔴 Failed after merging prasoon2211/binomial-iss3544 (aba9b71) into master (485b303).
@prasoon2211: Please fix the test failures.
✳️ Python 2.5.0-final-0: pass
✳️ Python 2.6.6-final-0: pass
✳️ Python 2.7.2-final-0: pass
✳️ Python 2.6.8-final-0: pass
✳️ Python 2.7.3-final-0: pass
✳️ PyPy 2.0.0-beta-1; 2.7.3-final-42: pass
✳️ Python 3.2.2-final-0: pass
✳️ Python 3.3.0-final-0: pass
✳️ Python 3.2.3-final-0: pass
✳️ Python 3.3.0-final-0: pass
🔴 Python 3.3.0-final-0: fail
✳️ Sphinx 1.1.3: pass

[prasoon2211]

So is it good enough to be merged? Seems that the bot is passing test for Python 3.3.0-final-0 once and failing at an other time.

[asmeurer]

Sorry, I've been busy. Yes, this looks ok to go.

[coveralls]

Changes Unknown when pulling aba9b71 on prasoon2211:binomial-iss3544 into * on sympy:master*.