bool, relational: added as_set method

[hargup]

as_set is the inverse method for existing as_relational
method for sets. as_set converts a univariate boolean or
relational expression to real set.

Example:

In [1]: from sympy import And, Or

In [2]: from sympy.abc import x

In [3]: And(x<2, x>-2).as_set()
Out[3]: (-2, 2)

In [4]: (x**2 > 4).as_set()
Out[4]: (-oo, -2) U (2, oo)

[mrocklin]

Cool!

What is the behavior of the following?

And(x > 0, y > 1).as_set()

Note that Set.as_relational doesn't handle this either. I just want to make sure that we raise a suitable error or that the answer is not ambiguous.

[smichr]

insert

Examples
========

(even for a single test spell it with an S)

[asmeurer]

Should this be implemented using a _as_set to dispatch. @mrocklin what's the advantage of doing it that way rather than just using as_set directly?

[hargup]

What is the behavior of the following?

And(x > 0, y > 1).as_set()

At the time you commented it was giving the wrong result as (0, oo). Now I have modified the code to raise a suitable error. I have also added a XFAIL to test to remind us of future work.

[skirpichev]

At the time you commented it was giving the wrong result as (0, oo)

No. But, perhaps, it does matter in which order I have run the above statements.

Now I have modified the code to raise a suitable error.

Which one? I don't see any difference:

In [1]: And(x>0, y>1).as_set()
Out[1]: (1, ∞)

In [2]: Or(x>0, y>1).as_set()
Out[2]: (0, ∞)

[hargup]

At the time you commented it was giving the wrong result as (0, oo)

No. But, perhaps, it does matter in which order I have run the above statements.

Sorry but I couldn't understand your comment. What I meant was that the code was buggy the time Matthew asked for the result of And(x>0, y>1).as_set(). Then I amended the commit to fix it.

The code on my system is raising the correct error (with an unintentional typo). I don't know why we are getting different results. See the lines of code which raises error here: https://github.com/sympy/sympy/pull/2781/files#diff-cf47a176c69dd7d5e3225858891e091cR288

from sympy import *

from sympy.abc import x, y

And(x>0, y>1).as_set()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-3-c4a8716c2ceb> in <module>()
----> 1 And(x>0, y>1).as_set()

/home/hargup/arbit_sympy_testing/sympy/logic/boolalg.pyc in as_set(self)
    286             return Intersection(*[arg.as_set() for arg in self.args])
    287         else:
--> 288             raise NotImplementedError("Sorry, And.as_set has not yet been"
    289                                       " implemented for mutivariate"
    290                                       " expressions")

NotImplementedError: Sorry, And.as_set has not yet been implemented for mutivariate expressions

Or(x>0, y>1).as_set()
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
<ipython-input-4-9d432be651cb> in <module>()
----> 1 Or(x>0, y>1).as_set()

/home/hargup/arbit_sympy_testing/sympy/logic/boolalg.pyc in as_set(self)
    348             return Union(*[arg.as_set() for arg in self.args])
    349         else:
--> 350             raise NotImplementedError("Sorry, Or.as_set has not yet been"
    351                                       " implemented for mutivariate"
    352                                       " expressions")

NotImplementedError: Sorry, Or.as_set has not yet been implemented for mutivariate expressions

[skirpichev]

On Fri, Jan 17, 2014 at 05:00:39AM -0800, Harsh Gupta wrote:

The code on my system is raising the correct error (with an unintentional
typo). I don't know why we are getting different results.

Sorry. That was my bad, perhaps, I've not run git fetch.

[mrocklin]

Should this be implemented using a _as_set to dispatch. @mrocklin what's the advantage of doing it that way rather than just using as_set directly?

I mostly followed tradition. The benefits I've seen though are shared docstrings and the ability to enforce code at the superclass level (see Set.contains)

[hargup]

There was a typo in 'multivariate', I have fixed it.

[hargup]

Travis is being timed out. Is there anything that I do about it?

[smichr]

Thanks. This is in.