Created a Set Difference class #7462

hargup · 2014-05-03T12:19:22Z

Todo list:

fix is that self.complement(other) behaves as other - self and self._complement(other) behaves as self - other.
Complement printers
Rebase

hargup · 2014-05-03T12:20:42Z

debugger22 · 2014-05-03T12:22:25Z

sympy/core/sets.py

+
+        >>> from sympy import Difference, FiniteSet
+
+        >>> Difference(FiniteSet(0, 1, 2), FiniteSet(1))


Probably a blank line here will create two different blocks in the docs.

Thanks you are right.

asmeurer · 2014-05-03T18:02:31Z

-A should probably return Difference(UniversalSet, A).

asmeurer · 2014-05-03T18:03:17Z

sympy/core/sets.py

+    is_Difference = True
+    # See if we will be representing sets in terms of differences,
+    # I guess we can always
+    # represent a set difference with Union, if yes do we know how?


This comment doesn't make any sense to me.

asmeurer · 2014-05-03T18:04:08Z

By the way, go easy on the [WIP] tags. This code could probably go in as is. It's better to merge pull requests early and just open new ones for new feature than to block a pull request on a lot of features before it gets merged.

hargup · 2014-05-07T05:01:13Z

-A should probably return Difference(UniversalSet, A).

This is the current behavior after the recent commits.

@asmeurer @mrocklin @skirpichev @debugger22 Please review.

skirpichev · 2014-05-07T08:20:38Z

On Tue, May 06, 2014 at 10:01:16PM -0700, Harsh Gupta wrote:

 -A should probably return Difference(UniversalSet, A).

I don't sure it's mathematically correct.

asmeurer · 2014-05-07T18:33:30Z

I don't sure it's mathematically correct.

How so?

asmeurer · 2014-05-07T18:34:28Z

See https://en.wikipedia.org/wiki/Set_complement#Absolute_complement. Insomuch as a universal set can be defined (and we have one defined, so I guess for us it can be), the absolute complement of a set is U - A.

mrocklin · 2014-05-07T18:41:05Z

Seems reasonable so far. It would be nice to accompany this work with a motivating use case.

asmeurer · 2014-05-07T18:52:42Z

There are tons of sets you can't represent without this. But probably the simplest example to show would be de'Morgan's laws.

skirpichev · 2014-05-08T08:21:08Z

See https://en.wikipedia.org/wiki/Set_complement#Absolute_complement.
Insomuch as a universal set can be defined (and we have one defined, so I
guess for us it can be), the absolute complement of a set is U - A.

I don't sure we really know what our ("defined") UniversalSet is. The reference
in the docstring doesn't define UniversalSet at all (but clearly shows
that this notion is paradoxal in the usual set theory).

asmeurer · 2014-05-08T19:20:39Z

I think the problems with UniversalSet are similar to the problems you get with having oo. Algebraically it makes sense most of the time, although you may have to leave some operations undefined to avoid inconsistency (in this case, probably PowerSet(UniversalSet) shouldn't work). It's also similar in the sense that oo is not a real number, but if you extend the set of real numbers somehow, then it is. SImilarly, UniversalSet is not a set, but if you allow collections that aren't sets, then it can be one of those (and set operations against those collections and sets sometimes, but not always, make sense).

hargup · 2014-05-09T09:42:40Z

@asmeurer I can't figure out the reason for the travis failure. The only error is with python 3.4 build.

debugger22 · 2014-05-09T09:45:11Z

See #7456

hargup · 2014-05-09T20:14:19Z

@asmeurer @mrocklin @skirpichev Do you think this PR is good to merge as it is.

+1 to @asmeurer 's comment. If we disagree on what UniversalSet should be we can sort it out in issue or on mailing list. Anyway there are issue with UniversalSet, we are implicitly assuming it to be Reals. S.Reals.complement returns EmptySet().

asmeurer · 2014-05-09T20:23:31Z

I would change that so that UniversalSet is the universal set.

hargup · 2014-05-09T20:37:33Z

I would change that so that UniversalSet is the universal set.

Agreed. But I feel that doing that might get a bit involved, now I'm leveraging the logic coded in _complement of classes like Interval and FiniteSet, that will probably have to be moved to __sub__ procedure. Doing the changes in this PR can unnecessarily delay merging Difference.

BTW what will happen if I create a branch say B out of this branch say A, and send a pull request for B. Then if this branch A gets merged in the master. Will the diff for the pull request of B still show the changes done in A.

skirpichev · 2014-05-10T08:50:45Z

On Fri, May 09, 2014 at 01:14:22PM -0700, Harsh Gupta wrote:

[1]@asmeurer [2]@mrocklin [3]@skirpichev Do you think this PR is good to
merge as it is.

I don't think we should use UniversalSet here, that's why I'm -1.

Should we wipe out the UniversalSet class at all - we can discuss
on the mailing list.

hargup · 2014-05-10T17:44:13Z

I don't think we should use UniversalSet here, that's why I'm -1.

I have use dUniversalSet just to define complement of A as U - A here https://github.com/sympy/sympy/pull/7462/files#diff-1c851859c57f806535bf5a6edfe8386fR140. I can't see how I can not use UniversalSet without not having a UniversalSet.

skirpichev · 2014-05-11T15:32:16Z

I have use dUniversalSet just to define complement of A as U - A

Yes, and I think - that's a bad idea.

asmeurer · 2014-05-12T02:16:48Z

Agreed. But I feel that doing that might get a bit involved

Just raise NotImplementedError for the things that are too much work.

BTW what will happen if I create a branch say B out of this branch say A, and send a pull request for B. Then if this branch A gets merged in the master. Will the diff for the pull request of B still show the changes done in A.

Yes, it should work, as long as you don't rebase.

I don't think we should use UniversalSet here, that's why I'm -1.

Would you rather the Reals be the universal set?

I think we should keep UniversalSet, just like we should keep oo and nan. They don't make mathematical sense with every operation, but they do make sense with some operations, and are useful in those cases.

Why exactly do you want to remove UniversalSet? It probably is better to move this to the mailing list.

skirpichev · 2014-05-12T06:32:09Z

On Sun, May 11, 2014 at 07:16:52PM -0700, Aaron Meurer wrote:

Would you rather the Reals be the universal set?

I think we should keep UniversalSet, just like we should keep oo and nan.

For oo and nan we can precisely restrict their usage to operations,
that make sense.

They don't make mathematical sense with every operation, but they do make
sense with some operations, and are useful in those cases.

Why exactly do you want to remove UniversalSet? It probably is better to
move this to the mailing list.

I don't sure it's a case for UniversalSet (if do, lets
document this). This is why oo argument doesn't work for me.

Practically, I think that most of time - we want some well defined
(universe) set instead if UniversalSet, e.g. Reals or Integers (context-dependent).

asmeurer · 2014-05-12T18:58:56Z

I would just think of UniversalSet as a standin for the actual universal set. It often does not matter what that is, as long as all your sets are subsets of that one.

For instance, having a universal set allows you to define an abstract "complement", -A. This is not only easier to keep track of than U - A, but it makes your collection of sets into a Boolean Algebra, under which &, |, and - are all very meaningful and useful operations.

I would keep UniversalSet, but be very conservative with the operations that are allowed with it (e.g., UniversalSet.contains(UniversalSet) should probably raise an error).

Are there any other computer algebra systems that can manipulate sets algebraically?

skirpichev · 2014-06-29T19:10:46Z

sympy/sets/sets.py

@@ -1529,33 +1571,6 @@ def _eval_imageset(self, f):
        return FiniteSet(*map(f, self))

    @property
-    def _complement(self):


The logic here was moved to Reals._complement.

hargup · 2014-06-29T19:32:09Z

As it should be __sub__ is now just a syntactic sugar and contains no logic, and same for .complement method for classes. All the logic of the Complement class is dispatched through the ._complement method in various classes. The only thing left to fix is that self.complement(other) behaves as other - self and self._complement(other) behaves as self - other.

skirpichev · 2014-08-04T11:33:06Z

Any news?

Lets fill some todo list:

fix is that self.complement(other) behaves as other - self and self._complement(other) behaves as self - other. // Probably, you should fix _complement methods (private).
Complement printers

@mrocklin, is there something else?

hargup · 2014-08-05T20:24:05Z

@skirpichev I have fixed both issues.

skirpichev · 2014-08-06T08:54:23Z

We have a doctest failure.

skirpichev · 2014-08-06T09:53:27Z

And I don't think we should use the difference syntax for printing of the set complement. It seems, there are a more standard and consistent notation:
http://en.wikipedia.org/wiki/Complement_%28set_theory%29

hargup · 2014-08-08T22:50:54Z

The tests timed out.

skirpichev · 2014-08-09T07:57:50Z

sympy/sets/tests/test_sets.py

-        Interval(0, 1),
-        ((Interval(neginf, 0, True, True) + Interval(1, inf, True, True))
-         * (Interval(neginf, 0, True, True) + Interval(1, inf, True, True))))
+    # It is trouble to do this test as the result can many


We should fix this problem. Would complement(Interval(-oo,oo)*Interval(-oo,oo)) work?

skirpichev · 2014-08-09T08:02:35Z

@mrocklin, could you take look. I'm going to merge this pr.

@hargup, we should fix mentioned above two tests.

skirpichev · 2014-08-09T08:17:42Z

sympy/sets/sets.py

@@ -1444,6 +1512,56 @@ def _boundary(self):
        return EmptySet()


+class UniversalSet(with_metaclass(Singleton, Set)):


We have two UniversalSet classes!

hargup · 2014-08-09T17:36:36Z

@skirpichev I merged your PR's and also rebased. The travis build also passed.

skirpichev · 2014-08-09T18:32:08Z

@hargup, I'm +1. Lets wait ack from @mrocklin.

hargup · 2014-08-10T06:06:08Z

@mrocklin can we merge this PR?

smichr · 2014-08-11T22:48:00Z

needs another rebase

Sergey B Kirpichev <skirpichev@gmail.com> helped with some fixes in the PR's #5 and #4 * Remove duplicated UniversalSet class * Reenable some old tests * Fix random test failure Conflicts: sympy/sets/tests/test_sets.py

hargup · 2014-08-13T02:27:28Z

@skirpichev @smichr @mrocklin I have resolved the merge conflicts also the travis build passed.

mrocklin · 2014-08-13T14:28:28Z

Sorry for being absent here. I say go ahead.

Created a Set Difference class

hargup · 2014-08-14T06:35:15Z

Thanks @asmeurer @skirpichev and @mrocklin, the PR is in. I have also updated the release notes https://github.com/sympy/sympy/wiki/Release-Notes-for-0.7.6.

hargup added the Sets label May 3, 2014

hargup self-assigned this May 3, 2014

debugger22 reviewed May 3, 2014
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asmeurer reviewed May 3, 2014
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hargup added the GSoC label May 6, 2014

hargup changed the title ~~[WIP]Created a Set Difference class~~ Created a Set Difference class May 7, 2014

hargup removed the imported label May 9, 2014

hargup added this to the GSoC 2014 Solvers: Create basic set infrastructure. milestone May 10, 2014

skirpichev reviewed Jun 29, 2014
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skirpichev added the Needs Better Patch label Aug 4, 2014

hargup removed the Needs Better Patch label Aug 5, 2014

skirpichev reviewed Aug 9, 2014
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hargup added 2 commits August 12, 2014 18:39

Created a Set Complement class

25a48af

Sergey B Kirpichev <skirpichev@gmail.com> helped with some fixes in the PR's #5 and #4 * Remove duplicated UniversalSet class * Reenable some old tests * Fix random test failure Conflicts: sympy/sets/tests/test_sets.py

Write printers for Complement

324aa9a

hargup added a commit that referenced this pull request Aug 14, 2014

Merge pull request #7462 from hargup/set_difference

6558cf3

Created a Set Difference class

hargup merged commit 6558cf3 into sympy:master Aug 14, 2014

hargup mentioned this pull request Aug 14, 2014

Fix Intersection Complement simplification #7865

Merged

This was referenced Oct 1, 2014

Add a test for issue #2799 #8158

Closed

S.UniversalSet + Interval(0, oo) takes forever. #2799

Closed

hargup mentioned this pull request Feb 3, 2015

added printer for SymmetricDifference #8902

Merged


		>>> from sympy import Difference, FiniteSet

		>>> Difference(FiniteSet(0, 1, 2), FiniteSet(1))

		@@ -1444,6 +1512,56 @@ def _boundary(self):
		return EmptySet()


		class UniversalSet(with_metaclass(Singleton, Set)):

Created a Set Difference class #7462

Created a Set Difference class #7462

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