subsets and subwords bug fix + improvements.

[hivert]

This patches improves subwords and subsets and deals with several issues:

1. It implements subsets for finite multisets (sets with repetitions).

sage: Subsets([2,2,3], multiset=True).list() 
[[], [2], [3], [2, 2], [2, 3], [2, 2, 3]] 

1. It implement __contains__ which was missing for subsets and subwords:
   Before:

sage: st = Subsets([1,2,2,3]); Set([1,2]) in st 
--------------------------------------------------------------------------- 
NotImplementedError                       Traceback (most recent call last) 

 After: 

sage: st = Subsets([1,2,2,3]); Set([1,2]) in st 
True 

1. It fixes a bug in smallest_positions:
   Before:

sage: sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3]) 
[4, 4, 4] 

 After: 

sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3]) 
False 

 which means that 113 is not a subword of 243312.  

4. It finally improves the doc and the tests.

Cheers,

Florent

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: subsets, subwords

Issue created by migration from https://trac.sagemath.org/ticket/5200

[hivert]

comment:2

It has been decided (direct talk with Nicolas + irssi with Mike) that the user has to explicitely set that he want multisets. Therefore, on the contrary that is anounced, the following is not working:

sage: Subsets([2,2,3]).list()
[[], [2], [3], [2, 2], [2, 3], [2, 2, 3]]

Instead one should write

sage: Subsets([2,2,3], multiset=True).list()
[[], [2], [3], [2, 2], [2, 3], [2, 2, 3]]

[hivert]

Description changed:

--- 
+++ 
@@ -1,45 +1 @@
-This patches deals with several issues concerning subwords and subsets:
-1. It implements subsets for finite multisets (sets with repetitions).
-   Before the patch:
-
-```
-sage: Subsets([2,2,3]).list()
-[{}, {2}, {3}, {2, 3}]
-```
-     After:
-
-```
-sage: Subsets([2,2,3]).list()
-[[], [2], [3], [2, 2], [2, 3], [2, 2, 3]]
-```
-1. It implement `__contains__` which was missing for subsets and subwords:
-   Before:
-
-```
-sage: st = Subsets([1,2,2,3]); Set([1,2]) in st
----------------------------------------------------------------------------
-NotImplementedError                       Traceback (most recent call last)
-```
-     After:
-
-```
-sage: st = Subsets([1,2,2,3]); Set([1,2]) in st
-True
-```
-1. It fixes a bug in smallest_positions:
-   Before:
-
-```
-sage: sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3])
-[4, 4, 4]
-```
-     After:
-
-```
-sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3])
-False
-```
-     which means that 113 is not a subword of 243312. 
-4. It finally improves the doc and the tests.
-
-Since this is my first trac submission, any comment about this text or the patch is strongly welcome... 
+I've uploaded a new patch according to remark of Nicolas and Mike. It should be ready for review and hopefully integration. 

[hivert]

Description changed:

--- 
+++ 
@@ -1 +1,41 @@
-I've uploaded a new patch according to remark of Nicolas and Mike. It should be ready for review and hopefully integration. 
+This patches improves subwords and subsets and deals with several issues: 
+1. It implements subsets for finite multisets (sets with repetitions). 
+
+``` 
+sage: Subsets([2,2,3], multiset=True).list() 
+[[], [2], [3], [2, 2], [2, 3], [2, 2, 3]] 
+``` 
+1. It implement `__contains__` which was missing for subsets and subwords: 
+   Before: 
+
+``` 
+sage: st = Subsets([1,2,2,3]); Set([1,2]) in st 
+--------------------------------------------------------------------------- 
+NotImplementedError                       Traceback (most recent call last) 
+``` 
+     After: 
+
+``` 
+sage: st = Subsets([1,2,2,3]); Set([1,2]) in st 
+True 
+``` 
+1. It fixes a bug in smallest_positions: 
+   Before: 
+
+``` 
+sage: sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3]) 
+[4, 4, 4] 
+``` 
+     After: 
+
+``` 
+sage.combinat.subword.smallest_positions([2,4,3,3,1,2],[1,3,3]) 
+False 
+``` 
+     which means that 113 is not a subword of 243312.  
+4. It finally improves the doc and the tests. 
+
+Cheers,
+
+Florent
+