Partitions() is buggy

[ferriszorro]

There are various bugs in Partitions/Compositions, especially when many constraints are combined:

sage: C = Partitions(10, min_part=2, max_slope=-1)
sage: [5,3,2] in C
True
sage: C.list()
[[10], [8, 2], [7, 3], [6, 4]]

sage: C = Compositions(5, max_part=2, min_slope=1, inner=[2])
sage: [2,1,2] in C
False
sage: C.list()
[[2, 1, 2]]

When slopes are equal, things often go wrong:

sage: C = Compositions(4, min_slope=0, max_slope=0)
sage: [1,1,1,1] in C
True
sage: C.list()
[[4], [2, 2]]

sage: C = Partitions(6, min_slope=-1, max_slope=-1)
sage: [3,2,1] in C
True
sage: C.list()
[[6]]

Contradictory length bounds still give results:

sage: C = Compositions(6, min_length=3, max_length=2)
sage: [4,1,1] in C
False
sage: C.list()[0]
[4, 1, 1]

sage: C = Compositions(3, max_length=2, inner=[1,1,1])
sage: [1,1,1] in C
False
sage: C.list()
[[1, 1, 1]]

sage: C = Compositions(10, outer=[4], inner=[1,1])
sage: [4,6] in C
False
sage: C.list()
[[4, 6], [3, 7], [2, 8], [1, 9]]

max_part is not respected:

sage: C = Compositions(4, max_part=2, min_slope=1)
sage: [1,3] in C
False
sage: C.list()
[[1, 3]]

This is horribly wrong:

sage: Compositions(7, max_part=4, inner=[1], min_slope=1).list()
[[3, 5], [1, 3, 4]]

The following command hangs:

sage: Compositions(4, inner=[2], outer=[2,2], min_slope=0).list()
...

Strange exception which really shouldn't be an exception:

sage: Compositions(10, inner=[1,1], max_slope=-1)
...
ValueError: floor does not satisfy the max slope condition

One possible fix is given by #17920.

[ferriszorro]

Partitions error

[ferriszorro]

#!diff # HG changeset patch # Date 1300721936 0 foo diff --git a/bar b/bar --- a/bar +++ b/bar @@ -1,2 +1,3 @@ baz quux +xyzzy

[ncohen]

Frédéric: the wontfix tickets should be set to 'positive review', otherwise Volker will not see them.

"Merry Christmas",

Nathann

[ncohen]

This being said this bug report is a real bug report O_o

[tmonteil]

I was very puzzled when i saw this ticket, since my Turing tests were not able to conclude (unless we just reached the singularity). I propose to reopen the ticket since the report is correct.

By the way, i am not sure the following is a correct behaviour:

sage: P = Partitions(5, min_slope=2)
sage: Q = Partitions(5)
sage: Q[0] 
[5]
sage: Q[0] in P
False

[tscrim]

This is actually bad input: the slopes should be negative (to be useful for partitions). From the documentation of Partitions:

- ``min_slope=k`` specifies that the partitions have slope at least
  `k`; the slope is the difference between successive parts.

The second input is actually correct, that is the only partition of 5 with a positive slope (provided you don't count trailing 0's, which is how Sage currently behaves). With that being said, the internal assumptions of IntegerListsLex are also being broken with min_slope > max_slope == 0, so it's no surprise bad data is being returned. So this should be a wontfix.

[ncohen]

Does this also qualify as bad input ?

sage: list(Partitions(5,length=4,min_slope=0))
...
ValueError: [1, 1, 1, 2] is not a valid partition

Nathann

[tscrim]

Currently yes. From the doc of IntegerListsLex (which is the underlying class):

   Note: Caveat: with the current implementation, the constraints
     should satisfy the following conditions:

     * The upper and lower bounds themselves should satisfy the
       slope constraints.

     * The maximal and minimal slopes values should not be equal.

     * The maximal and minimal part values should not be equal.

[ncohen]

Currently yes. From the doc of IntegerListsLex (which is the underlying class):

Cool. So the strategy is to close as wontfix the attempts to change that because, after all, it is not a bug ?

Nathann

[tscrim]

The other option would be to recycle this ticket to use for rewriting IntegerListsLex, but in terms of historical documentation, I think this would best done on a new ticket.

[ferriszorro]

OK, this ticket should be closed

[vdelecroix]

Replying to tscrim:

This is actually bad input: the slopes should be negative (to be useful for partitions). From the documentation of Partitions:

- ``min_slope=k`` specifies that the partitions have slope at least
  `k`; the slope is the difference between successive parts.

This is confusing: the difference between a and b is a-b and not b-a. But hopefully, it is clear in the doctest.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​87fb103	17507: change error msg, add doctest
​cd71e2b	Merge branch 'u/rws/minor_error_with_integral_n__' of trac.sagemath.org:sage into tmp
​2edddbb	trac #17548: Partitions() involving min_slope argument is buggy

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​0919653

trac #17548: Partitions() involving min_slope argument is buggy

[ncohen]

Aahahahahah.

Okay, I spent the last 2h30 hours writing all the equations needed to ensure that there is a solution, and with all possibilities that there are I give up.

I will add a stopgap for this feature as it returns wrong results.

Nathann

[ncohen]

Stopgap created at #17637.

Nathann

[tscrim]

It's not a wrong result, it's invalid input because it violates the assumptions.

[ncohen]

(the branch does not actually contain useful code. Switching this to needs_work)

It's not a wrong result, it's invalid input because it violates the assumptions.

I was not able to write a patch that checks all assumptions and returns an exception in this case. If these assumptions are so complicated to check we cannot ask the users to check them for themselves before calling the function. Some of them are probably calling this function on bad input, and they are taking a big risk.

Nathann

[ncohen]

(there is nothing to review here)

[vdelecroix]

Hello,

Two bug-feature report.

1. Depending on the input, the floor is sometimes 0 and sometimes 1:

   sage: IntegerListsLex(5, length=3).list()               # ok: it is 0
   [[5, 0, 0],
    [4, 1, 0],
    [4, 0, 1],
   ...
    [0, 2, 3],
    [0, 1, 4],
    [0, 0, 5]]
   sage: IntegerListsLex(5, length=3, max_slope=0).list()   # ok: it is 0
   [[5, 0, 0], [4, 1, 0], [3, 2, 0], [3, 1, 1], [2, 2, 1]]
   sage: IntegerListsLex(5, max_slope=0).list()             # now it is 1
   [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]]
   

2. The iterator is sometimes completely wrong when the set is infinite:

   sage: it = iter(IntegerListsLex(5))
   sage: for _ in range(10): print it.next()
   [5]
   [4, 1]
   [4, 0, 1]
   [4, 0, 0, 1]
   [4, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 0, 1]
   

[ncohen]

This function should be replaced by smaller, more dedicated functions. Making it all fit in something so general makes it very hard to manage.

And wrong, too.

Nathann

[tscrim]

Replying to vdelecroix:

1. Depending on the input, the floor is sometimes 0 and sometimes 1:

   sage: IntegerListsLex(5, length=3).list()               # ok: it is 0
   [[5, 0, 0],
    [4, 1, 0],
    [4, 0, 1],
   ...
    [0, 2, 3],
    [0, 1, 4],
    [0, 0, 5]]
   sage: IntegerListsLex(5, length=3, max_slope=0).list()   # ok: it is 0
   [[5, 0, 0], [4, 1, 0], [3, 2, 0], [3, 1, 1], [2, 2, 1]]
   sage: IntegerListsLex(5, max_slope=0).list()             # now it is 1
   [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]]
   

This is not a bug because this has trailing 0's and there is no way to have a non-trailing 0 in the last output. See this part of the documentation:

Two valid integer lists are considered equivalent if they only
differ by trailing zeroes. In this case, only the list with the
least number of trailing zeroes will be produced.

It's subtle, but again, not a bug.

2. The iterator is sometimes completely wrong when the set is infinite:

   sage: it = iter(IntegerListsLex(5))
   sage: for _ in range(10): print it.next()
   [5]
   [4, 1]
   [4, 0, 1]
   [4, 0, 0, 1]
   [4, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 0, 1]
   

This is also not a bug because there are no other conditions on the lists and each of these are the next in lex ordering.

[jdemeyer]

Replying to tscrim:

2. The iterator is sometimes completely wrong when the set is infinite:

   sage: it = iter(IntegerListsLex(5))
   sage: for _ in range(10): print it.next()
   [5]
   [4, 1]
   [4, 0, 1]
   [4, 0, 0, 1]
   [4, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 1]
   [4, 0, 0, 0, 0, 0, 0, 0, 0, 1]
   

This is also not a bug because there are no other conditions on the lists and each of these are the next in lex ordering.

This is a bug! An iterator (finite or infinite) must eventually return every element of the set.

[tscrim]

Replying to jdemeyer:

This is also not a bug because there are no other conditions on the lists and each of these are the next in lex ordering.

This is a bug! An iterator (finite or infinite) must eventually return every element of the set.

It does, but it is doing it by lex ordering, which is different than by length-then-lex ordering. Its the same as doing a Cartesian product of {1,2} x NN and getting [1, 0], [1, 1], [1, 2], ... Is that a bug to you then too?

[jakobkroeker]

Is that a bug to you then too?

formally not, but the design is unfortunate. I suggest to change the behaviour.

Jakob

[jdemeyer]

Replying to tscrim:

It does, but it is doing it by lex ordering, which is different than by length-then-lex ordering.

OK, listing all elements in lex ordering might not be possible. Fine, then raise an exception instead of returning a wrong answer.

Its the same as doing a Cartesian product of {1,2} x NN and getting [1, 0], [1, 1], [1, 2], ... Is that a bug to you then too?

Of course that's a bug.

[was]

Replying to jdemeyer:

Replying to tscrim:

It does, but it is doing it by lex ordering, which is different than by length-then-lex ordering.

OK, listing all elements in lex ordering might not be possible. Fine, then raise an exception instead of returning a wrong answer.

Its the same as doing a Cartesian product of {1,2} x NN and getting [1, 0], [1, 1], [1, 2], ... Is that a bug to you then too?

Of course that's a bug.

+1 -- It is a reasonable basic principle that when iterating over a set S, for every x in S the iterator must eventually return x, as (Jereon said above). If this is impossible due to constraints on the order of iteration, there should be an error...

[tscrim]

The branch I've attached fixes the length bounds and when min_slope == max_slope. However these violate the internal assumptions:

sage: C = Compositions(4, max_part=2, min_slope=1)
sage: Compositions(7, max_part=4, inner=[1], min_slope=1)

since the ceiling defaults to max_part, which is always 2/4 and has a slope of 0 and violates the min_slope condition (i.e., the ceiling must be increasing).

Also FTR, the last one in the description is the error message that was wanted (precisely because it violates the conditions).

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​44d1cfb

Fixes for min_slope == max_slope and length conditions.

[jdemeyer]

Replying to tscrim:

the last one in the description is the error message that was wanted (precisely because it violates the conditions).

My point with the last one is that it should simply be allowed input. There is no fundamental reason why

sage: Compositions(10, inner=[1,1], max_slope=-1)

shouldn't "just work".

[jdemeyer]

Replying to tscrim:

These violate the internal assumptions

Then you really should add checks in the code raising an exception if the condition is not satisfied. If you do add such checks, make sure to add them to IntegerListsLex and not the Partitions/Compositions front-ends.

But even better would be to just allow such input.

[aschilling]

Replying to jdemeyer:

Replying to tscrim:

These violate the internal assumptions

Then you really should add checks in the code raising an exception if the condition is not satisfied. If you do add such checks, make sure to add them to IntegerListsLex and not the Partitions/Compositions front-ends.

But even better would be to just allow such input.

In principle, all these bugs should now be fixed with #17979. Please check!