More partition parents and fixes to global options

[Travis Scrimshaw]

Currently the following breaks:

sage: P = Partitions(5, max_length=4)
sage: loads(dumps(P))

since PartitionOptions does not pickle, hence the IntegerListsLex, which takes it as an (optional) input, does not.

The proposed solution is two-fold:

• Add a class for partitions that inherit from IntegerListsLex (or use it as an iterator).
• Add a warning when using the global_options parameter that the resulting class might not pickle.

Here's also a discussion on sage-combinat-devel:

​https://groups.google.com/forum/?fromgroups=#!topic/sage-combinat-devel/Hyak8ndRi4o

I'm also going to add parent classes for k-regular partitions.

[Travis Scrimshaw]

Here's the initial branch, still a little more work to be done.

[git]

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

​7982d3a

Iniital fix and added regular partitions.

[git]

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

​7982d3a

Iniital fix and added regular partitions.

[git]

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

​1adb368	Added deprecation to IntegerListLex global_options arg. Fixed doctests.
​4143c96	Merge branch 'develop' into public/combinat/partitions_constraints-15525

[Travis Scrimshaw]

Okay, ready for consumption.

[git]

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

​c477d6c

Merge branch 'public/combinat/partitions_constraints-15525' of trac.sagemath.org:sage into public/combinat/partitions_constraints-15525

[git]

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

​03dcda9

Merge branch 'public/combinat/partitions_constraints-15525' of trac.sagemath.org:sage into public/combinat/partitions_constraints-15525

[Frédéric Chapoton]

one failing doctest, see patchbot report

[git]

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

​82f4fd5	Merge branch 'public/combinat/partitions_constraints-15525' of trac.sagemath.org:sage into public/combinat/partitions_constraints-15525
​0cc28a0	Fixing some things.

[Kevin Dilks]

So far only noticing very minor issues.

• In the definition of being \ell-regular, it should mention that m_i is the multiplicity of i in the partition. The first time I looked at this, I thought that m_i was maybe referring to the part sizes. In the source code you can just search for 'm_i' to see what it means, but in the HTML doc 'm_i' is always going to be Tex'd and harder to search for. Also, character_polynomial() doc used a_i to refer to the multiplicity of i in a permutation alpha, so maybe that should be changed to m_i to be consistent.
• Does the code ever check that \ell is an integer, and preferably a nonnegative one?

[git]

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

​1ec481d

Addressing Kevin's comments.