Implement WQSym

[tscrim]

The combinatorial Hopf algebra indexed by ordered set partitions. We implement the monomial basis.

[tscrim]

Darij, you will probably want more documentation (including references). Feel free to add. Otherwise this should be ready.

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New commits:

​7d5f9c0	Moving shuffle products with overlap to combinat/shuffle.py.
​3fab3a3	Extending shuffle products with overlap to more general iterables.
​1548a26	Added set of all ordered set partitions.
​5021445	Initial version of WQSym and new folder for CHAs.

[darij]

"deprecation=987654"???

[git]

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

​a60d29a	Merge branch 'public/combinat/extend_shuffle_product-15597' of trac.sagemath.org:sage into qs
​99c91e7	getting rid of zero
​588f20f	Merge branch 'public/combinat/implement_wqsym-25133' of trac.sagemath.org:sage into wqsym
​349de85	technical fixes to src/sage/combinat/set_partition_ordered.py

[git]

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

​543f3fb	trivial speedup
​aa04534	adapting to changes in the quasi-shuffles ticket

[git]

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

​3c86209

document WQSym (spartanic)

[git]

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

​b80c004	Doing some doc moving.
​6d4a74b	Put a total ordering on elements of OrderedSetPartitions_all.
​89bfa23	Implementing the Characteristic and Cone bases.

[git]

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

​4fe0066

more doctests

[git]

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

​f4ad056

Fixing documentation to Cone basis.

[git]

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

​60662be

review M and X bases of WQSym

[git]

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

​3b67a89

customize hash on OrderedSetPartition (Travis)

[git]

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

​24e9b0f

correct degree_on_basis

[git]

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

​8a36664	documentation fixes
​b4a3af9	implement WQSym -> QSym projection

[darij]

Positive review according to Travis.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​fc6b2ae

fix to_quasisymmetric_function

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. Last 10 new commits:

​361b4df	Merge branch 'public/combinat/fqsym' of trac.sagemath.org:sage into wqsym_real
​5dad9df	implement the inclusion NSym -> FQSym
​474d8f9	Having to_ncsym() and to_fqsym() implemented generically for elements only.
​c833ba6	implement FiniteWord.to_ordered_set_partition()
​5dc2bfe	Merge branch 'public/combinat/wqsym2' of git://trac.sagemath.org/sage into public/combinat/wqsym2
​85634b2	outsource to_ordered_set_partition
​72bcd46	implement the inclusion FQSym -> WQSym
​a5512ed	polish Travis's edits
​7394bf7	Added deprecations to Bases.ParentMethod.to_ncsym(_on_basis).
​235f69b	implement the inclusion NCSym -> WQSym

[git]

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

[darij]

Ignore -- I accidentally pushed to the wrong branch. I push-forced the right one back now.

[amypang]

Thank you Darij and Travis for your hard work!

Some other bases that would be nice to code, if you guys have time - these are the sums of M's over some order on ordered set partitions, so maybe the only work is to code the orders:

• Q basis of Bergeron-Zabrocki (​https://arxiv.org/abs/math/0509265 start of section 6);
• The fundamental and multiplicative bases from Novelli-Thibon (​https://arxiv.org/abs/math/0605061 lines 55-56; section 2.6 and line 47).
• Their dual bases in the dual of WQSym.

Let me know if I can help. (But I'm in an antipodal timezone from you.)

[tscrim]

Please open up follow-up tickets for each of these bases and feel free to work on them today. I/We can work on them tomorrow for us.

[amypang]

I opened #25151 and #25152. Maybe two will do for now? I looked at the current WQSym code and am not confident I can write anything useful... I'll try to make comments in those tickets. I'll be online for another 2 hours.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​3e46798	Initial addition of Franco's FSym code.
​f75e10d	if w1 is a word, return a word, else a list
​3f8f272	added doc test, minor change for test of Composition, correct import
​06fd19d	Merge branch 'public/25018/bug_in_shuffle' of git://trac.sagemath.org/sage into public/combinat/extend_shuffle_product-15597
​72f2de6	Merge branch 'public/combinat/extend_shuffle_product-15597' of git://trac.sagemath.org/sage into public/combinat/implement_wqsym-25133

[git]

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

​4252484	Merge branch 'public/combinat/extend_shuffle_product-15597' of git://trac.sagemath.org/sage into public/combinat/implement_wqsym-25133
​82240b2	Fixing some details and making Symmetric capitalized in the name.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​9d90234	Initial additional of global options to WQSym
​fd61441	Added two global options for display of elements of WordQuasiSymmetricFunctions.

[git]

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

[tscrim]

Was accidentally pushed to the wrong branch.

[git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

​bc276dd

Merge branch 'public/combinat/implement_wqsym-25133' of git://trac.sagemath.org/sage into public/combinat/implement_wqsym-25133

[tscrim]

Trivial conflict in master reference list.