Add monomial basis to FQSym

[tscrim]

The monomial basis of Aguiar and Sottile (see 1.3 in ​http://www.math.tamu.edu/~sottile/research/pdf/SSym.pdf ; the formula (1.13) is most important, and triangularity should do the rest, if we make sure that the order is right).

Depends on #25131
Depends on #25141

CC: @sagetrac-sage-combinat @darijgr @alauve @zabrocki @saliola @amypang

Component: combinatorics

Keywords: IMA coding sprint, CHAs, permutations

Author: Darij Grinberg

Branch: 8dc0c5c

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/25136

[darijgr]

Branch: public/combinat/fqsym2

[darijgr]

Commit: e79d2d3

[darijgr]

Author: Darij Grinberg

[darijgr]

New commits:

acf384b	G-basis and bugfixes
e79d2d3	Merge branch 'public/combinat/fqsym' of trac.sagemath.org:sage into fq2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

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
58d17ad	Merge branch 'public/combinat/wqsym_morphisms-25141' of trac.sagemath.org:sage into fq2
7dd85ff	implement the M basis of FQSym
faad461	fix documentation
2acec00	Merge branch 'WQS' into fq2

[sagetrac-git]

Changed commit from e79d2d3 to 2acec00

[sagetrac-git]

Changed commit from 2acec00 to 78a4253

[sagetrac-git]

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

78a4253

overload coproduct on M-basis for speed

[darijgr]

Changed dependencies from #25131 to #25131, #25141

[darijgr]

comment:4

There it is. (I'm Darij, logging in through github.)

[sagetrac-git]

Changed commit from 78a4253 to ef1f3b7

[sagetrac-git]

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

ef1f3b7

link FQSym doc

[darijgr]

comment:6

PS. Since the branch has become rather tortuous, here are all the commits that need reviewing:

sagemath/sagetrac-mirror@7dd85ff

sagemath/sagetrac-mirror@faad461

sagemath/sagetrac-mirror@78a4253

sagemath/sagetrac-mirror@ef1f3b7

[sagetrac-git]

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

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
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.
eb52ae3	Merge branch 'public/combinat/implement_wqsym-25133' of trac.sagemath.org:sage into homs
2d6d158	Merge branch 'public/combinat/wqsym_morphisms-25141' of trac.sagemath.org:sage into homs
70ccf5f	changes necessitated by renaming in #25133
98fca9c	Merge branch 'public/combinat/fqsym2' of trac.sagemath.org:sage into homs

[sagetrac-git]

Changed commit from ef1f3b7 to 98fca9c

[sagetrac-git]

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

416a8c0

more corrections due to recent merge

[sagetrac-git]

Changed commit from 98fca9c to 416a8c0

[sagetrac-git]

Changed commit from 416a8c0 to 6e40666

[sagetrac-git]

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

2dfbcac	Fixing issue with capitalization.
4f2ddfe	Merge branch 'public/combinat/fqsym2' of git://trac.sagemath.org/sage into public/combinat/fqsym2
beeea6a	Abstracting methods to DRY.
6e40666	Calling the M basis the monomial basis.

[darijgr]

Reviewer: Travis Scrimshaw

[sagetrac-git]

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

c8c6906	Merge branch 'public/combinat/wqsym_morphisms-25141' of git://trac.sagemath.org/sage into public/combinat/wqsym_morphisms-25141
9d90234	Initial additional of global options to WQSym
fd61441	Added two global options for display of elements of WordQuasiSymmetricFunctions.
c828b0e	Some reviewer changes.
ba70317	A few more reviewer changes.
6e50492	updated doc string for intended usage vis.a.vis packed words
27b9a98	doctest and Travis' check
0efedd0	Merge branch 'public/combinat/wqsym_options-25155' of git://trac.sagemath.org/sage into public/combinat/wqsym_morphisms-25141
728ff81	Merge branch 'public/combinat/wqsym_morphisms-25141' of git://trac.sagemath.org/sage into public/combinat/wqsym_morphisms-25141
8dc0c5c	Merge branch 'public/combinat/fqsym2' of git://trac.sagemath.org/sage into 25136

[sagetrac-git]

Changed commit from 6e40666 to 8dc0c5c

[darijgr]

comment:12

Trivial rebase over one of the dependencies.

[darijgr]

comment:13

wake up patchbots

[darijgr]

comment:14

File "src/sage/combinat/ncsym/bases.py", line 640, in sage.combinat.ncsym.bases.NCSymBases.ElementMethods.to_wqsym
Failed example:
    (4*p[[1,3],[2]]-p[[1]]).to_wqsym()
Expected:
    4*M[{1, 2, 3}] + 4*M[{2}, {1, 3}] + 4*M[{1, 3}, {2}] - M[{1}]
Got:
    4*M[{2}, {1, 3}] - M[{1}] + 4*M[{1, 2, 3}] + 4*M[{1, 3}, {2}]

Can't reproduce this one. But it's from a few versions ago, so maybe it's fixed now.

[darijgr]

comment:15

The last patchbot is happy now, so I think this is ready to go.

[vbraun]

Changed branch from public/combinat/fqsym2 to 8dc0c5c

[fchapoton]

Changed commit from 8dc0c5c to none

[fchapoton]

comment:17

FQSYM doctests now take way too long..

[darijgr]

comment:18

Are they still taking too long if you pull #25326 as well? One of the things I did in #25326 was optimizing FQSym, particularly the M basis.

(NB: I don't know how long doctests should take on Cygwin, so I have no way to tell if I'm doing things right.)