Hopf algebra: FQSym, WQSym, PQSym, PBT

[sagetrac-elixyre]

I begin implementation of some Hopf algebra: FQSym, and WQSym PQSym.
(And some quotients: PBT, Baxter, Stalactic)
I try to follow the NCSF-QSym design.

Depends on #10963
Depends on #15573
Depends on #15578
Depends on #15595
Depends on #15611
Depends on #15597

CC: @hivert @darijgr @kevindilks @zabrocki @amypang @alauve

Component: combinatorics

Keywords: hopf algebra, sagedays65

Author: Jean-Baptiste Priez

Branch/Commit: u/kdilks/ticket/13793 @ 0e1c0f8

Issue created by migration from https://trac.sagemath.org/ticket/13793

[sagetrac-elixyre]

comment:1

I'm student of F. Hivert and N. M. Thiéry at Orsay (Univ Paris-Sud).
Jean-Baptiste Priez

[sagetrac-elixyre]

some modification of categories + fqsym with several basis

[sagetrac-elixyre]

Attachment: cha-EliX-jbp.patch.gz

Attachment: fsym-EliX-jbp.patch.gz

FSym as FQSym quotient + some modification in Coalgebras' cateogory

[sagetrac-elixyre]

default coercion for tensors

[sagetrac-elixyre]

comment:2

Attachment: tensor-coercion-maurice.patch.gz

[sagetrac-elixyre]

Author: Jean-Baptiste Priez

[darijgr]

comment:5

How is this going? Is Malvenuto-Reutenauer already functional? I'm looking for a neat implementation of M-R lately (I have my own but it is very basic and probably too slow).

[sagetrac-elixyre]

tutorial how to use the lib

[sagetrac-elixyre]

Attachment: how_to_use_cha_lib.pdf.gz

an other tutorial

[sagetrac-elixyre]

comment:6

Attachment: cha.pdf.gz

Hello,

I'm sorry, I have to do that post since long time.

Rémi Maurice (Univ. MLV, France) and I have develop a library of combinatorial Hopf algebras. That one contains M-R, Loday-Ronco and some other.

M-R is clean (I think).

The two previous files contains tutorial about how to use the library.

(There is two way to notify to sage where is the lib: one with export and an other with the file "init.sage"... You just have to use one.)

Jean-Baptiste

[darijgr]

comment:7

Cool! And I see you've implemented dendriform algebras... this was on my (farther) plans.

But I can't get the library to run (5.11beta3):

sage: from chasage.all import *
---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
<ipython-input-1-05ba675cf388> in <module>()
----> 1 from chasage.all import *

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/all.py in <module>()
----> 1 from combinat.all import *
      2 
      3 from patches.all import *

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/combinat/all.py in <module>()
----> 1 from cha.all import *
      2 
      3 from packed_words import PackedWords, PackedWord
      4 from set_partition_into_lists import SetPartitionIntoLists, SetPartitionIntoList

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/combinat/cha/all.py in <module>()
----> 1 from fqsym import FreeQuasiSymmetricFunctions
      2 FQSym = FreeQuasiSymmetricFunctions
      3 
      4 from wqsym import WordQuasiSymmetricFunctions
      5 WQSym = WordQuasiSymmetricFunctions

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/combinat/cha/fqsym/__init__.py in <module>()
     76 from sage.categories.category import Category
     77 
---> 78 from chasage.combinat.cha.categories.bidendriform_bialgebras import BidendriformBialgebras
     79 from chasage.combinat.cha.categories.diese_product_category import GradedAlgebrasWithDieseProduct
     80 from chasage.combinat.cha.tools.generic_basis import GenericBasis

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/combinat/cha/categories/bidendriform_bialgebras.py in <module>()
     46 from sage.categories.tensor import tensor
     47 
---> 48 from chasage.combinat.cha.categories.dendriform_algebras import \
     49     DendriformAlgebras
     50 from chasage.combinat.cha.categories.dendriform_coalgebras import \

/home/darij/sage-5.11.beta3/devel/sage-main/cha/chasage/combinat/cha/categories/dendriform_algebras.py in <module>()
     76 from sage.misc.lazy_attribute import lazy_attribute
     77 
---> 78 from sage.categories.category_with_axiom import \
     79     CategoryWithAxiom_over_base_ring
     80 from sage.categories.category_types import Category_over_base_ring

ImportError: No module named category_with_axiom
sage: 

Are you assuming #10963? Or the whole sage-combinat queue?

[sagetrac-elixyre]

comment:8

Sorry I forget that in the beamer... You have to install a stable version of combinat and if the categories don't have change so much then it must be ok.

[tscrim]

comment:9

Just as a note (and to cc myself on this ticket), NCSym and it's dual is at #15150, and we'll want everything to work together at the end of the day.

[tscrim]

comment:10

[Duplicate post]

[sagetrac-elixyre]

Last 10 new commits:

b7f9945	Ticket 13793: FQSym (or the Malvenuto-Reutenauer Hopf algebra) and some categories
8399005	Ticket 15578: append missing import
a9499a0	Ticket 15578: append a missing import
416a081	Default antipode implementation for graded connected Hopf algebras
5ccf253	Merge branch 'u/SimonKing/ticket/10963' of trac.sagemath.org:sage into public/ticket/10963
14e63b6	Merge ticket/15506 into ticket/10963 to fix recursion error
6147777	Trac 15506: Add a test (review commit)
3d978e9	Merge branch 'develop' into public/ticket/10963
0c907cf	Reverted cached_function to weak_cached_function.
588c276	Fixed ncsym/bases.py doctest.

[sagetrac-elixyre]

Branch: u/elixyre/ticket/13793

[sagetrac-elixyre]

Dependencies: #10963, #15573, #15578, #15595

[sagetrac-elixyre]

Commit: b7f9945

[sagetrac-git]

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

18270d2	Merge branch '15595/shuffle' into 13793/cha
9730233	fast Shuffle product compatible with iterable objects (use linear extension)

[sagetrac-git]

Changed commit from b7f9945 to 18270d2

[sagetrac-git]

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

4cb8d3d	Merge branch '15597/quasi_shuffle' into 13793/cha
d466ab9	Merge branch '15611/packed_words' into 13793/cha
0104d00	Ticket 15611: Packed Words
edab189	first version of the quasi-shuffle product

[sagetrac-git]

Changed commit from 18270d2 to 4cb8d3d

[sagetrac-elixyre]

Changed dependencies from #10963, #15573, #15578, #15595 to #10963, #15573, #15578, #15595, #15611, #15597

[sagetrac-git]

Changed commit from 4cb8d3d to b227b12

[sagetrac-git]

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

b227b12	Ticket 13793: WQSym as - a bidendriform bialgebra - with internal product - with diese product
a19f374	Merge branch '15611/packed_words' into 13793/cha
6fc6703	Ticket 15611: fix Shifted concatenation...
10645a8	Merge branch '15611/packed_words' into 13793/cha
c15335e	Ticket 15611: fix empty shifted shuffle of packed words + test on quasi shifted shuffle
0539b79	Merge branch '15611/packed_words' into 13793/cha
3291c96	Merge branch '15597/quasi_shuffle' into 15611/packed_words
aa338f4	Ticket 15597: fix an extrem case: empty list with a special elem_constructor
0e62e54	Merge branch '15611/packed_words' into 13793/cha
8c8cc96	Ticket 15611: fix the shifted quasi shuffle of ordered set partition

[sagetrac-git]

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

9c9bf65

Ticket 13793: fix the category of realizations

[sagetrac-git]

Changed commit from b227b12 to 9c9bf65

[kevindilks]

Changed keywords from hopf algebra to hopf algebra, sagedays65

[kevindilks]

comment:21

I'm going to work on trying to get more of the features developed in the independent CHA repository integrated into Sage proper.

[darijgr]

comment:22

Thanks a load for this!

[kevindilks]

Changed branch from u/elixyre/ticket/13793 to u/kdilks/ticket/13793

[kevindilks]

Changed commit from 9c9bf65 to 0e1c0f8

[kevindilks]

New commits:

2b9102b	Ticket 13793: Fixed minor merge issues
0e1c0f8	Ticket 13793: Fixed minor merge issues attempt 2

[kevindilks]

comment:25

This is a very large and ambitious undertaking, so we're going to try and split it up into more manageable tickets, adding only a few features at a time. I just want to make sure that I have the right idea about what order things should be tackled in, dependencies, and that they're broken up into small enough pieces before I create new tickets.

• Adding 'connected' to graded_hopf_algebras_with_basis.py as one ticket

• Dendriform_algebras/dendriform_coalgebras/bidendriform_bialgebras as one ticket.

• Operator_tools.py as one ticket.

• Ordered_set_partition, packed_words, and quasi_shuffle as one ticket.

I believe those four tickets would all be independent of each other, and all further features will depend on them.

• Next would be implementing the framework which within this ticket is located in combinat/hopf_algebras/categories/ (dialgebras, diese product, polynomial realization, quadrialgebras, scalar_product). This would probably be broken up into a few tickets, but I don't know enough about them yet to know which ones go together).

Once all of the previous framework has been added, then we can implement individual CHAs, which would probably each be their own ticket, and rely on all the previous tickets.

• Implementations for FQSym and WQSym are included in this ticket.

• PBT already has its own ticket (Planar Binary Trees (Loday-Ronco) Hopf Algebra and some binary tree methods #13855) and I believe it includes an implementation.

• There are a few more where code exists as part of the external CHA package, but have not yet been integrated into any Trac ticket (FSym, PQSym, WSym).

[zabrocki]

comment:26

Yes, please open all of these tickets and do all of the programming. Thank you. ;)

Seriously, this sounds like a good plan and I can help review and add doc tests or whatever.

[sagetrac-elixyre]

comment:27

Hello,

Thank you very much about your work! :-)

Replying to @kevindilks:

• Ordered_set_partition, packed_words,

I have created a ticket about packed words and ordered set partition : #15611

and quasi_shuffle as one ticket.

and an other one about quasi-shuffle #15597.

• Next would be implementing the framework which within this ticket is located in combinat/hopf_algebras/categories/ (dialgebras, diese product, polynomial realization, quadrialgebras, scalar_product). This would probably be broken up into a few tickets, but I don't know enough about them yet to know which ones go together).

I don't know enough too about dialgebras, diese product and quadrialgebras to be sure that this code is essential... The notion of polynomial realization should generalized the realization in Sym and QSym...

Thanks!!

[amypang]

comment:29

I am hiring a research assistant for ~3 months to work on this ticket, and also write some related code for my research. The start date is flexible, and the person needs to come to my campus in Hong Kong. This might be a good opportunity for a graduated undergrad / grad student / postdoc to travel a bit in between studies / jobs. The person needs to have a good coding background and some math background, he/she doesn't need to specifically know about these algebras since I can teach CHAs pretty easily. Let me know via the comments here, or email, if you have people to recommend, thanks.

[darijgr]

comment:31

Thanks, Amy, for getting this taken care of! That's going to make Sage a lot more useful to me.

[amypang]

comment:32

Replying to @darijgr:

Thanks, Amy, for getting this taken care of! That's going to make Sage a lot more useful to me.

I wouldn't hold your breath. When I said "flexible start date", I'm thinking anytime 2018/2019, though if someone very suitable wanted to start now I'd of course take him/her.

So I'm in no rush for this code, but since I have grant money for this sort of thing, I hope I can do something nice for the community. If you think of anyone, please let me know!

[fchapoton]

comment:33

For information:

PBT is done in #23763 ; Grossmann-Larson is work-in-progress in #23406

[fchapoton]

comment:34

see #23987 for a minimal implementation of FQSYM