Opened 9 years ago

Last modified 5 years ago

#13793 new task

Hopf algebra: FQSym, WQSym, PQSym, PBT

Reported by: elixyre Owned by: sage-combinat
Priority: minor Milestone: sage-6.4
Component: combinatorics Keywords: hopf algebra, sagedays65
Cc: florent.hivert@…, darij, kdilks, zabrocki, amypang, alauve Merged in:
Authors: Jean-Baptiste Priez Reviewers:
Report Upstream: N/A Work issues:
Branch: u/kdilks/ticket/13793 (Commits, GitHub, GitLab) Commit: 0e1c0f860dd6eedda803f2d853b5efcc90b342fa
Dependencies: #10963, #15573, #15578, #15595, #15611, #15597 Stopgaps:

Status badges

Description

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.

Attachments (5)

cha-EliX-jbp.patch (38.4 KB) - added by elixyre 9 years ago.
some modification of categories + fqsym with several basis
fsym-EliX-jbp.patch (13.7 KB) - added by elixyre 9 years ago.
FSym as FQSym quotient + some modification in Coalgebras' cateogory
tensor-coercion-maurice.patch (3.6 KB) - added by elixyre 9 years ago.
default coercion for tensors
how_to_use_cha_lib.pdf (143.2 KB) - added by elixyre 9 years ago.
tutorial how to use the lib
cha.pdf (419.7 KB) - added by elixyre 9 years ago.
an other tutorial

Download all attachments as: .zip

Change History (39)

comment:1 Changed 9 years ago by elixyre

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

Last edited 9 years ago by elixyre (previous) (diff)

Changed 9 years ago by elixyre

some modification of categories + fqsym with several basis

Changed 9 years ago by elixyre

FSym as FQSym quotient + some modification in Coalgebras' cateogory

Changed 9 years ago by elixyre

default coercion for tensors

comment:2 Changed 9 years ago by elixyre

  • Cc florent.hivert@… added

comment:3 Changed 9 years ago by elixyre

  • Authors set to Jean-Baptiste Priez

comment:4 Changed 9 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:5 Changed 9 years ago by darij

  • Cc darij added

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).

Changed 9 years ago by elixyre

tutorial how to use the lib

Changed 9 years ago by elixyre

an other tutorial

comment:6 Changed 9 years ago by elixyre

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

comment:7 Changed 9 years ago by darij

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?

comment:8 Changed 9 years ago by elixyre

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.

comment:9 Changed 9 years ago by tscrim

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.

comment:10 Changed 9 years ago by tscrim

[Duplicate post]

Last edited 9 years ago by tscrim (previous) (diff)

comment:11 Changed 8 years ago by elixyre

  • Branch set to u/elixyre/ticket/13793
  • Commit set to b7f99456867e4b119e670c132be916f9c0a6e257
  • Dependencies set to #10963, #15573, #15578, #15595

Last 10 new commits:

b7f9945Ticket 13793: FQSym (or the Malvenuto-Reutenauer Hopf algebra) and some categories
8399005Ticket 15578: append missing import
a9499a0Ticket 15578: append a missing import
416a081Default antipode implementation for graded connected Hopf algebras
5ccf253Merge branch 'u/SimonKing/ticket/10963' of trac.sagemath.org:sage into public/ticket/10963
14e63b6Merge ticket/15506 into ticket/10963 to fix recursion error
6147777Trac 15506: Add a test (review commit)
3d978e9Merge branch 'develop' into public/ticket/10963
0c907cfReverted cached_function to weak_cached_function.
588c276Fixed ncsym/bases.py doctest.

comment:12 Changed 8 years ago by git

  • Commit changed from b7f99456867e4b119e670c132be916f9c0a6e257 to 18270d21c0cc75da94505c5c1bf1a94ba49138f2

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

18270d2Merge branch '15595/shuffle' into 13793/cha
9730233fast Shuffle product compatible with iterable objects (use linear extension)

comment:13 Changed 8 years ago by git

  • Commit changed from 18270d21c0cc75da94505c5c1bf1a94ba49138f2 to 4cb8d3d1fe8e81c4fa5de6e15e572629916e3352

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

4cb8d3dMerge branch '15597/quasi_shuffle' into 13793/cha
d466ab9Merge branch '15611/packed_words' into 13793/cha
0104d00Ticket 15611: Packed Words
edab189first version of the quasi-shuffle product

comment:14 Changed 8 years ago by elixyre

  • Dependencies changed from #10963, #15573, #15578, #15595 to #10963, #15573, #15578, #15595, #15611, #15597

comment:15 Changed 8 years ago by git

  • Commit changed from 4cb8d3d1fe8e81c4fa5de6e15e572629916e3352 to b227b12181cd48a49c6a1474d00efa60ecbcdbc9

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

b227b12Ticket 13793: WQSym as - a bidendriform bialgebra - with internal product - with diese product
a19f374Merge branch '15611/packed_words' into 13793/cha
6fc6703Ticket 15611: fix Shifted concatenation...
10645a8Merge branch '15611/packed_words' into 13793/cha
c15335eTicket 15611: fix empty shifted shuffle of packed words + test on quasi shifted shuffle
0539b79Merge branch '15611/packed_words' into 13793/cha
3291c96Merge branch '15597/quasi_shuffle' into 15611/packed_words
aa338f4Ticket 15597: fix an extrem case: empty list with a special elem_constructor
0e62e54Merge branch '15611/packed_words' into 13793/cha
8c8cc96Ticket 15611: fix the shifted quasi shuffle of ordered set partition

comment:16 Changed 8 years ago by git

  • Commit changed from b227b12181cd48a49c6a1474d00efa60ecbcdbc9 to 9c9bf65e4b5a5335b422ccddbd447dd48317797d

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

9c9bf65Ticket 13793: fix the category of realizations

comment:17 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:18 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:19 Changed 8 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:20 Changed 7 years ago by kdilks

  • Cc kdilks added
  • Keywords sagedays65 added

comment:21 Changed 7 years ago by kdilks

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

comment:22 Changed 7 years ago by darij

Thanks a load for this!

comment:23 Changed 7 years ago by kdilks

  • Branch changed from u/elixyre/ticket/13793 to u/kdilks/ticket/13793

comment:24 Changed 7 years ago by kdilks

  • Cc zabrocki added
  • Commit changed from 9c9bf65e4b5a5335b422ccddbd447dd48317797d to 0e1c0f860dd6eedda803f2d853b5efcc90b342fa

New commits:

2b9102bTicket 13793: Fixed minor merge issues
0e1c0f8Ticket 13793: Fixed minor merge issues attempt 2

comment:25 follow-up: Changed 7 years ago by kdilks

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 (#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).

comment:26 Changed 7 years ago by zabrocki

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.

comment:27 in reply to: ↑ 25 Changed 7 years ago by elixyre

Hello,

Thank you very much about your work! :-)

Replying to kdilks:

  • 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!!

comment:28 Changed 7 years ago by amypang

  • Cc amypang added

comment:29 Changed 5 years ago by amypang

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.

comment:30 Changed 5 years ago by amypang

  • Cc alauve added

comment:31 follow-up: Changed 5 years ago by darij

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

comment:32 in reply to: ↑ 31 Changed 5 years ago by amypang

Replying to darij:

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!

comment:33 Changed 5 years ago by chapoton

For information:

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

comment:34 Changed 5 years ago by chapoton

see #23987 for a minimal implementation of FQSYM

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