Opened 9 years ago
Last modified 5 years ago
#13793 new task
Hopf algebra: FQSym, WQSym, PQSym, PBT
Reported by:  elixyre  Owned by:  sagecombinat 

Priority:  minor  Milestone:  sage6.4 
Component:  combinatorics  Keywords:  hopf algebra, sagedays65 
Cc:  florent.hivert@…, darij, kdilks, zabrocki, amypang, alauve  Merged in:  
Authors:  JeanBaptiste 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: 
Description
I begin implementation of some Hopf algebra: FQSym, and WQSym PQSym. (And some quotients: PBT, Baxter, Stalactic) I try to follow the NCSFQSym design.
Attachments (5)
Change History (39)
comment:1 Changed 9 years ago by
comment:2 Changed 9 years ago by
 Cc florent.hivert@… added
comment:3 Changed 9 years ago by
comment:4 Changed 9 years ago by
 Milestone changed from sage5.11 to sage5.12
comment:5 Changed 9 years ago by
 Cc darij added
How is this going? Is MalvenutoReutenauer already functional? I'm looking for a neat implementation of MR lately (I have my own but it is very basic and probably too slow).
comment:6 Changed 9 years ago by
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 MR, LodayRonco and some other.
MR 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.)
JeanBaptiste
comment:7 Changed 9 years ago by
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) <ipythoninput105ba675cf388> in <module>() > 1 from chasage.all import * /home/darij/sage5.11.beta3/devel/sagemain/cha/chasage/all.py in <module>() > 1 from combinat.all import * 2 3 from patches.all import * /home/darij/sage5.11.beta3/devel/sagemain/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/sage5.11.beta3/devel/sagemain/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/sage5.11.beta3/devel/sagemain/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/sage5.11.beta3/devel/sagemain/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/sage5.11.beta3/devel/sagemain/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 sagecombinat queue?
comment:8 Changed 9 years ago by
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
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:11 Changed 8 years ago by
 Branch set to u/elixyre/ticket/13793
 Commit set to b7f99456867e4b119e670c132be916f9c0a6e257
 Dependencies set to #10963, #15573, #15578, #15595
Last 10 new commits:
b7f9945  Ticket 13793: FQSym (or the MalvenutoReutenauer 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.

comment:12 Changed 8 years ago by
 Commit changed from b7f99456867e4b119e670c132be916f9c0a6e257 to 18270d21c0cc75da94505c5c1bf1a94ba49138f2
comment:13 Changed 8 years ago by
 Commit changed from 18270d21c0cc75da94505c5c1bf1a94ba49138f2 to 4cb8d3d1fe8e81c4fa5de6e15e572629916e3352
comment:14 Changed 8 years ago by
 Dependencies changed from #10963, #15573, #15578, #15595 to #10963, #15573, #15578, #15595, #15611, #15597
comment:15 Changed 8 years ago by
 Commit changed from 4cb8d3d1fe8e81c4fa5de6e15e572629916e3352 to b227b12181cd48a49c6a1474d00efa60ecbcdbc9
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

comment:16 Changed 8 years ago by
 Commit changed from b227b12181cd48a49c6a1474d00efa60ecbcdbc9 to 9c9bf65e4b5a5335b422ccddbd447dd48317797d
Branch pushed to git repo; I updated commit sha1. New commits:
9c9bf65  Ticket 13793: fix the category of realizations

comment:17 Changed 8 years ago by
 Milestone changed from sage6.1 to sage6.2
comment:18 Changed 8 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:19 Changed 8 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:20 Changed 7 years ago by
 Cc kdilks added
 Keywords sagedays65 added
comment:21 Changed 7 years ago by
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
Thanks a load for this!
comment:23 Changed 7 years ago by
 Branch changed from u/elixyre/ticket/13793 to u/kdilks/ticket/13793
comment:24 Changed 7 years ago by
 Cc zabrocki added
 Commit changed from 9c9bf65e4b5a5335b422ccddbd447dd48317797d to 0e1c0f860dd6eedda803f2d853b5efcc90b342fa
comment:25 followup: ↓ 27 Changed 7 years ago by
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
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
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 quasishuffle #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
 Cc amypang added
comment:29 Changed 5 years ago by
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
 Cc alauve added
comment:31 followup: ↓ 32 Changed 5 years ago by
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
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
comment:34 Changed 5 years ago by
see #23987 for a minimal implementation of FQSYM
I'm student of F. Hivert and N. M. Thiéry at Orsay (Univ ParisSud). JeanBaptiste Priez