Open alauve opened 6 years ago
Commit: 85d2d72
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
b144c19 | removing AssertionError calls |
dad7e7b | moving from Set to frozenset; zapping doctest errors that creeped in from earlier changes |
306b3fe | modified subset method to behave the way expected from `__init__` method in CombinatorialFreeModule |
c68b518 | updated minimaj crystal reference |
4af474f | mostly adding doc tests and examples; improved a few methods |
89284be | finished adding tests/examples for all functions; but found some errors to be corrected (see new TODO) |
830f5ae | zapping bugs within `__init__` handling of constraints |
d3e375a | create module for the Hopf algebras on ordered multiset partitions |
d18f780 | revamped tests for satisfying constraints |
85d2d72 | Merge branch 'public/combinat/implement-ordered-multiset-partitions-25148' into public/combinat/implement_hopf_algebra_on_OMPs-25543 |
Branch pushed to git repo; I updated commit sha1. New commits:
c7dff31 | implement the dual of the Hopf algebra on ordered multiset partitions |
659132f | fix merge conflicts in references |
8e5aa52 | Merge branch 'public/combinat/implement-ordered-multiset-partitions-25148' into public/combinat/implement_hopf_algebra_on_OMPs-25543 |
Branch pushed to git repo; I updated commit sha1. New commits:
0ec37d7 | work on _antipode; added temporary test code at EOF |
Branch pushed to git repo; I updated commit sha1. New commits:
bd3a383 | importing cartesian_product |
Branch pushed to git repo; I updated commit sha1. New commits:
4598426 | modified .split(), which was ignoring repeats |
ad3a3e7 | Merge branch 'public/combinat/implement-ordered-multiset-partitions-25148' into public/combinat/implement_hopf_algebra_on_OMPs-25543 |
9942bf2 | improved antipode on H basis; moved duality_pairing; other small changes |
Branch pushed to git repo; I updated commit sha1. New commits:
b112d43 | Merge branch 'public/combinat/implement-ordered-multiset-partitions-25148' into public/combinat/implement_hopf_algebra_on_OMPs-25543 |
Please use python3 syntax for print (and for the rest also)
Branch pushed to git repo; I updated commit sha1. New commits:
fb35251 | a bit of cleaning up |
N.B. I still have a lot more work to do in this file. I will give an alert when it's ready for a closer look.
Branch pushed to git repo; I updated commit sha1. New commits:
1a66fcd | implementing powersum basis and its dual |
Just a remark that this ticket is still not ready for a close look. (Nearly ready, but there are still a few big errors to track down, as well as some coercions/morphisms to add.)
I still have to track down some degree issues, but I think the ticket merits a closer look now.
Some more superficial comments:
OMPBasis_OMPNSym
to OMPNSymBasis_abstract
(at least, that is my understanding of its role).around which the primitive is built.
This is overindented:
.. TODO::
- sort out the degree issues above. (search for "wrong!!!")
For this:
.. TODO: Do we need these tests, or are they checked within TestSuite?::
the answer is yes, they are checked by the _test_antipode
unless I am misremembering something.
.. MATH::
needs a blankline before it (see coproduct_on_basis
).TestSuite
tests in the __init__
method rather than the class-level doc.*Warning:*
-> .. WARNING::
.__classcall_private__
will need doctests.Thanks, Travis! Extremely helpful, as usual.
The free (noncommutative) algebra generated by finite nonempty sets is given a Hopf algebra structure, with coproduct on finite sets
K
given by\Delta(K) = \sum_{I \sqcup J = K} I \otimes J
.This Hopf algebra gives formulas for primitives and antipode in other (combinatorial) Hopf algebras via "transfer of structure" as described in [LM2018]. This transfer was already implemented (in the special case of NCSYM) via :meth:`
It would be nice to implement this transfer for other cases. Getting this Hopf algebra and its dual within SageMath would be a good first step.
REFERENCE:
[LM2018] Lauve, Mastnak. Bialgebra coverings and transfer of structure. :arxiv:
1803.02691
.Depends on #25148
CC: @tscrim @darijgr @zabrocki @alauve @saliola @amypang
Component: combinatorics
Keywords: IMA coding sprint, CHAs, ordered multiset partitions
Author: Aaron Lauve
Branch/Commit: public/combinat/implement_hopf_algebra_on_OMPs-25543 @
5b8cab9
Issue created by migration from https://trac.sagemath.org/ticket/25543