Opened 7 years ago
Closed 7 years ago
#19255 closed defect (fixed)
remove adams_operation
Reported by:  zabrocki  Owned by:  

Priority:  minor  Milestone:  sage6.9 
Component:  combinatorics  Keywords:  
Cc:  alauve, darij, aschilling, tscrim, nthiery, hivert, sagecombinat, mhansen, elixyre  Merged in:  
Authors:  Mike Zabrocki, JeanBaptiste Priez  Reviewers:  Darij Grinberg, Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  5f785a2 (Commits, GitHub, GitLab)  Commit:  5f785a2df1f0f3fc033fe7e5d933914fcf7d43e4 
Dependencies:  Stopgaps: 
Description
adams_operator
was added at the level of bialgebras and is defined as \mu^{n1} \circ \Delta^{n1}
however in symmetric functions the method adams_operation
is an alias to frobenius
. Since this is confusing. We propose removing adams_operation
as an alias for frobenius
. adams_operation
was added in #14775, adams_operator
will be added in #18678.
The documentation explains: The n
th Frobenius operator is also the n
th Adams operator of the \Lambda
ring of symmetric functions over the integers. This does not seem to agree with what we found in a paper by Aguiar and Lauve "The characteristic polynomial of the Adams operators on graded connected Hopf algebras" which says the Adams operators are the "Hopf powers or Sweedler powers" and it gives the definition that was defined at the level of bialgebras.
Change History (18)
comment:1 Changed 7 years ago by
 Branch changed from u/public/symmetric_functions/remove_adams_op to public/symmetric_functions/remove_adams_op
 Commit set to c75f51d6a4a3e69a6d3ad95ecd51cb7f09caebd1
comment:2 Changed 7 years ago by
 Branch changed from public/symmetric_functions/remove_adams_op to u/public/symmetric_functions/remove_adams_op
 Commit c75f51d6a4a3e69a6d3ad95ecd51cb7f09caebd1 deleted
comment:3 Changed 7 years ago by
 Branch changed from u/public/symmetric_functions/remove_adams_op to public/symmetric_functions/remove_adams_op
 Commit set to c75f51d6a4a3e69a6d3ad95ecd51cb7f09caebd1
New commits:
c75f51d  remove the line 'adams_operation = frobenius' (and comments about the adams operation in frobenius method)

comment:4 Changed 7 years ago by
Please keep the comment about the Adams operator of the lambdaring. That at least is correct.
Also there is a similar problem with QSym.
comment:5 Changed 7 years ago by
Thanks Darij. JeanBaptiste is here visiting and we wanted to check with you that it is ok to remove the aliases. Can you explain how the terminology is correct? What are we taking as the definition of "Adams operator of the lambdaring"?
comment:6 Changed 7 years ago by
Every lambdaring canonically has Adams operations defined on it ( https://www.encyclopediaofmath.org/index.php/Lambdaring ). The symmetric functions have a canonical lambdaring structure. (There is yet another one on their homogeneous components, but I'm talking about the one on the whole ring.) The Adams operations of this lambdaring structure are the Frobenius operators. This is in Hazewinkel's various texts.
I think there are good reasons for Aguiar and Lauve calling their operators "Adams operators", but I don't think these reasons come from lambdaring theory.
comment:7 Changed 7 years ago by
I see now. Both operations are Adams operators.
frobenius
is the Adam's operator for the bialgebra p_r \circ p_n = p_{rn}
and \Delta^{\circ}(p_n) = p_n \otimes p_n
. Thanks. We will try to make that clear.
comment:8 Changed 7 years ago by
 Commit changed from c75f51d6a4a3e69a6d3ad95ecd51cb7f09caebd1 to 233a05c9655fa90b297109944b9c96345aa8fd55
Branch pushed to git repo; I updated commit sha1. New commits:
233a05c  remove methods adams_operator to avoid conflict with the natural Adams operator of the bialgebra

comment:9 Changed 7 years ago by
LGTM. Do the doctests agree?
I positively hope noone has used the aliases yet, since I have no idea how deprecation works.
comment:10 Changed 7 years ago by
Good point. It will take a while to deprecate the aliases, but long term its better not to have both adams_operation
and adams_operator
comment:11 Changed 7 years ago by
 Commit changed from 233a05c9655fa90b297109944b9c96345aa8fd55 to 3264c679c434df7b87bbe01d6d887f0175c434f9
Branch pushed to git repo; I updated commit sha1. New commits:
3264c67  add deprecation of adams_operation methods in sf and qsym

comment:12 Changed 7 years ago by
 Cc elixyre added
comment:13 Changed 7 years ago by
 Status changed from new to needs_review
comment:14 Changed 7 years ago by
+ The Frobenius operator is the Adam's operator for the bialgebra + `p_r \circ p_n = p_{rn}` and `\Delta^{\circ}(p_n) = p_n \otimes p_n`.
That's wrong. I think the n
th Adams operator of this bialgebra would send p_k
to p_{k^n}
.
I also don't think that this is a good way to understand the Frobenius.
comment:15 Changed 7 years ago by
 Commit changed from 3264c679c434df7b87bbe01d6d887f0175c434f9 to 5f785a2df1f0f3fc033fe7e5d933914fcf7d43e4
Branch pushed to git repo; I updated commit sha1. New commits:
5f785a2  update comment following the darij's recommandations

comment:16 Changed 7 years ago by
LGTM. If the tests run, this ticket is good. Thanks for the disambiguation!
comment:17 Changed 7 years ago by
 Reviewers set to Darij Grinberg, Travis Scrimshaw
 Status changed from needs_review to positive_review
Tests pass for me, so given Darij's comments, positive review.
comment:18 Changed 7 years ago by
 Branch changed from public/symmetric_functions/remove_adams_op to 5f785a2df1f0f3fc033fe7e5d933914fcf7d43e4
 Resolution set to fixed
 Status changed from positive_review to closed
Good point about the conflicting terminology. I don't mind removing these aliases (but I fear I have no time whatsoever to actually do any of the job myself).