[sage-combinat-devel] Ticket #13935 : coercion for Hopf algebra coproduct (and maybe other things...)

[Jean-Baptiste Priez]

I propose a patch 
(trac_13935_coercion_of_coproduct_of_Hopf_algebra-EliX-jbp.patch) to coerce 
elements like: 

Let F[2,1,3]  be an 
element of the fundamental basis of the FreeQuasiSymmetric functions Hopf 
algebra (FQSym) and G an other basis. 

sage: G(F[2,1,3] 
.coproduct()) 

G[] # G[2, 1, 3] + G[1]  # 
G[1, 2] + G[2, 1] # G[1]  + 
G[2, 1, 3] # G[]

Some one may be must move my code (in Categories i think or anywhere)...

Jean-Baptiste Priez

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Re: [sage-combinat-devel] Ticket #13935 : coercion for Hopf algebra coproduct (and maybe other things...)

[Nicolas M. Thiery]

Hi,

On Wed, Jan 09, 2013 at 06:08:13AM -0800, Jean-Baptiste Priez wrote:
>I propose a patch
>(trac_13935_coercion_of_coproduct_of_Hopf_algebra-EliX-jbp.patch) to
>coerce elements like: 
> 
>Let F[2,1,3] be an element of the fundamental basis of
>the FreeQuasiSymmetric functions Hopf algebra (FQSym) and G an other
>basis. 
> 
>sage: G(F[2,1,3].coproduct()) 
> 
>G[] # G[2, 1, 3] + G[1] # G[1, 2] + G[2, 1] # G[1] + G[2, 1, 3] # G[]
> 
>Some one may be must move my code (in Categories i think or anywhere)...

I just discussed with Jean-Baptiste. I see the merit of this short and
reasonably meaningful syntax. But on the other hand it deviates from
the standard semantic of P(x) which is to convert/coerce x to an
element of P. I would recommend instead to use something like:

sage: GG = G.tensor_square()
sage: GG(F[2,1,3].coproduct())

Then what remains to implement is:
- tensor products of module morphisms
- an appropriate P._coerce_map_from(P1) in
  CombinatorialFreeModule_Tensor which, if
  - P is the tensor product of A,B, ...
  - P1 is the tensor product of A1,B1, ...
  - there are morphisms A1->A, B1->B, ...
  returns the induced morphism P1->P

I remember discussing this already. With whom? Do we have a ticket?

Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" 
http://Nicolas.Thiery.name/

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