#19278: FQSym (Malvenuto-Reutenauer) Hopf algebras
-------------------------------------+-------------------------------------
Reporter: elixyre | Owner:
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-6.9
Component: combinatorics | Keywords:
Merged in: | Authors: Jean-Baptiste
Reviewers: | Priez
Work issues: | Report Upstream: N/A
Commit: | Branch:
358423348671721e1987cf99e2be1237ab0bbd45| public/hopf_algebras/fqsym
Stopgaps: | Dependencies: #19264
-------------------------------------+-------------------------------------
A first version of the Hopf algebra of Malvenuto-Reutenauer.
This ticket provides several bases and the product and the coproduct.
Other operators should be provided in others tickets (bidendriform, inner
product, scalar product, polynomial realizations, etc).
Those tickets should be create soon (the tickets number should be
inventoried here).
{{{
sage: F = FQSym(QQ).F()
sage: F[3,1,2] * F[1,2]
F[3, 1, 2, 4, 5] + F[3, 1, 4, 2, 5] + F[3, 1, 4, 5, 2] + F[3, 4, 1, 2, 5]
+ F[3, 4, 1, 5, 2] + F[3, 4, 5, 1, 2] + F[4, 3, 1, 2, 5] + F[4, 3, 1, 5,
2] + F[4, 3, 5, 1, 2] + F[4, 5, 3, 1, 2]
sage: F[3,1,2].coproduct()
F[] # F[3, 1, 2] + F[1] # F[1, 2] + F[2, 1] # F[1] + F[3, 1, 2] # F[]
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/19278>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
