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

Let F[2,1,3] <http://trac.sagemath.org/sage_trac/log/?revs=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] <http://trac.sagemath.org/sage_trac/log/?revs=1-3>
.coproduct()) 

G[] # G[2, 1, 3] + G[1] <http://trac.sagemath.org/sage_trac/changeset/1> # 
G[1, 2] + G[2, 1] # G[1] <http://trac.sagemath.org/sage_trac/changeset/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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