Hi Nicolas,

Could you confirm the following bug?  It seems to appear both with and
without combinat applied:

----------------------------------------------------------------------
| Sage Version 4.4, Release Date: 2010-04-24                         |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
Loading Sage library. Current Mercurial branch is: combinat
sage: D = CombinatorialFreeModule(QQ, Partitions(), prefix='d');
sage: d = D.basis();
sage: s = SymmetricFunctions(QQ).schur()
sage: def func(p):
....:     if len(p)==0: return 1
....:     else: return p[0]
sage: D_to_Schur = D.module_morphism(diagonal=func, codomain=s)
sage: Schur_to_D = ~D_to_Schur
sage: D_to_Schur(Schur_to_D(2*s([2,1])))
-12*s[2, 1]

Note that the following seems to work, though:

sage: X = CombinatorialFreeModule(QQ, Partitions(), prefix='x');
sage: x = X.basis()
sage: D_to_X = D.module_morphism(diagonal=func, codomain=X)
sage: X_to_D = ~D_to_X
sage: D_to_X(X_to_D(2*x[Partition([2,1])]))
2*x[[2, 1]]

Preparing for a talk seems to be a good spotlight for bugs!

Cheers,
Jason

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