Hi Nicolas,

> Just to make sure (and for future regression tests), could you send a
> little session demonstrating this?

sorry, I changed the code accidentalness in one of my patches to make
it work... I undid the changes.

After pulling again, you should get the problem I had:

sage: ct = CartanType(['A',3])
sage: L = ct.root_system().root_lattice()
sage: L.simple_root(1)
alpha[1]
sage: L.simple_root(1).associated_coroot()
...
-> 1777         assert domain.base_ring()    == codomain.base_ring()
...
AssertionError

The reason for the error is as described.

> The conceptual way (and thus independent on the realization at hand)
> is to take the scalar product of beta with the simple coweight
> corresponding to alpha. This should (be made to) work; however there
> are things to straighten out around scalar products and coweights ...

yes, but currently, such a scalar product is not available, is it?
Also conceptually, these coefficients are used to define the
coweights, so it seems to me like the wrong way to access them. Or am
I wrong?

Thanks, Christian

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