In the Cartan type documentation (cartan_type.py) we find the following statement:
The direction of the arrows is the **opposite** (i.e. the
transpose)
of Bourbaki's convention, but agrees with
Kac's.
For example, in type `C_2`, we
have::
sage: C2 = DynkinDiagram(['C',2]);
C2
O=<=O
1
2
C2
sage:
C2.cartan_matrix()
[ 2
-2]
[-1
2]
This appears in the reference manual on this page:
http://www.sagemath.org/doc/reference/combinat/sage/combinat/root_system/cartan_type.html
It is correct that Bourbaki's Cartan matrix is the transpose of Kac.
However both have
the same convention regarding Dynkin diagrams: the arrow points from the
long root
to the short.
I think we should correct this.
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