Hello Nathann,

Thanks again..

Yesterday evening I made a pause about my sagemath worries...and read 
(again) one math paper...including Schnyder woods, and once again authors 
are
requiring that the graph is "maximum planar" (or "triangulated") and, as 
you have discovered, my example is not maximum planar (easy to find a new 
edge, keeping planarity).

I will need more evening time to add a "frontend" procedure, with a planar 
graph as input (like mine) and a maximum planar graph as output. Procedure 
parametrized by
some constraints : my main work topic is about 2D planar graph, hence I 
will start using constraint like : add one,two or three extra-vertices (in 
the dreamed plot, in the outer
face) and add edges from one of that three extra-vertices.

Yes I understand that you work only on some part of the code....for 
sagemath improvement, I will search to know if the code can be improved 
with a clockwise constraint given by embedding, or equivalently a 
constraint about the sign of the signed area . For two examples :

if 'B':['D','F'] in embedding then : BDF triangle has vertices B,D,F 
reading clockwise  (signed area is positive)

if "E'['C','G',',I','A'] in embedding then ECGIA pentagon has vertices, 
E,C,G,I,A reading clockwise (signed area is positive)


Dominique






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