draw all faces of alcoves (affine root system)

asked 2019-02-07 09:12:48 -0500

oloid gravatar image

updated 2019-02-08 02:29:45 -0500

FrédéricC gravatar image

I am trying to plot alcoves for in a rank 3 affine root system with some of those alcoves highlighted by having all faces drawn and the others only shown as a wire frame.

The manual on visualising root systems at sagemath.org is quite useful, but I have some effects show that I don't understand.

For some reason while the fundamental alcove will have all faces shown many of the others have not, that is, some faces are missing. Below you find one example code that I have done. For the chosen seq one face is missing, the red one. For other choices of seq one might even see only one face drawn. How do I force to have all faces shown?

L = RootSystem(["A",3,1]).ambient_space()
P = RootSystem(["A",3,1]).weight_space(extended=True)
Lambda = P.fundamental_weights()
W = L.weyl_group()
W0=W.classical()
plot_options = L.plot_parse_options()
seq=[2,3,1,2]  
t = 1*Lambda[1]-1*Lambda[2]+1*Lambda[3]
Alcoves=[W.from_reduced_word(w.reduced_word()) for w in W0]
p = L.plot_fundamental_chamber("classical")
p += L.plot_fundamental_weights()
p += L.plot_alcoves(alcoves=Alcoves, wireframe=True)
p += L.plot_alcoves(alcoves=[W.from_reduced_word(seq)])
p += L.plot_alcoves(alcoves=[W.from_reduced_word([])])
p += plot_options.family_of_vectors({t: L(t)})
p.show(frame=False)
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