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# load library
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load('http://jan.ucc.nau.edu/ns46/invariant/tactical.sage')
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# create the incidense matrix
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edges = [(0,1), (0,2), (0, 8), (1,2), (2,3), (3,4), (3,5), (4,5), (5,6), (6,7), (6,8), (7,8)]
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g=Graph(edges)
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g.show(save_pos=True,figsize=[2,2],vertex_size=120)
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M=g.incidence_matrix()
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print(M)
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# M =designs.projective_plane(2).incidence_matrix() # Fano
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# find tactical decompositions
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cols=tactical_decompositions(M)
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for i,col in enumerate(cols):
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        print(i,":",col)
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# show poset
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ps=poset(cols)
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ps.show()
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# show orbit poset
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ops=orbit_poset(M,cols)
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ops.show()
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