@@ -533,26 +533,27 @@ def lift_cross_ratios(A, lift_map=None):
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EXAMPLES::
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+ sage: # needs sage.graphs
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sage: from sage.matroids.advanced import lift_cross_ratios, lift_map, LinearMatroid
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- sage: R = GF(7) # needs sage.graphs
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- sage: to_sixth_root_of_unity = lift_map('sru') # needs sage.graphs sage. rings.number_field
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- sage: A = Matrix(R, [[1, 0, 6, 1, 2],[6, 1, 0, 0, 1],[0, 6, 3, 6, 0]]) # needs sage.graphs
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- sage: A # needs sage.graphs
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+ sage: R = GF(7)
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+ sage: to_sixth_root_of_unity = lift_map('sru') # needs sage.rings.number_field
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+ sage: A = Matrix(R, [[1, 0, 6, 1, 2],[6, 1, 0, 0, 1],[0, 6, 3, 6, 0]])
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+ sage: A
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[1 0 6 1 2]
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[6 1 0 0 1]
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[0 6 3 6 0]
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- sage: Z = lift_cross_ratios(A, to_sixth_root_of_unity) # needs sage.graphs sage. rings.finite_rings sage.rings.number_field
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- sage: Z # needs sage.graphs sage. rings.finite_rings sage.rings.number_field
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+ sage: Z = lift_cross_ratios(A, to_sixth_root_of_unity) # needs sage.rings.finite_rings sage.rings.number_field
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+ sage: Z # needs sage.rings.finite_rings sage.rings.number_field
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[ 1 0 1 1 1]
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[ 1 1 0 0 z]
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[ 0 -1 z 1 0]
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- sage: M = LinearMatroid(reduced_matrix=A) # needs sage.graphs
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- sage: sorted(M.cross_ratios()) # needs sage.graphs
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+ sage: M = LinearMatroid(reduced_matrix=A)
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+ sage: sorted(M.cross_ratios())
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[3, 5]
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- sage: N = LinearMatroid(reduced_matrix=Z) # needs sage.graphs sage. rings.finite_rings sage.rings.number_field
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- sage: sorted(N.cross_ratios()) # needs sage.graphs sage. rings.finite_rings sage.rings.number_field
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+ sage: N = LinearMatroid(reduced_matrix=Z) # needs sage.rings.finite_rings sage.rings.number_field
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+ sage: sorted(N.cross_ratios()) # needs sage.rings.finite_rings sage.rings.number_field
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[-z + 1, z]
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- sage: M.is_isomorphism(N, {e:e for e in M.groundset()}) # needs sage.graphs sage. rings.finite_rings sage.rings.number_field
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+ sage: M.is_isomorphism(N, {e:e for e in M.groundset()}) # needs sage.rings.finite_rings sage.rings.number_field
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True
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"""
@@ -752,14 +753,15 @@ def split_vertex(G, u, v=None, edges=None):
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EXAMPLES::
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+ sage: # needs sage.graphs
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sage: from sage.matroids.utilities import split_vertex
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- sage: G = graphs.BullGraph() # needs sage.graphs
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- sage: split_vertex(G, u=1, v=55, edges=[(1, 3)]) # needs sage.graphs
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+ sage: G = graphs.BullGraph()
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+ sage: split_vertex(G, u=1, v=55, edges=[(1, 3)])
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Traceback (most recent call last):
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...
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ValueError: the edges are not all incident with u
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- sage: split_vertex(G, u=1, v=55, edges=[(1, 3, None)]) # needs sage.graphs
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- sage: list(G.edges(sort=True)) # needs sage.graphs
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+ sage: split_vertex(G, u=1, v=55, edges=[(1, 3, None)])
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+ sage: list(G.edges(sort=True))
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[(0, 1, None), (0, 2, None), (1, 2, None), (2, 4, None), (3, 55, None)]
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"""
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if v is None :
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