@@ -344,6 +344,7 @@ def PermutationGroup(gens=None, *args, **kwds):
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Note that we provide generators for the acting group. The
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permutation group we construct is its homomorphic image::
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+ sage: # needs sage.combinat
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sage: a = lambda g, x: vector(g*x, immutable=True)
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sage: X = [vector(x, immutable=True) for x in GF(3)^2]
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sage: G = SL(2,3); G.gens()
@@ -1547,6 +1548,7 @@ def representative_action(self,x,y):
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TESTS::
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+ sage: # needs sage.graphs
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sage: g = graphs.PetersenGraph()
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sage: g.relabel(list("abcdefghik"))
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sage: g.vertices(sort=True)
@@ -3706,6 +3708,7 @@ def has_regular_subgroup(self, return_group=False):
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But the automorphism group of Petersen's graph does not::
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+ sage: # needs sage.graphs
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sage: G = graphs.PetersenGraph().automorphism_group()
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sage: G.has_regular_subgroup()
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False
@@ -3767,6 +3770,7 @@ def blocks_all(self, representatives=True):
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Picking an interesting group::
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+ sage: # needs sage.graphs
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sage: g = graphs.DodecahedralGraph()
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sage: g.is_vertex_transitive()
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True
@@ -3776,12 +3780,12 @@ def blocks_all(self, representatives=True):
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Computing its blocks representatives::
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- sage: ag.blocks_all()
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+ sage: ag.blocks_all() # needs sage.graphs
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[[0, 15]]
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Now the full block::
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- sage: sorted(ag.blocks_all(representatives = False)[0])
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+ sage: sorted(ag.blocks_all(representatives= False)[0]) # needs sage.graphs
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[[0, 15], [1, 16], [2, 12], [3, 13], [4, 9],
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[5, 10], [6, 11], [7, 18], [8, 17], [14, 19]]
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@@ -3977,6 +3981,7 @@ def minimal_generating_set(self):
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EXAMPLES::
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+ sage: # needs sage.graphs
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sage: g = graphs.CompleteGraph(4)
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sage: g.relabel(['a','b','c','d'])
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sage: mgs = g.automorphism_group().minimal_generating_set(); len(mgs)
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