︠6abbb7dc-d53a-43f0-95c5-5c86cf167f8b︠ ︡4ea70b97-f6e7-4dfe-9aae-8a41f0e09137︡ ︠a48639af-09f9-448c-a997-8947cac77cc7s︠ triangle = SymmetricGroup(3) triangle.list() ︡db03ae06-93a9-40a4-aa30-c6f6844c1bc9︡{"stdout":"[(), (1,2), (1,2,3), (1,3,2), (2,3), (1,3)]"}︡{"stdout":"\n"}︡{"done":true}︡ ︠7d8a4fc9-7085-403e-b93c-720e16460407s︠ triangle.cayley_graph(generators=[(1,2),(1,2,3)]).show(edge_labels=True) ︡733d61f2-c981-4321-80cd-21408ac994c0︡{"file":{"filename":"/projects/f351622c-d261-4717-abee-4c0bfa210e88/.sage/temp/compute4-us/25744/tmp_JYPvvt.svg","show":true,"text":null,"uuid":"0b1d0b48-425e-4ac3-8235-2e1d4dd27f99"},"once":false}︡{"done":true}︡ ︠d1e2ef56-b4b4-4115-994c-9264df152d1c︠ triangle.cayley_graph(generators=[(1,2),(1,3)]).show(edge_labels=True) ︡d021f709-f693-4326-8e3f-5eb7dfcc15e7︡{"file":{"filename":"/projects/f351622c-d261-4717-abee-4c0bfa210e88/.sage/temp/compute4-us/25744/tmp_Ln3PGm.svg","show":true,"text":null,"uuid":"14b787e3-d07f-4d0e-906a-5304d7466664"},"once":false}︡{"done":true}︡ ︠f2bff1b8-a7dc-4c8e-82eb-69a1879752f3s︠ G=PermutationGroup([[(1,2,3,4),(5,6,7,8)],[(1,5,8,4),(2,6,7,3)]]) ︡14587e8c-60c2-4951-8c6e-19cf7e2d99e6︡{"done":true}︡ ︠c843b42f-251b-4033-87bd-7013bd395c7as︠ G.list() ︡477953e0-209f-4fe7-8e9e-0135a4abfc5e︡{"stdout":"[(), (1,2,3,4)(5,6,7,8), (1,5,8,4)(2,6,7,3), (1,3)(2,4)(5,7)(6,8), (1,6,3)(4,5,7), (1,6,8)(2,7,4), (1,8)(2,7)(3,6)(4,5), (1,7)(2,3)(4,6)(5,8), (1,7)(2,8)(3,4)(5,6), (1,4,3,2)(5,8,7,6), (1,2)(3,5)(4,6)(7,8), (1,7)(2,6)(3,5)(4,8), (1,5)(2,8)(3,7)(4,6), (1,4,8,5)(2,3,7,6), (2,4,5)(3,8,6), (1,3,8)(2,7,5), (1,3,6)(4,7,5), (1,6)(2,5)(3,8)(4,7), (2,5,4)(3,6,8), (1,8,3)(2,5,7), (1,8,6)(2,4,7), (1,5,6,2)(3,4,8,7), (1,4)(2,8)(3,5)(6,7), (1,2,6,5)(3,7,8,4)]\n"}︡{"done":true}︡ ︠f2a3ca27-a70b-41bd-bc9d-8a551497292fs︠ G.cayley_graph().show() ︡9a1d4f9c-aece-41e6-8229-0271badfeab2︡{"file":{"filename":"/projects/f351622c-d261-4717-abee-4c0bfa210e88/.sage/temp/compute4-us/31429/tmp_iEF9FU.svg","show":true,"text":null,"uuid":"1893b8b1-ef17-49f1-b40b-e53409cf3138"},"once":false}︡{"done":true}︡ ︠62a75c48-1f3d-4aaf-a816-74dade263f8as︠ G.list() ︡d95d537f-b9cd-4b85-b361-fa78aa8db82c︡{"stdout":"[(), (1,2,3,4)(5,6,7,8), (1,2,6,5)(3,7,8,4), (1,5,8,4)(2,6,7,3), (1,6,8)(2,7,4), (1,3,8)(2,7,5), (1,6,3)(4,5,7), (1,6)(2,5)(3,8)(4,7), (2,5,4)(3,6,8), (1,3)(2,4)(5,7)(6,8), (1,8)(2,7)(3,6)(4,5), (1,7)(2,3)(4,6)(5,8), (1,5,6,2)(3,4,8,7), (1,7)(2,6)(3,5)(4,8), (1,7)(2,8)(3,4)(5,6), (1,4,3,2)(5,8,7,6), (1,4)(2,8)(3,5)(6,7), (1,5)(2,8)(3,7)(4,6), (1,4,8,5)(2,3,7,6), (1,2)(3,5)(4,6)(7,8), (1,8,6)(2,4,7), (1,3,6)(4,7,5), (2,4,5)(3,8,6), (1,8,3)(2,5,7)]\n"}︡{"done":true}︡ ︠6dab7ef3-1056-41a8-b21f-ab047e353aea︠ PermutationGroup?G=A ︡20e2a3c8-fe59-4f35-9ca6-01de4c836a42︡ ︠b1d805d8-ab9e-4a20-a4f4-0a5c91afdd87s︠ cc=G.conjugacy_classes() ︡6272cdea-1ca7-4bb8-bef5-445c9c407417︡{"done":true}︡ ︠392b4fb2-e187-4e7c-a898-f56136f99534s︠ for c in cc: print c,"---", len(c.list()) ︡00e59984-cd45-4ee1-8346-b09e574440ae︡{"stdout":"Conjugacy class of () in Alternating group of order 5!/2 as a permutation group --- 1\nConjugacy class of (1,2)(3,4) in Alternating group of order 5!/2 as a permutation group --- 15\nConjugacy class of (1,2,3) in Alternating group of order 5!/2 as a permutation group --- 20\nConjugacy class of (1,2,3,4,5) in Alternating group of order 5!/2 as a permutation group --- 12\nConjugacy class of (1,2,3,5,4) in Alternating group of order 5!/2 as a permutation group --- 12\n"}︡{"done":true}︡ ︠8d23c948-753d-4f86-a7f6-5b0c1d4a6114︠ G sigma=G.list()[2] ︡4f5ea70f-9a61-40e6-ac90-b11dab3e01f7︡{"done":true} ︠0dbbc980-670c-463d-9452-6fa32b19ec26o︠ ︡408d6296-93ca-44f0-af55-45f89db66479︡ ︠83ee2a44-1b45-445e-8220-772375370f7f︠ sigma.sign ︡b76e1f4d-e919-4895-a277-0b274806e64d︡ ︠a413b1e3-8561-4546-a795-8dc79d92a994s︠ map(lambda g:[g,sigma.conjugate(g)],G.list()) ︡58ef3ba3-e5b7-404b-9815-6ca9a17e810e︡{"stderr":"Error in lines 1-1\nTraceback (most recent call last):\n File \"/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 995, in execute\n exec compile(block+'\\n', '', 'single') in namespace, locals\n File \"\", line 1, in \n File \"\", line 1, in \n File \"sage/structure/element.pyx\", line 459, in sage.structure.element.Element.__getattr__ (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/element.c:4254)\n return self.getattr_from_category(name)\n File \"sage/structure/element.pyx\", line 472, in sage.structure.element.Element.getattr_from_category (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/element.c:4363)\n return getattr_from_other_class(self, cls, name)\n File \"sage/structure/misc.pyx\", line 300, in sage.structure.misc.getattr_from_other_class (/projects/sage/sage-7.5/src/build/cythonized/sage/structure/misc.c:1928)\n raise dummy_attribute_error\nAttributeError: 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement' object has no attribute 'conjugate'\n"}︡{"done":true}︡ ︠c2611269-5890-4ff0-9407-09df6bd7181f︠