Sage Reference Manual
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52,54,12,43],defn:[16,52,36,25],"break":54,singmast:30,rationalfield:34,directproduct:[52,50,51],determinant_charact:2,without:[44,54,51],affine_group:[42,29],model:[12,43,31],dimension:[54,12,29],execut:52,among:54,dihedr:[33,5,25,49,47,48,51,52,54],cateori:28,resp:[35,11,34],is_semi_regular:52,rest:43,invalid:51,aspect:[43,54],speed:[32,30,31],versu:52,europ:43,miscellan:[],alternatinggroup:[52,2,34,54,5],except:[33,12,47],identif:52,irreducible_charact:[21,2,52],real:[35,38,19,13],abeliangroupel:[27,28,31],psl:[48,52,25,54],normalize_args_:13,read:30,lowercentralseri:51,relabel:52,psp:[48,52,54],rear:[52,30],psu:[48,52,54],composition_seri:52,chap69:49,fox_deriv:10,integ:[2,3,5,8,9,10,50,13,18,19,21,22,24,26,27,28,29,30,31,33,34,35,38,23,39,41,42,43,46,47,49,51,52,54],either:[18,10,54,11,47,52,28,43,30,31],output:[2,3,5,7,8,9,10,50,12,13,18,20,21,22,24,26,28,30,31,33,34,49,37,23,39,41,42,43,47,51,52,53,54],magma:31,disjoint_union_enumerated_set:54,automorphismgroup:52,conjugacy_classes_subgroup:52,nicola:52,cubie_fac:30,nonzero:2,saliola:2,definit:[33,35,36,50,12,13,52],legal:[30,31],inject:52,base_r:[33,35,36,13,49,38,23,39,26,41,54,31],complic:[52,21,51],permutationgroup:[33,34,25,49,51,52,54],refer:[54,49,38,43,12,51,52,42,29,30,31],word_problem:[34,20,21,27,30,31],power:[2,47,19,54,10,43,39,12,42,29,31],smith_form_gen:3,grouplibgap:14,ration:[32,19,35,21,38,10,54,24,11,39,26,42,29,31],is_rat:19,broken:54,homspac:6,semidirect_product:[52,51],group_gener:[24,11,46],immut:[20,23,8,27,31],"throw":33,artin:[],comparison:[10,51],central:[52,2],joyner:[33,34,22,6,20,21,49,9,47,38,26,52,13,41,27,23,25,54,30,31],degre:[2,3,49,11,13,16,20,21,25,26,28,29,31,33,34,36,38,23,39,41,42,44,47,51,52,54],act:[34,5,35,51,54,11,39,12,13,52,42,29,30],morphism:[32,4,22,6,25,24,51,52,28],routin:[3,31],effici:[52,47],eval:[52,33,49],determint:13,elementari:[52,42,54,31],permgroup_el:34,global_opt:16,mathematiqu:43,invert_v:16,your:[14,25,21,50,52],ontuplesset:52,log:47,start:[50,54],interfac:[2,33,49,50,52,14],low:49,lot:[43,30],strictli:54,is_cycl:[3,5,51,52,54,31],polycycl:52,"__invert__":[28,50,8,9],tupl:[2,3,7,8,10,50,20,21,27,28,31,33,34,49,36,23,43,46,47,51,52,54],regard:[30,31],procedur:[49,31],inject_vari:[43,10,51],longer:31,multiplication_nam:47,tripl:[49,31],possibl:[7,10,13,52,43,30],"default":[37,3,7,49,9,10,11,13,19,20,21,28,30,31,33,34,35,23,43,47,50,51,52,54],index_set:[35,11,46,54,10],miguel:[43,10,51],embed:[52,32,28,51],sylowsubgroup:52,clrr:30,hellman:47,creat:[48,32,52,3,5,35,54,23,49,10,43,46,24,11,51,34,42,25,29,30,31],dual_abelian_group:[20,23,31],mike:52,semidihedralgroup:54,is_grouphomset:4,clrf:30,file:52,again:[52,3,30,51],googl:52,hybrid:30,orient:43,qqbar:32,field:[2,22,49,9,10,11,13,16,19,20,21,24,25,26,28,29,37,32,33,35,36,38,23,39,41,42,47,52,53,31,54],freegroup:[18,33,52,47,50,10,51,14,43],valid:[37,51,52,43,30,31],make_permgroup_element_v2:34,you:[23,33,5,54,21,9,10,43,50,47,52,51,14,42,28,29,30,31],sequenc:[52,31],symbol:[52,28,54,30,5],vertex:12,shortlex:51,polynomi:[34,49,10,54,52,43],is_matrixgroupel:9,reduc:[52,51,43,5],directori:27,descript:[52,54],finitelygeneratedmatrixgroup_gap_with_categori:[49,9],symmetricgroup:[2,34,19,5,7,52,54,30],potenti:32,additiveabeliangroup_class:3,represent:[33,34,5,35,54,13,49,9,47,38,37,50,39,51,52,26,41,42,43,30,31],all:[3,5,7,49,12,13,16,18,19,21,26,28,29,30,31,33,35,36,38,23,41,42,43,47,51,52,54],forget:[25,42,29,31],illustr:[34,43,54],alg:12,matrix_group:[49,33,39],scalar:[2,9,23],cameron:[52,54,30],follow:[34,22,35,51,47,54,48,24,13,52,43,30,31],disk:43,vertex_label:38,rewrot:30,articl:[47,29,12,51,52,42,43],is_matrixgrouphomset:53,init:[16,32],program:[25,30],orthogonalmatrixgroup_gener:13,operand:9,norm:2,fals:[3,5,8,9,10,11,18,19,20,21,27,28,30,31,32,33,34,35,38,43,46,47,49,50,51,52,53,54],ellipticcurvetorsionsubgroup_with_categori:32,util:3,euclideangroup:29,veri:[33,25,47,23,12,52],ticket:[16,32,33,22,10,54,47,51,52,43,31],strand:43,induct:2,generator_matric:49,list:[2,3,5,7,8,9,10,50,12,19,20,21,22,27,28,30,31,33,34,49,23,43,46,47,48,51,52,54],matrixgroupmorphism_im_gen:22,ramification_module_decomposition_hurwitz_curv:[52,54],adjust:32,small:[33,5,49,38,47,51,52,54],conjugacy_classes_iter:54,module_composition_factor:[33,49],abeliangroup_subgroup:31,quicker:19,unnorm:43,automorphism_group:52,finitegroup:[52,18,36],zero:[28,37,3,10,31],design:49,pass:[32,10,50,51,52,28,43,30],further:52,string_to_tupl:34,isnorm:52,bilinear:[35,13],what:[52,42,29],abc:[46,6,20,8,23,27,31],sub:31,section:[49,31],lpurpl:30,abl:32,version:[2,5,6,49,9,11,12,13,16,25,22,24,26,29,30,33,34,35,36,38,41,42,46,47,51,52,53],is_irreduc:2,intersect:[52,47,31],as_finitely_presented_group:52,polgaloi:52,method:[5,6,7,49,10,16,19,20,21,22,25,27,30,31,32,33,34,38,23,43,47,51,52,54],full:[33,37,9,47,51,52,42,54],hash:[54,47],additiveabeliangroupwrapp:32,sophist:52,behaviour:52,modular:[49,54],ambient_spac:24,solari:52,abeliangroup_class:[28,31],strong:52,modifi:[41,52,26],smit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