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Sage Reference Manual

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Search.setIndex({envversion:42,terms:{finite_r:12,orthogon:[5,18,10],prefix:21,sum_of_monomi:14,consider:0,whose:[27,19,14,15,25,10],typeerror:[19,0,14,30,31,17,24,32,10],concret:[],under:[17,19,14,32],hermann:25,everi:[20,19,14,0],voronoi_relevant_vector:18,sage_object:14,affect:10,correct:[26,19,10,0],vector:[],matric:[15,19,30,10,0],cmp:[24,14],quotient_modul:[9,21],ngen:[26,10],direct:[26,1,10],consequ:19,second:[27,19,0,22,30,25],pointwise_inverse_funct:14,even:[26,19,0,14,31,25,10],euclidean:[20,19,1,18,25],neg:[25,19,1,31,14],kantor:[19,1],zero_submodul:[26,31,10],"new":[19,0,18,30,24,25,10],symmetr:[15,25,31],modulemorphismfromfunct:14,freequadraticmodule_ambient_pid:31,abov:[26,27,19,1,30,25,10],never:[19,30],here:[26,19,14,30,24,25,10],met:19,freemodulelineargroup:25,abstractli:26,interpret:[19,30],michal:25,fg_pid:[17,26,2],anymor:24,godement:25,submodule_with_basi:[31,10],is_freemodulehomspac:20,precis:[26,19,0,14,1,7,25,10],fraction_field:10,aka:[],fourier:1,isomorph:[26,25,10],linearli:[5,25,31,10],format_spec:25,total:[19,14,10],unit:5,plot:19,graphics3d:19,describ:[25,19,30,14,10],would:[19,14],num_bound:19,"__two__":19,deviat:1,call:[26,27,19,0,14,16,1,25,17,30,31,5,24,7,8,18,10,32],freemodule_submodule_with_basis_pid:[18,10,31],recommend:[25,14],type:[26,32,12,0,25,20,16,1,22,18,30,2,19,4,17,24,7,8,9,10,31],tell:0,gen_lattic:18,relat:[],notic:[26,19,0,20,30,25,10],warn:1,"__iter__":27,linear_form:25,hold:[25,30,18],must:[26,27,19,0,1,22,30,31,17,25,18,10],springer:25,word:[25,22],room:21,work:[26,19,14,25,32,10],introduc:[26,25],root:[5,19,18],overrid:26,give:[30,26,19,1,10],want:[2,19],on_basi:14,end:[20,30,25,0],thing:[26,19,30,10],hom:[26,19,0,14,20,22,30,17,25,32],"_element_constructor_":24,how:[26,19,30,14,10],freemodule_gener:[25,27,10,31],verifi:10,updat:[25,18,14],recogn:19,change_of_basi:25,after:14,befor:[19,14,0],wrong:30,make_freemoduleelement_generic_dens:19,demonstr:[19,30,22],attempt:19,third:[25,30,22,0],compfullysym:25,exclud:26,perform:[26,27,19,15,1,25,18],green:19,first:[26,27,19,14,1,22,30,31,25,18,10],order:[26,27,19,14,2,24,25,18,10],oper:[19,0,14,16,1,30,4,25,8],composit:14,over:[],becaus:[25,30,14,10],familli:25,privileg:25,orthogonalis:18,phi_on_basi:14,modules_with_basi:14,irang:25,modulemorphismfrommatrix:14,img:22,fix:[26,19,0,22,7,5,9,10],"__class__":14,better:[19,30,22,14],schmidt:[5,18],easier:0,them:[14,10,21],matrix_rep:25,thei:[26,25,19,10],safe:[26,19],modularsymbol:10,choic:[25,9,14],sparse_vector:19,unpickl:4,arrow:19,each:[26,19,0,14,22,30,31,25,32,10],debug:[26,15],side:[15,30,25,14,0],freemodule_submodule_field:[31,10],mean:[8,25,1,10,26],symmetri:25,user_to_echelon_matrix:10,wonderli:19,extract:5,unbound:25,palat:19,plot3d:19,linear:[],wherea:19,situat:[30,10],infin:[26,19,1,2,32,10],free:[],standard:[30,19,1,18,10],"__setitem__":19,zolotareff:18,zeta6:24,traceback:[26,19,0,14,1,17,30,31,5,24,32,10],zeta3:24,unabl:[19,30],subtl:26,onto:[26,32,0],sageobject:14,polyhedron:[15,18],rang:[26,12,14,0,15,1,21,19,30,25,8,9,10],render:14,freemodulehomspac:[20,22],independ:[26,27,14,31,25,10],rank:[],necess:19,restrict:[],unlik:19,alreadi:[25,31,10],set_change_of_basi:25,agre:[31,10],primari:14,cartesian:25,nomin:30,wildli:0,top:14,sometim:19,feulner:[27,19,7],too:[25,32],tol:[19,16],similarli:[26,27,14],inexact:19,freemodule_generic_field:[31,10],technic:[26,14],fullfil:0,silli:2,target:[25,18],keyword:[30,19,1,14,10],provid:[27,19,0,14,1,22,29,25,18,10],cross_product:19,project:[27,14,21,25,18,10],matter:[19,30],thu:[26,19,10,0],latitud:19,purkayastha:27,boston:25,biglieri:18,raw:25,aforement:21,seed:[26,18],"__main__":[20,24,22],seem:19,incompat:[19,30],minu:25,latter:[20,32,25],thoma:[27,19,7],inner_product:[19,31,10],though:[26,19,14,10],uses_ambient_inner_product:10,object:[27,19,22,30,25,10],monomi:14,tensorfreemodul:25,letter:25,everyth:26,don:[26,19],simplif:4,doc:24,doe:[19,0,14,30,31,24,25,10],declar:[25,19],parentmethod:[21,14],sum:[26,19,14,15,1,25,10],dot:[5,6,23,19],quadraticfield:[19,9,10],biject:0,opposit:19,random:[26,19,18,10],sage:[0,1,2,3,4,5,6,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,7,30,31,32],radiu:[15,18],involv:[25,10],despit:[26,0],vectorspacemorph:30,column_matrix:0,choleski:15,oct:[8,16,1],congruenc:[24,10],wide:19,stop:19,cryptographi:18,report:10,bar:19,"_add_":24,patch:26,bad:30,soroosh:28,fair:19,diamond_cut:15,result:[26,27,19,0,14,1,31,25,18,10],fail:[5,10],themselv:14,best:[18,14],definit:[19,0,1,31,25,10],tensor:[25,19,31,10],wikipedia:19,elementwis:4,mul:14,attribut:[18,14],accord:[25,19],"17330740711759e15":18,extend:[26,30,14,10,32],vectorspacehomspace_with_categori:[20,22],cuspid:[24,10],extens:[24,32,0],finitedimensionalmoduleswithbasi:24,expos:25,howev:[26,19,0,30,31,25,18,10],hamming_weight:[19,7],uni:14,kwd:[26,19,0,14,4,18,10],conjug:19,"2nd":25,permut:14,wider:14,diff:[6,19],integermod_int64:12,assum:[26,25,19,14],degener:26,nonsens:[19,10],numpi:[],three:[22,19,10,0],been:[26,24,19,25],much:[2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