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Sage Reference Manual

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Search.setIndex({envversion:42,terms:{four:[30,34,16],prefix:[30,34,16,42],is_open:29,jacobian_matrix:0,graph_v:[9,32],whose:[0,24,34,25,36,28,4,37,14,30,5,41,16,17,38,6,18,19,42],typeerror:25,graph_c:4,hermann:36,intersection_nam:[0,33,32,24,41,34,2,36,37,4,30,5,15,16,17,38,6,19,42],"01_0":28,everi:34,"_kl":24,nice_deriv:[18,10],arcco:[2,18,26],sage_object:[30,26],affect:18,c_spher:[0,34,35,4,30,20,16,6,19,42],tangentspac:[9,3,28,16,35],spher_coord:16,vector:[0,8,36,12,13,3,37,4,15,16,17,6,42],red:[30,4,10],set_coord:20,j_k:[24,28],direct:[2,18,28,17],consequ:[2,13,37,41],second:[24,34,10,28,20,16],blue:[9,20,32],asin:[2,18],disk:[0,34,35,28,30,20,16,19,15],neg:[33,24,34,28,16,41],"new":[0,2,3,32,5,6,9,13,14,20,16,17,19,24,25,28,29,30,4,33,34,35,37,38,41,42],symmetr:[0,41,24,28,16],topolog:[7,8],uv_to_r:34,behavior:[18,3,10],here:[8,24,34,35,3,26,28,30,5,15,16,38,19,42],freemodulelineargroup:36,set_axes_label:10,p_2:3,interpret:[34,2,37,30,16,42],p_1:20,michal:[0,2,3,32,5,6,9,10,20,18,19,24,26,28,29,30,33,35,37,38,41,42],godement:36,precis:[24,34,26,28,32,30,16,18],ext_pow_free_modul:17,permit:[2,37],stereos_w:[24,15],isomorph:[0,19],differentiabl:16,total:32,label_color:[9,20],unit:[0,34,2,28,30,5,15,16,35,38,19,42],plot:[4,9,10,32,30,20,42],graphics3d:[4,9,10,32,30,20],describ:[8,24,34,35,28,16,41],would:[30,20,42],has_coerce_map_from:[33,2,36,37,5,17,38,41],call:[33,32,9,24,34,10,35,25,36,26,28,4,37,30,20,16,6,18,19,42],typo:30,recommend:[13,36,29,30,20,17,42],type:[0,2,3,32,6,10,13,14,15,16,17,18,19,24,25,26,28,29,30,4,33,34,35,36,37,41,42],aut:35,relat:[6,30,19,16,35],notic:[41,19],berlin:[34,16],linear_form:41,hold:[17,3,10],must:[0,2,32,5,6,9,10,13,20,16,17,18,19,15,24,26,28,30,4,34,36,37,38,42],multicoordfunct:[30,26,19],springer:[0,2,3,32,5,6,9,13,14,20,16,17,19,24,25,28,29,30,4,33,34,35,37,38,41,42],word:[30,18,26,28,42],ch_xyz_xyz:19,differentialform:6,endow:[35,13,3,30,42],i_k:24,i_i:24,give:[32,9,34,10,28,4,30,20,16,42],diffscalarfieldalgebra:[33,37,16,17,38,41],cartan:[6,28],subchart:[2,30,34,19,42],canonicalize_rad:10,ordinari:[30,42],hom:[0,14,19,4,25],coordcofram:[35,42],updat:[2,16],coord_expr:4,end_point_offset:4,change_of_basi:[35,16],after:[2,29,34,16,37],x_min:[30,32],wrong:[30,10],adic:[30,34,16],law:[38,14,36,5,25],meaningful:30,third:[2,24,20,37],compfullysym:[28,16],canonical_chart:13,first:[32,24,34,2,13,28,4,37,30,15,16,35,6,41,42],order:[24,34,2,28,30,20,16,35,19,42],oper:[0,32,24,34,2,13,36,26,28,4,37,29,30,5,15,16,35,38,18,19,42],v_v:24,composit:[0,14,19,4,25],over:[0,2,3,32,5,6,10,13,14,15,16,17,18,19,24,25,26,28,30,33,34,36,37,38,41,42],display_comp:[24,28],becaus:[33,2,3,28,37,16,41],v_d:28,coord_funct:[0,34,2,26,28,4,37,41,16,19],privileg:[30,42],vari:30,tensorfieldfreemodul:[33,41,28,16],vectorfieldfreemodul:[41,32,36,28,16],irang:[34,24,28,16,35],fix:[6,30,32,16],declare_union:[0,33,32,24,41,34,2,36,37,4,29,30,5,15,16,17,38,6,19,42],old_chart:20,them:[24,34,2,28,4,37,30,20,16,19,42],v_1:16,v_2:16,proce:[34,16],arrow:[18,9,26,32],each:[0,24,34,35,26,28,32,30,41,16,6,18,19,42],side:[30,34,16,42],mean:[0,32,24,34,2,13,3,28,4,37,30,5,20,35,38,6,18,19,42],diff_degre:[13,16,42],unbound:16,plot3d:30,cosin:[2,18,26],coord_func_symb:[0,2,26,28,37,30,18],infin:[34,13,32,30,4,16,42],free:[33,8,32,9,24,36,35,3,28,4,37,15,16,17,6,41],standard:[0,33,9,24,41,34,10,2,28,32,35,37,15,16,17,6,18,19],convent:[24,26,28,32,16,18,41],angl:41,traceback:[9,24,34,25,26,28,32,16,6,18],c_cart_d:[30,15,42,28],confus:10,sageobject:[30,26],mathbb:[2,13],rang:[34,35,26,32,30,4,16,18,42],render:10,independ:[2,37,34,6],rank:[33,8,24,3,28,32,16,17,6,41],restrict:[33,37,32,24,41,34,2,36,28,4,35,30,5,15,16,17,38,19,42],jacobian_det:26,instruct:[34,16],alreadi:[41,24,2,28,30,20,18,19,42],a_inter_b:29,thick:[30,4],tangentvector:[9,3],cartesian:[0,33,32,9,41,34,2,26,28,4,30,20,16,35,6,42,19,15],top:[2,34],xim:41,necessarili:[6,17],similarli:[9,24,34,28,4,14,30,32,16,19],consol:[24,2,28,30,18,19],f_2:[35,28,32],namespac:[35,29,36,17],abrig:24,conserv:24,zero_scalar_field:[2,37,34],manifold_homset:[14,25],keyword:[30,28],provid:[0,2,32,6,9,13,14,20,16,17,19,15,24,25,26,28,29,30,4,34,36,37,41,42],expr:[0,24,10,2,26,28,32,37,16,35,18,19],project:[0,8,34,19,16],matter:[30,24,34,16,42],boston:36,raw:[30,34,16,42],ch_spher_cart:19,minu:[38,2,5,15,19],en_w:[24,15],latter:[32,34,2,42,37,4,29,30,20,16,18,15],transmit:30,even:[2,3,18,37,16],shall:[10,26,32,30,4,18],object:[0,32,9,24,34,10,2,36,26,37,4,35,30,20,16,17,18,19,15],regular:[34,19,16],letter:[24,34,35,30,16,41,42],simplic:10,doi:[13,16],dom:19,doe:[24,34,10,30,5,16,38,18,19,42],declar:[0,32,34,2,13,28,4,37,29,30,20,16,18,19,42],section:8,dot:24,opposit:24,random:[33,34,2,28,29,30,20,16,35,19],sage:[0,2,3,4,5,6,8,9,10,13,14,20,16,17,18,19,15,24,25,26,28,29,30,32,33,34,35,36,37,38,41,42],radiu:30,syntax:[13,30,42],involv:[9,24,34,10,2,26,28,32,37,30,5,16,38,18,41,42],despit:10,"__call__":[38,5,4],infti:[30,34,16],reconstruct:26,t02:17,t01:17,riemannian:[33,24,2,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