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Sage Reference Manual

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Search.setIndex({envversion:42,terms:{is_coprim:15,is_cyclotomicfield:18,odlyzko_bound_totallyr:14,mapabsolutetorelativenumberfield:22,"_descr":20,is_algebraicfield_common:20,four:[11,18],is_s_integr:15,whose:[14,15,1,19,11,18,20],typeerror:[20,23,18,15],anroot:20,concret:20,under:[9,1,18,5,20,24,7],some_el:23,hilbert_class_field_defining_polynomi:18,worth:20,everi:[18,20,1,10,0],return_pari_object:[14,11],vastli:[18,15],galois_closur:[1,18,0,16],bdd_height_iq:19,sage_object:[20,16],arprec:20,look:[14,7],algebraicnumber_bas:20,z18:18,reduced_gram_matrix:18,z12:18,factori:[18,12],vector:[9,15,22,1,18,23,20,13,21,0],zeta49:18,verif:20,aaecc:23,relativeord:9,"57a1":15,deprecationwarn:15,realintervalfield:20,numberfield_cyclotomic_with_categori:18,ngen:[9,15,16,18,20,13,0],direct:[20,18,0,24],"10e":11,get_aa_golden_ratio:20,consequ:20,second:[14,15,18,3,11,12,20,24,7],ilist:18,even:[9,15,1,18,24,20,0],clf_from_k:18,elt_fwd:20,neg:[15,21,18,19,20,0,24],biject:0,k_over_rel:18,"new":[14,9,15,18,2,4,20],ever:9,elimin:2,qflll:18,never:[20,9],here:[14,0,15,1,2,11,18,20],"8857805861880480e":0,gens_valu:[13,18,15,17],ramification_group:[15,16],primes_of_degree_one_it:[3,18],precis:[0,15,1,18,19,20],galoi:[],fraction_field:9,pari_rnfnorm_data:18,defining_polynom:18,isomorph:[],numberfieldfractionalideal_rel:21,schur:20,cohn:2,parallelepip:19,change_nam:[18,22,9,0,12],printa:2,residue_field:[18,9,15],algebraicpolynomialtrack:20,total:[],univ:14,numberfield_gener:[18,0],unit:[],describ:[20,11,15,0],would:[9,0,16,23,18,19,12,20],num_bound:18,getrecursionlimit:20,numberfieldtow:[1,18,0,21],call:[14,24,9,0,16,15,23,1,18,19,4,5,20,13,21,12,7],recommend:23,type:[14,9,0,16,15,22,1,2,10,18,23,20],tell:10,number_field_bas:[10,18],relat:[18,20,12,6],composita:18,notic:[1,9,0],warn:[18,15,0],an_muldiv_r:20,hold:[20,15],must:[14,9,0,15,23,1,18,11,20,21,7],springer:[3,14,2],complex_embed:[1,18],word:[20,23],quartic:21,henri:[14,2],work:[15,0,1,18,10,19,4,20,13,21,7],abelian_gp:[13,17],abs_non_arch:1,endow:18,overrid:18,give:[14,9,0,16,15,1,2,17,11,18,5,20,19,13,24],isolating_interv:20,want:[0,15,18,11,4,20],keep:[14,20],plist:18,krull_dimens:9,end:[20,18,5],thing:20,hom:[20,16,18,0,5],length:[14,11,9,18,21],how:[20,1,18],idealcoprim:15,answer:[20,1,18,4],verifi:[20,18,15],bcoord:15,lam:15,mess:9,chines:18,after:[3,20,18],befor:[3,20,1,18,4],wrong:[18,20,4,0,9],adic:18,demonstr:18,attempt:[20,6],third:[20,11],is_subord:9,exclud:18,k_bnf:15,maintain:20,default_base_hom:5,"_rnfisnorm":1,unramifi:[18,15,16],order:[],origin:20,composit:[22,18,0],is_squar:[20,1,18],degree_divisor:4,over:[],fall:20,becaus:[9,0,18,3,12,20,21,24],fab:11,basis_to_modul:15,vari:20,"0704285924714907491782135494859351061e12":18,fix:[0,15,16,23,1,18,3,11,20,24],"__class__":1,better:[0,15,18,10,20,24],carri:12,is_galois_absolut:0,sigma_a:7,easier:[14,11],split:[],them:[18,20,9,0],thei:[9,15,18,12,20,21,0,7],database_gap:[18,16],"break":16,promis:18,"16240385609l":11,choic:[15,21,16,23,1,18,0],numberfield_quadratic_with_categori:18,alex:18,maprelativetoabsolutenumberfield:22,unpickl:20,zeta_funct:18,totallyreal_data:2,each:[14,9,0,15,1,2,11,18,17,20,21],is_s_unit:15,mean:[18,20,1,15,0],zeta_:18,is_cm:[18,0],journ:14,is_exact:[20,23],extract:18,universalcyclotomicfield:[23,18],zetan:18,martinet1980:14,c38:[18,17],got:[1,18],unexp:20,forth:18,cyclotomic_gener:20,linear:[15,19,9,0],situat:[3,4],infin:[23,1,18,10,20,13],free:[9,15,1,18,13,21,0],standard:[23,16],nth:2,ntl:[18,0],an_addsub_expr:20,zeta9:[18,0,5],zeta8:18,angl:20,zeta6:[1,18],zeta5:[23,18],zeta4:18,zeta3:[22,1,23,18,5],filter:20,ish:18,unabl:[20,18],inverse_mod:[1,24],confus:0,sageobject:[20,16],rang:[14,9,0,15,1,2,3,18,20,19,13,21],invertible_residu:15,independ:[1,18,15],rank:[9,15,23,19,18,13,21,0],necess:[19,18],unlik:18,alreadi:[20,18],messag:4,"_assume_disc_smal":18,agre:21,dedekind:18,numberfieldelement_rel:1,sometim:[20,11,15],toi:20,too:[18,20,11,15,4],john:[14,9,15,19,1,2,11,18,13,6],convert_test:20,zeroth:6,somewhat:[3,21,15],technic:[20,12],primes_of_degree_one_list:[3,18],preserve_embed:[18,0],target:7,keyword:[20,0],provid:[23,9,0,15,22,1,18,5,13,7],torsion_gen:13,zero:[14,9,15,19,23,1,2,11,18,20,21,24],matter:[20,21],integral_elements_in_box:11,entri:[14,11,24,18],equationord:[1,9],behavior:20,l_over_k:0,l_over_f:18,is_numberfieldel:1,rai:15,rat:20,increment:[11,2],seem:[14,11],absolute_degre:[18,9,0],ellipticcurv:15,bre97:23,latter:[18,4,16],integral_split:[21,15],field_ord:23,l_to_k:[22,0],evalu:20,simplifi:[20,4],insur:20,though:[9,0],object:[14,0,16,1,2,11,18,12,20,13,24],descend_mod_pow:1,number_field_factori:18,don:[14,9,4,18],numberfieldfractionalid:[21,15],complex_numb:20,coerce_embed:[18,7],doe:[0,15,23,1,18,20,13,21],dummi:18,echelonized_basis_matrix:15,unchang:20,section:[14,11,15,7],primitive_root_of_un:18,specified_complex_embed:18,random:[9,15,23,2,3,11,18,17,20,13,21],primes_of_bounded_norm_it:18,poldegre:4,bail:18,infinityr:18,involv:[20,9,18],despit:20,explain:11,timestr:14,d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