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Sage Reference Manual

1
Search.setIndex({envversion:42,terms:{represent:[7,6,3,10,2],finite_r:[0,6,2,4,5,7,8,9,10,11,12,13,14,15,16,17],code:[4,13,17],partial:[0,11],is_subcategori:4,finite_field_prime_modn:[0,6,17,10],illustr:[8,15,4],global:4,roe:[0,13,16],four:16,residuefield:0,prefix:13,ellipt:0,deprecationwarn:[7,6,15],follow:[4,13,10,15,16,2],disk:16,whose:[8,11,3,5],typeerror:[3,12],depend:4,albrecht:[5,17,10,2],kfix:[14,11,12],demey:[15,13],elsewher:15,articl:13,get_object:4,pth_root:3,under:[6,10,16],some_el:[3,13],norm:0,inject:11,digit:7,random:[6,4,7,10,13,15],everi:[3,13,16,2],string:[8,5,13,2],fals:[6,3,4,5,7,9,10,11,13,2,16,17],uniquefactori:[0,4],sage_object:[10,16,2],fall:[0,13],veri:[0,4],affect:4,ticket:[0,3,4,9,10,13,15,2],late_import:7,seealso:12,log_repr:[6,10,2],foo:13,doesn:0,level:3,z16:4,list:[4,9,13,15,5,2],residuefieldfactori:0,iter:[15,13,10],factori:[0,4],arithmeticerror:5,vector:13,frobeniusendomorphism_givaro:12,small:0,initialis:4,dimens:[4,13],finitefield_ntl_gf2eel:2,work:[0,6,11,3,13],factored_unit_ord:[4,13],natur:15,ngen:[3,13],direct:[8,4],consequ:4,second:[4,16],multi_polynomial_id:0,pass:13,further:13,odd:4,codomain:[0,11,12],append:13,compat:[7,6,3,13,16],index:[0,1,3,9,16],what:4,reductionmap:0,compar:[3,13],neg:[0,4],section:[0,11,12],set_random_se:7,integer_represent:[10,2],integermod:4,version:[0,3,4,8,13,17,15,5],is_irreduc:7,"new":[0,6,10,16,13],method:[6,3,7,13,11,10,2],contrast:4,construct:[6,3,4,7,8,13,11,17,15],is_finit:[3,4,13],finitefield_pari_ffelt_with_categori:10,cython:[4,2],coerce_map_from:0,gener:[0,6,2,3,4,5,7,8,10,14,13,15,16,17],never:3,coeffici:[0,13,2],here:[14,4,13],closur:[],shouldn:10,simon:4,let:3,conway_polynomial_:13,lex:0,surject:11,modifi:16,sinc:[4,13,11,14,17,15],valu:[3,13,10],square_roots_of_on:4,search:1,divisor:[0,4,16,13],unpickle_finitefieldelement_pari_ffelt:5,root:[6,2,3,4,7,8,10,13,15,5,17],precis:4,c18:4,algebraic_closure_finite_field:[3,13],behav:4,implement:[],proof:[4,13],quotient:[0,4,16,13],is_perfect:13,c140:4,via:[],finitefielditer:13,extra:[0,4,13],pseudoconwaylattic:16,primit:[6,7,8,9,13,17,15,16],modul:[7,1,3],element_givaro:[6,10],deprec:[],"boolean":[3,13,16],subcategori:4,famili:[3,16],powerseriesr:[6,10],coercion:[0,3,4,10,13],convert_map_from:0,unit:[13,4,10,2],highli:10,from:[0,6,3,4,7,9,13,11,12,5,15,16,2],unit_group_expon:[4,13],would:4,memori:[6,10],has_coerce_map_from:4,frob:[6,11,12,13],two:[5,3,9,4,13],next:[13,8,15,4,10],call:[0,6,3,4,5,7,10,11,12,13,15,16,17],finitefield_givaro_with_categori:10,recommend:3,nativeintstruct:2,care:4,type:[],commut:4,more:[7,6,4,10,13],gf2e:2,identitymorph:[6,13],desir:13,minim:[6,3,7,8,10,13,16,2],comparison:[6,11,13],henc:[11,4,13],relat:4,problem:[13,10],probabilist:4,frobeniusendomorphism_prim:14,warn:[0,4],a_times_b_plus_c:[6,10],particular:[3,4],known:16,rueth:13,must:[6,4,7,8,13,10,15,17],logarithm:5,none:[0,6,2,3,4,7,8,9,10,13,15,17],join:4,sectionfinitefieldhomomorphism_prim:14,alia:[8,3],flori:16,uniqu:[0,3,4,13,16,5],conceptu:3,groebner_basi:0,ubar:0,can:[0,6,3,4,9,13,15,16,2],endian:7,create_key_and_extra_arg:[0,4],malb:[10,2],zech:[6,10],def:4,pierr:16,control:[7,6,10],bogu:4,give:[7,6,17,13,2],scrimshaw:13,calcul:[0,6,10],accept:3,t_fix:[11,12],is_noetherian:4,want:4,david:[0,2,4,16,13],cardin:[0,6,3,4,7,8,10,13,2],krull_dimens:4,alwai:[3,4,13,11,17,16],cours:[15,4],multipl:[6,2,3,4,5,7,8,10,13,15,16,17],z21:13,tbar:0,rather:16,anoth:13,hom:[0,11,9,12],first_lexicograph:9,perhap:4,"_element_constructor_":10,divis:4,how:[13,10],fpp:0,answer:4,symposium:16,updat:4,map:[0,3,4,13,11,14,15],algebra:[],chines:4,after:[0,7],variant:13,sagex:4,befor:[0,2],unit_group:4,mai:[6,3,4,10],end:9,is_integermodr:4,data:[0,3,10],c10:4,essenti:0,johnson:13,tfix:[11,12],divid:[0,4,16],correspond:[3,4],residuefinitefield_givaro_with_categori:0,element:[],inform:[4,2],commutativ:4,allow:4,zbar:0,finitefield_pari_ffelt:[0,8],lambda:3,order:[0,6,2,3,4,5,7,8,9,10,11,13,15,16,17],multivari:0,inessenti:0,composit:4,is_squar:[3,5,4,10,2],over:[0,6,2,3,4,5,7,8,10,11,13,15,16,17],move:0,becaus:[3,13,10],algebraicclosurefinitefield_pseudo_conway_with_categori:3,report:4,through:13,same:[3,14,4,13,15],equip:4,paramet:4,perfect:[13,10],log_to_int:[6,10],fetch_int:[7,6,10,2],group:[6,4,5,7,8,9,13,17,15,16,2],save:[15,4],as_finite_field_el:3,chosen:[4,5],fix:[0,4,9,10,11,12,14,15,2],fixed_field:[14,11,12],whether:[0,4,16,13],drawback:13,algebraicclosurefinitefield:3,pcl:16,comprehens:15,therefor:13,might:[4,13],easier:13,ideal:[0,4],them:[3,13],doctest:[0,6,4,7,13,10,15,5,2],"return":[0,6,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17],thei:[3,16,15],python:[15,5,4,10],extra_arg:4,supersed:13,poly_repr:[7,6,10],initi:[0,3,4,8,13,17,15,5],ring_of_integ:0,framework:0,instead:[0,6,7,10,13,5],now:[0,13],finitefield_prime_modn:[0,17],choic:4,conway_polynomi:[3,5,16],name:[0,6,2,3,4,7,8,10,11,12,13,15,5,17],trac:[0,6,3,4,7,9,10,13,15,2],edit:10,revert:4,unpickl:13,separ:13,each:[3,4,13],finitepolyextel:[5,10,2],found:[0,4],prime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