Search.setIndex({envversion:42,terms:{freealgebrael:[26,21],differentialgcalgebra:11,woodi:[16,15,19],four:16,prefix:[20,9,24,1],woodz:[16,15,19],"0_2":16,"0_3":16,"0_0":16,"0_1":16,whose:[0,18,10,11,5,27,6,7,15],typeerror:[16,25,27,12,11],orthogon:6,under:[23,11,1,20,12,26],preliealgebra:22,digit:[0,16],everi:[16,1,20,24,2,25,6,7,13],vastli:17,steenrod_algebra:[16,15,19],map_coeffici:20,quantiz:[7,28],sage_object:11,interior_product:7,degeneraci:26,vector:[0,16,17,10,11,3,2,25,27,6,7,14,13,28],math:[0,16,9,1,24,4,5,7,15],dual_pbw_basi:4,ngen:[16,17,12,26,27,6,7,13,28],direct:[16,13,12],consequ:1,second:[0,16,18,19,11,1,2,25,5,6,13],int_express:[25,13,2],cyclic_right_subid:6,even:[11,1,12,2,25,13,6,28],theta_series_vector:6,s_4:16,neg:[0,16,17,18,19,25,15],quaternionfractionalid:6,birkhoff:[26,4,21],make_mono_admiss:0,"new":[5,16,6,15,12],symmetr:[18,24,12,20,5,7,28],topolog:16,long_option_nam:[25,13,2],ongo:13,elimin:0,abov:[16,17,18,20,12,25,26,6,7],never:[26,18,20],here:[16,17,19,11,1,20,2,26,22,15,6,7,13],path:[25,13,2],interpret:[18,7,14,20,19],affineniltemperleyliebtypea:9,precis:[16,6,19,1],galoi:18,groupalgebra:12,fraction_field:20,q_e1:19,q_e0:19,studi:[0,16],isomorph:[16,18,11,1,20,26,6,7],schur:[],nilcoxet:22,linearli:[0,16,6],total:11,univ:[16,1],unit:[],constuct:5,cliffordalgebra:[7,28],describ:[20,15,19,11],would:[0,6,13],arnon_a_long:[16,15],num_bound:27,has_coerce_map_from:12,call:[0,1,24,4,5,6,7,9,11,12,13,15,16,17,18,19,2,20,25,26,27,28],type:[],tell:[13,2],apar:25,finitedimensionalalgebrahomset:23,relat:[0,16,9,19,11,1,24,26,18,7,15,28],warn:[25,6,13,2],steenrodalgebra_gener:[16,15,19],hold:5,must:[0,16,23,17,19,1,11,2,25,4,27,6,7,13],springer:18,word:[26,11,4,1],multinomi:0,lambda:[16,19,1,20,6,28],work:[0,16,17,1,11,20,2,25,26,5,15,6,7,13],unitari:[27,23,14],introduc:26,root:[9,24,1],overrid:11,i_m:0,give:[0,16,17,19,11,1,24,2,25,26,13,7,28],unit_pseudoscalar:7,allud:12,cartan:[0,16,15,19,1],want:[16,6,15],david:[26,6,3,12,21],on_basi:7,brandtmodul:6,shuffl:[],thing:[16,26],krain:16,hom:23,classifi:16,how:[19,7,11,12,1],answer:[16,12,1],verifi:[5,25,6,7,2],updat:12,lam:[24,20],recogn:19,gradedcommut:22,after:[0,16,18,19],diagram:24,befor:[6,20,19],is_decompos:16,beauti:16,i_2:0,i_1:0,domin:20,third:[16,25,13,15,2],environ:[25,13,2],quaternionalgebraelement_rational_field:6,mechan:1,unramifi:6,order:[16,18,19,1,20,12,2,25,26,5,6,13],oper:[0,16,11,1,2,25,13,7,28],composit:20,deform:1,over:[16,23,17,18,10,1,11,20,12,15,25,26,4,5,27,6,7,14,13,28],becaus:[0,16,6,7,1],matsumoto:1,chain_complex:7,nilcoxeteralgebra:24,incid:22,ideal_fract:6,comm_rlex_long:[16,19],fit:12,fix:[0,18,12,6,7,15],better:11,exterioralgebraboundari:7,induct:16,hamilton_quatalg:[17,3],them:[0,16,15,11],thei:[0,16,19,11,1,12,2,7],trail:[0,16,19],interrupt:[25,13,2],schurtensormodul:18,kohnen:6,choic:[16,6,7,15,1],postnikov:9,reutenau:4,haphazardli:1,each:[0,16,18,19,11,1,12,6,7,15,28],complet:[22,25],side:[0,18,11,1,25,26,27,7,14],mean:[16,13,25,6,2,15],quadratic_form:[6,7],palmieri:[0,16,19,11,12,15],hann:[25,13,2],emul:13,symmetricgroup:12,newli:16,rewrit:[6,7,20],daniel:1,adapt:13,arnon_a:[16,15],arnon_c:[16,15],linear:[0,16,23,18,1,12,5,6,7],algebrael:[3,21,5,2,14,28],situat:[16,12],infin:[16,19,25,27,6,15],free:[],standard:[16,18,19,1,2,25,5,15,6,7,13],nth:[0,16],publ:16,workaround:1,milnor_basi:15,traceback:[16,17,9,19,1,11,24,12,25,26,4,5,27,6,13],filter:[7,15],heck:[],isn:16,"2_1":16,confus:5,sageobject:11,rang:[16,11,1,20,26,4,6,7,28],right_id:6,grade:[],pst_rlex:[16,15,19],independ:[0,6],rank:[6,7,24,17,11],restrict:[16,15,26,6,7,13],alreadi:[0,25,17],messag:15,conjugaci:1,agre:[26,4],primari:[0,16,27],steenrod_misc:19,cartesian:7,rewritten:7,top:16,sometim:16,master:[25,13,2],similarli:15,john:[0,16,19,11,12,15],wood_i:[16,15],seper:[25,13,2],is_nilpot:[16,14],lower:[25,19],wood_z:[16,15],somewhat:1,wall_long_mono_to_str:19,proposit:6,grassmann:7,target:11,keyword:[16,25,13,11,2],princeton:[0,16],provid:[16,17,25,26,7,15],project:[25,13,7,2],free_algebra_quotient_el:3,simple_reflect:[9,1],kazhdan:1,fashion:5,mind:20,aforement:16,seed:[25,13,2],wall_mono_to_str:19,seen:28,seem:[7,12],minu:28,latter:20,modp_splitting_data:6,thoma:[18,24],though:[11,12,1],object:[16,17,11,20,13,25,22,6,7,2,15],what:16,monomi:[0,16,17,11,20,2,26,7,15,28],current_r:[13,2],doi:1,don:[16,11,20,12,6,15],doc:[25,13,2],doe:[0,9,11,12,26,13],g_algebra:26,comm_llex:[16,15,19],sum:[0,16,11,1,24,12,20,4,6],quadraticfield:6,opposit:13,random:[12,2,25,27,6,14,13],sage:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],syntax:[25,13,11,2],pst_deg:[16,15,19],iwahori_hecke_algebra:[24,1],quadratr:7,absolut:[25,13,2],menu:[25,13,2],comm_deg:[16,15,19],s_t:19,idiosyncrat:1,is_commut:[16,12,26,4,27,6,7,13],axiom:5,intvec:[25,13,2],cochain:7,counit_on_basi:[16,12],finite_dimensional_algebra_morph:23,congruent:0,report:[0,25,13,2],net:[25,13,2],bar:[5,1],piggi:1,twice:[16,6,18],bad:[25,13,2],bab:4,bac:4,baa:4,datatyp:[25,13,2],num:16,result:[0,16,18,19,2,25,5,13,7,15],fail:0,hash:[19,1],subject:[6,7,9,28,1],coxet:[],ix86:[25,13,2],said:[7,11],tensor:[16,7,18],is_valid_profil:19,cabcba:4,wikipedia:[18,1,4,5,7,28],figur:16,mul:[26,4],approach:[16,9],attribut:[16,25,13,2],accord:16,extend:[16,7],maximal_ord:6,extens:[16,28],lazi:[5,16],steenrod_algebra_misc:[15,19],hashabl:19,fault:12,howev:[26,13,20],algebraswithbasi:[9,4],against:25,browser:[25,13,2],com:7,kwd:[16,6,7,15],"2nd":11,permut:[7,18,19,12],diff:11,assum:[16,9,11,1,26,27,7,14],degener:[13,7],wood_abcdedfg_i:19,three:[0,6,17,26,1],been:[0,16,15,19,11],ringhomset_gener:23,trigger:1,interest:[7,28,11],basic:[16,2,1],quickli:[22,1],commutative_r:13,maximal_id:[27,23],argument:[0,16,17,19,1,11,2,25,26,4,5,15,6,7,13],lift:[13,7,11],coproduct_on_basi:[16,7,4,12,20],ident:[5,27,26,19,28],properti:[16,18,1,2,6,7,28],normal_form:[25,13,2],freealgebra:[17,21,25,26,5,13,2],calcul:[18,1],pairwis:2,differential_multigrad:11,koszul:11,homset:23,anticommut:[0,7,11],kwarg:27,i_elt:20,exterior:[0,16,7,22,11],poly_reduc:[25,13,2],sever:[16,15,11],product_on_basi:[16,9,1,20,12,26,4,18,15],weyl_group:9,perform:15,suggest:1,make:[16,19,11,20,12,13,25,6,2,15],complex:7,split:6,q_e2:19,coxeter_group:1,nil:[],lyndon:[26,4],hand:[16,18,1],rais:[23,17,19,11,25,27,6],reuten1993:4,redefin:11,thu:[16,26,20,15,11],inherit:[16,7,11],weakli:18,thi:[0,1,24,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,22,2,20,25,26,27,28],has_no_braid_rel:9,left:[16,18,1,25,27,6,14,28],identifi:[25,6,7,13,2],just:[0,16,11,1,6,7,14,15],basis_mono_to_str:15,constant_coeffici:7,finitedimensionalalgebraid:[27,23,10],cliffordalgebrael:7,yet:[26,6,7,13],characterist:[16,18,11,2,25,6,14,13,28],easi:[16,22,11],interfer:26,conjug:[6,7,20],schur_algebra:18,els:[16,19],expon:[16,11],elt:[16,1,21,26,4,7,14,28],sanit:7,applic:[5,16,6],bbbaaa:4,preserv:[7,11],combinatorialfreemodule_tensor:18,inadmiss:0,specif:18,arbitrari:[16,7,18,12],negat:7,pst_llex:[16,15,19],groenewold:28,underli:[16,23,17,9,1,3,2,25,26,27,6,7,13],right:[0,16,18,1,25,27,6,14,28],nilpot:14,deal:7,manual:16,interv:7,maxim:[27,6],intern:[16,11,2,25,13,7,15],lift_module_morph:7,indirect:[0,16,15,26,6,13,28],module_express:[25,13,2],degree_on_basi:[16,7,15],subclass:19,track:0,kleinfourgroup:12,condit:[16,19,12,25,26,6],core:[25,13,2],plu:[16,6,18],sensibl:12,annal:[0,5],subspac:[6,7,11],vector_spac:[6,10],cabacb:4,clifford_conjug:7,quaternion:[],convert_perm:19,bruhat:1,"super":7,plug:19,"_mono_to_str":19,algebra_gener:[16,9,1,24,12,26,4,5,7,28],deneufchatel:4,slightli:1,literatur:16,unfortun:[16,12],bbca:4,wxyz:7,steenrodalgebra:[0,16,15,19],adem:[0,16,15,19],produc:0,lieb:[],duke:9,soc:[5,16,15,4,1],degbound:[25,13,26],xyz:[6,26,4],"float":6,encod:7,bound:[16,24,13,25,26,6,2,15],funtion:19,q_exp:[0,16],suffici:20,support:[16,17,1,26,6,7,13],transform:16,freealgebra_gener:[13,26],avail:[16,17,1,2,25,26,22,13],finitedimension:[5,22],fraction:[6,20,1],overhead:6,not_a_basi:19,analysi:5,acbcba:4,form:[0,16,17,9,10,19,1,12,2,25,26,27,5,15,6,7,13],altogeth:0,normalize_profil:19,synonym:[16,19,2,25,13,15],"true":[0,1,24,3,4,5,6,7,9,11,12,13,14,15,16,17,18,19,21,2,23,20,25,26,27,28],reset:[25,13,2],max_slop:15,coeff:[0,16],maximum:[16,11],until:0,cabcab:4,fundament:1,classic:20,hardcod:6,exist:[16,1,25,5,27,7,14],check:[16,23,18,19,11,1,20,26,4,5,27,6,7,14,15],is_equival:6,when:[0,16,19,11,1,2,25,15,6,7,13],role:[16,7],jone:1,test:[0,16,17,9,19,1,20,11,24,12,21,25,26,3,4,27,18,6,7,13],node:24,convert_to_milnor_matrix:15,intend:[15,1],term_repr:28,consid:[16,18,2,25,13,7],kottwitz:1,additiveabeliangroup_fixed_gens_with_categori:11,faster:[0,26,7,15],furthermor:[0,16,26,19],a_long:16,freealgebraquotientel:[17,3],ignor:[0,16,6,15],freemonoid:26,time:[16,13,1,20,2,25,6,15],matrix_act:17,concept:7,chain:7,global:[13,26],row:[0,27,6,10],decid:6,depend:[0,16,19,1,2,25,13,7],inject_shorthand:1,rueth:6,mphost:[25,13,2],text:19,rham:7,xi_i:15,multilinear:7,to_dual_pbw_el:4,string:[16,19,11,2,25,4,27,15,13,7,6,28],zhang:15,exact:[6,12],dim:[7,15],singular_idx_fil:[25,13,2],gram_matrix:6,level:[6,15,11],iter:[0,16,28,11],dic:11,item:11,is_associ:27,quick:16,prevent:12,slower:6,sign:[0,28,11],"_repr_term":15,hash_involut:1,spectral:16,eform:7,appear:[16,20,15,6,7,13],current:[16,1,24,2,25,26,22,6,13],"2x2y2z3":[25,13,2],deriv:[13,7,26],gener:[0,1,24,4,5,6,7,9,10,11,12,13,15,16,17,18,19,2,20,25,26,27,28],coeffici:[0,16,11,1,20,2,25,6,7,28],satisfi:[16,19,11,20,25,5,6,7],explicitli:[5,17,7,1],address:6,along:[16,7],endow:[7,11],lam2005:24,from_base_r:27,commonli:[7,20],regardless:[16,11],extra:[6,15],modul:[16,8,17,18,19,11,20,12,2,25,26,5,6,7,13,28],"81y2x14":[25,13,2],basis_matrix:[6,10],prove:[0,16,1],univers:[0,16,4,5,7,28],reorder:18,acbb:4,is_quaternionalgebra:6,"fr\u00e9d\u00e9ric":4,peopl:[25,13,2],finit:[],"4xy5":[25,13,2],examin:11,"_basi":1,rlex:[16,15,19],billbo:[25,13,2],noncommutative_id:25,tokyo:1,jbar:6,uniqu:[16,1,12,2,25,26,27,6,7,14,13],cat:5,minimum:16,whatev:[25,13,2],assume_associ:27,webster:18,purpos:[25,13,17,2],problemat:12,steenrod_algebra_bas:[16,15],vector_express:[25,13,2],stackexchang:7,cardin:[5,16,27],verlag:18,alwai:[16,6,12,1],differenti:[],z12y2x2:[25,13,2],multipl:[],"0611617v2":20,write:[0,16,18],comm_rlex:[16,15,19],pure:[16,7,15],cntrlc:[25,13,2],parameter:6,map:[16,23,11,1,12,5,27,6,7],product:[0,16,18,1,20,12,26,4,5,6,7,15,28],mat:[26,17],max:16,xzy:4,classification_of_clifford_algebra:7,mai:[16,18,19,11,1,2,25,4,22,15,13,14,6],underscor:0,quaternionalgebra_abstract:6,data:[0,16,19,3,2,25,6,7,13],practic:[0,12],abcabc:4,mathweb:0,inform:[16,7,15,19,1],"switch":[16,6],preced:[5,13],combin:[0,16,6,1],arnona_long_mono_to_str:19,ibsn:5,milnor:[0,16,15,19],freealgebra_letterplac:[13,26],equip:[7,18],braid:[9,24,1],mainli:17,dynam:13,group:[],supercent:7,platform:[25,13,2],mptransp:[25,13,2],main:[0,11,15,19,1],prime:[0,16,19,20,6,15],non:[0,16,18,19,1,2,25,26,5,13,15,28],initi:[0,16,19,1,11,20,12,3,4,5,6,7,28],hamilton:17,now:[0,13,28,11],hall:[],nor:16,term:[0,16,17,9,19,1,11,20,12,2,25,26,5,18,13,7,15],name:[0,16,17,19,11,27,2,25,26,4,22,5,15,6,7,13,28],didn:20,oliv:20,separ:11,milnor_multiplication_odd:0,attributeerror:16,compil:[25,13,2],domain:[16,23,12,6,7,28],arg0:6,replac:[25,13,2],arg2:[6,26],weylgroup:[24,1],ensur:6,coprim:6,intrins:15,intersection_of_row_modules_over_zz:6,happen:[25,1],take_shortcut:6,shown:7,sbasi:18,space:[0,16,17,9,10,1,11,24,18,6,7,28],profil:[16,15,19],differentialweylalgebrael:28,formula:[0,16],factori:[0,6,26],gram:6,"2x5y":[25,13,2],"3_1":16,envelop:28,quaternion_ord:6,theori:[5,15,1],org:16,care:[25,13,7,2],wai:[16,11,20,12,22,7,15,28],wrong:15,recov:1,turn:[19,1],place:13,parts_in:15,think:7,first:[0,16,18,19,11,1,24,2,25,15,6,20,13,28],origin:[16,13,2],reimplement:26,directli:[18,1,20,26,7,28],kernel:[25,13,7,2],onc:[0,19,11,1,7,15],wedg:7,fast:17,oppos:7,ring:[],lexicograph:[16,25,13],size:[16,10,6,11,12,26,27,13,15],given:[0,1,24,4,5,6,7,10,11,12,13,14,15,16,18,19,2,23,20,25,27,28],convent:11,associ:[],numberfield:6,necessarili:[16,23],finitedimensionalalgebrael:[27,14],quaternionalgebrafactori:6,conveni:[0,16,1],copi:[26,1],specifi:[16,19,11,1,5,6,7,15,28],k_schur_noncommutative_vari:24,attempt:[25,19,1],than:[16,17,18,19,11,1,25,26,6,15],serr:[0,16,15,19],freealgebraelement_letterplac:2,were:0,posit:[0,16,9,19,20,24,13,26,18,6,2,15,28],seri:[5,6,4],sai:[20,19],repr_from_monomi:28,ann:[0,16,1],row_modul:6,ani:[0,16,9,19,11,1,20,25,6,7,15],notimplementederror:[5,16,6,26],ambigu:12,letterplace_id:25,unadorn:16,squar:[0,16,11,1,7,15],characteristic_polynomi:14,moreov:[26,1],rideal:6,note:[16,17,19,11,1,20,2,25,26,5,13],ideal:[],denomin:6,take:[0,16,19,11,1,2,25,15,6,7,13],interior:7,green:18,left_tabl:27,arnona:[16,15,19],bbac:4,begin:[5,22],sure:[25,6,11,13,2],trace:[5,6],normal:[1,2,25,5,6,13],multipli:[0,16,18,12,6,13],sagemath:16,enter:19,beta:[16,19],abus:7,specialjordanalgebra:5,pair:[0,16,18,19,6,7,28],ideal_monoid:13,latex:[19,28],renam:11,quaternionalgebra:[6,17],combinatorialfreemodul:[16,9,20,12,26,4,5,18,7],milnor_multipl:0,arnon:[16,15,19],"81y14x2":[25,13,2],show:[0,5],cheat:26,hack:1,corner:26,counit:[16,18,20,12,4,7],fifth:[25,13,2],ground:[5,16,7],quotient_ring_el:11,onli:[0,16,17,18,1,20,11,24,12,2,25,26,15,6,7,13],slow:17,ideal_nc:25,homogeneous_generator_noncommutative_vari:24,term_ord:13,wood:[16,15,19],dict:11,supercenter_basi:7,variou:[16,22,6,15,1],get:[16,18,19,20,12,2,25,13],dekker:5,repr:28,soon:13,milnor_mono_to_str:[15,19],cannot:[20,1],gen:[16,17,10,1,11,20,12,2,25,26,4,5,27,6,7,13,28],requir:[19,13,25,27,6,7,2,15],ramanujan:1,cohomology_raw:11,jordan_algebra:5,comultipl:18,yield:[13,2],basis_coeffici:11,london:[16,15,4],where:[0,16,9,19,1,18,11,20,2,25,4,5,15,6,7,13,28],is_coboundari:11,summari:16,loeffler:12,monomial_coeffici:16,stanlei:24,assumpt:[25,26,7],greenpoli:18,infinit:16,make_mono_admissible_:0,monoid:[5,13,17,26,1],enumer:[6,20],label:24,behind:1,between:[],"import":[0,16,23,18,19,11,1,20,12,26,6,15,28],spars:26,chapoton:4,parent:[16,23,18,1,11,20,12,2,26,4,5,27,6,7,14,28],differentialweyl:22,monomial_basi:[17,20],comm:[16,15,19],integermodr:12,come:7,accbab:4,mono:[0,16,19],quiet:[25,13,2],serre_cartan:[16,15],quaternionfractionalideal_r:6,mani:[16,11,1,26,6,15,28],among:[25,13,11,2],ascii_art:7,anti:7,nicola:1,prasad:1,pseudoscalar:7,use_latex:28,invert:[5,6,7,15,1],invers:[23,1,20,7,14,15],voight:6,valueerror:[16,23,19,11,1,27,6],wood_mono_to_str:19,yzx:4,resolut:[25,13,2],andrew:1,monogr:4,quatalg:6,repres:[0,16,18,19,11,2,25,15,6,7,13],former:15,those:[16,6,28,15,11],"case":[0,16,18,19,11,1,2,25,26,15,6,7,13],thesi:16,quotientringel:11,ctrl:[25,13,2],henc:[0,6,7,15],marcel:5,monk:[0,16,15],"100th":[16,19],ambient:[25,6,7,1],normalize_basis_at_p:6,supercommut:7,par:7,xi_degre:15,author:[0,16,18,19,1,11,20,12,2,25,21,3,4,26,5,15,6,7,13,28],alphabet:[18,4],admit:[27,14],same:[0,16,23,17,18,19,1,20,2,25,15,6,7,13],gcalgebra:11,binari:[0,16],html:[0,25,13,2],left_matrix:14,document:[16,19,11,2,25,13,7,15],hermit:6,finish:7,laurentpolynomialr:[20,1],hash_involution_on_basi:1,improv:[16,3],defn:11,arnona_long:[16,19],appropri:[16,7,15,28],without:[16,1,2,25,27,13],triang__lib:[25,13,2],model:[17,12],dimension:[],ccc:4,free_algebra_quoti:[17,3],manifold:7,execut:[25,13,2],adem5:16,dihedr:12,resp:[25,13,2,1],steinitz:20,isometri:7,schuralgebra:18,speed:7,free_algebra_element_letterplac:2,miscellan:[],mathscinet:1,except:[5,16,15],versa:[25,13,2],real:6,psi:7,around:[25,13,11,12,2],pst_revz:[16,15,19],mon:[16,26,17],pst:[16,15,19],mod:[0,16,19,6,7,15],steenrodalgebra_mod_two_with_categori:16,integ:[0,16,17,9,19,1,20,11,24,12,15,25,26,4,5,18,6,7,13],either:[0,16,18,19,11,1,2,25,5,27,13,7,15],output:[0,16,23,17,18,19,11,12,2,25,27,15,6,7,13,28],nice:[6,12],may_weight:16,oddli:11,cabb:4,cohomologyclass:11,ascend:6,bobber:6,"_klheckebasi":1,magma:6,mr0908150:1,a11:16,nonzero:[0,16,6,7],gross:6,definit:[6,7,4],"27y8x8":[25,13,2],exit:[25,13,2],poli:[25,13,2],mathcal:19,base_r:[1,24,12,20,26,4,6],complic:16,refer:[0,16,9,1,24,20,4,5,18,6,7,15,28],power:[0,16,18,20,5,6,7],bivari:7,garbag:18,ration:[0,23,17,18,1,11,24,12,25,26,4,5,27,6,7,13,28],bar_on_basi:1,raum:12,polynomialr:[25,13,2,20,1],acb:4,central:11,cbab:4,comm_deg_long:[16,19],lie_algebra_homolog:7,stand:16,act:[28,7,9,24,1],constructionfunctor:12,morphism:[],effici:17,elementari:20,quotient_r:[17,11],hnf:6,quotientring_nc:11,groupalgebrafunctor:12,your:[25,13,2],area:1,start:[0,11,15,1],interfac:[25,13,2],low:19,unam:[25,13,2],witt:[26,4,21],minimal_polynomi:14,tupl:[0,16,18,19,11,2,25,6,7,15],regard:7,jul:5,procedur:[0,25,13,2],s_16:16,inject_vari:[28,11],longer:16,notat:[16,7,11],tripl:[0,19],ternari:6,possibl:[0,16,1,2,25,5,13,15],"default":[0,16,23,10,19,1,11,24,12,2,25,26,27,15,6,7,14,13,28],index_set:9,miguel:11,jordanalgebrasymmetricbilinear:5,differentialgcalgebra_multigrad:11,cba:4,creat:[16,23,18,11,1,20,12,2,25,26,3,27,22,6,7,14,13,28],certain:[16,6,20,1],littlewood:20,decreas:[25,13,15,24],file:[18,15,19],mccrimmon:5,denot:[7,20,4],reduct:[25,13,2],"_steenrod_serre_cartan_basis_nam":19,field:[16,23,17,18,10,1,20,11,24,12,15,25,26,4,5,27,6,7,14,13,28],binomi:0,valid:[19,11],weyl_algebra:28,you:[0,16,19,11,12,26,6,15],architectur:[25,13,2],free_algebra_letterplac:[13,17],create_kei:[6,26],colon:[25,13,2],"0th":[16,6,11],sequenc:[0,16],symbol:[16,6,15],commutative_dga:11,polynomi:[16,18,1,20,2,25,26,6,14,13,28],briefli:19,brandt:6,reduc:[16,1,2,25,5,6,13],bcab:4,directori:[25,13,2],descript:[16,15,19],goe:15,adam:16,escap:[25,13,2],is_gener:16,cpu:[25,13,2],togeth:[0,16,19,11,1,15],represent:[16,18,19,11,1,3,12,28],all:[0,16,18,19,1,20,11,24,2,25,26,4,27,5,15,6,7,13],sci:[16,1],consider:12,pth:[0,16],illustr:23,alg:26,bull:[5,16,15],scalar:[16,7,20],disc:6,deprecationwarn:16,"_repr_":[16,19,11],pst_mono_to_str:19,follow:[0,16,18,19,1,2,25,27,5,15,6,7,13],schur_representative_from_index:18,articl:[18,1,4,5,7,28],tail:[25,13,2],norm:[5,6],liter:[25,13,2],fals:[16,9,10,19,1,11,12,15,26,3,27,6,7,14,13,28],is_homogen:[16,11],"0309168v3":1,veri:[16,14],fac:1,ticket:[0,11,20,12,2,25,26,6,7,13],exterioralgebracoboundari:7,pbw:[26,4,21],list:[0,16,17,19,11,27,2,25,26,22,15,6,7,13,28],arithmeticerror:13,nil_coxeter_algebra:24,sane:6,letterplace_polynomi:2,function_factori:[25,13,2],dimens:[16,17,18,10,19,11,26,6,7,15],correct:[26,7],hallalgebramonomi:20,zero:[0,16,23,18,19,11,2,25,5,27,6,7,14,13,28],pass:[16,6,7,15,19],further:1,casual:15,bilinear:[5,6,7],aba:4,abb:4,abc:[6,7,26,4],sub:[16,19],section:20,delet:0,version:[0,16,19,1,11,20,12,2,25,26,3,4,5,15,6,7,13,28],intersect:6,consecut:15,method:[0,16,18,19,11,1,20,15,26,27,6,7,13],full:[16,6,19],themselv:7,is_submodul:6,variat:1,ideal_gener:10,one_basi:[16,9,20,12,26,4,7],modular:6,is_zerodivisor:14,excess:16,modifi:[13,25,6,2,15,28],valu:[0,16,18,19,11,1,20,2,25,26,6,7,13],search:[8,13,25,19,2],nblock:[25,13,2],divisor:14,doctest:[0,16,3,15,26,6,13,28],action:[26,17,18,1],symmetricfunct:[18,20],idxfil:[25,13,2],quotient:[],via:[],primit:16,transit:1,c_1:[13,7],deprec:[16,7],c_3:7,c_2:[13,7],thought:7,famili:[16,9,12,26,4,5,7,28],abeliangroup:12,coercion:[26,13,20,12],clifford:[],ring_nam:[25,13,2],distinct:[16,7],multigrad:11,two:[0,16,23,17,18,19,1,11,20,12,2,25,26,4,27,15,6,7,14,13,28],coverag:3,a51:16,finite_dimensional_algebra_id:10,is_cohomologous_to:11,taken:[7,9,15],more:[0,16,17,18,19,1,11,12,2,25,4,15,6,7,13],desir:[25,13,2],canon:[7,18,15,19],an_el:[16,9,1,24,12,20,4,18,15],flag:23,particular:[16,6,7,1],known:[16,18,1,20,25,7,14],ideal_express:[25,13,2],cach:[0,19,11,13,25,26,6,15],none:[0,16,23,10,19,1,11,2,25,26,27,5,15,6,7,14,13,28],include_basi:6,remain:[16,19],"11x10":[25,13,2],lm_divid:2,cartan_typ:1,deg:[16,7,19,11],steenrod_algebra_basi:[16,15],accept:[25,13,11,15,2],yx5:[25,13,2],is_noetherian:[16,6],huge:7,cours:[16,25,13,26,3],awkward:16,divid:[0,2,15,1],rather:[16,11,15,19,1],anoth:[17,11,1,2,25,6,7,13],hugh:18,mapl:0,divis:[16,2,25,6,13,28],exterioralgebradifferenti:7,simpl:[16,28,1],yxz:4,resourc:[25,13,2],top_class:16,comm_llex_long:19,reflect:[16,7,11,1],catalog:[],okai:19,no_repeat:15,onto:7,assign:[25,13,2],height:16,sect:1,arnonc:[16,19],matrixspac:[26,17],multivari:[1,2,25,26,13,28],help:[16,25,13,2],ith:16,gl_irreducible_charact:18,matthieu:4,paper:[0,16,15],through:[0,18,20,26,27,7],acbcab:4,poincar:[26,4,21],paramet:[1,20,2,25,27,13],iwahoriheck:22,brows:16,wrt:2,im_gen:11,might:[25,13,2],unique_represent:[17,11,1,5,7,28],good:[16,6],"return":[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,21,23,20,25,26,27,28],order_of_level_n:6,antihomomorph:16,framework:[26,1],oxford:4,set_degbound:[25,13],bigger:25,leading_monomi:16,subid:[25,6,13,2],easili:12,iff:16,mpport:[25,13,2],compris:13,additive_abelian:11,to_monoid_el:26,found:[25,6,13,4,2],intervent:1,truncat:[16,15],valuat:6,weight:[],steenrod_basis_error_check:[16,15],functor:[7,12],realli:[23,7],generator_degre:13,connect:[7,20],quantum:[9,1],differential_matrix:11,cdg_algebra:11,atomic_basi:15,admiss:[0,16,15],"_milnor_on_basi":[16,15],is_field:[16,26,6,13,12],print:[16,11,13,25,6,2,15],variable_nam:[6,4],matha:1,arnonc_basi:15,reason:[0,7],base:[],finitedimensionalalgebra:[27,23,14,10],put:[26,11],s_coeff:7,basi:[0,1,2,4,5,6,7,10,11,12,13,14,15,16,17,18,19,21,23,20,25,26,27,28],thread:[25,13,2],omit:[0,11],cacbab:4,perhap:7,base_extend:27,obviou:12,schubert:9,misc:28,number:[0,16,17,19,1,20,24,12,2,25,26,4,27,15,6,7,13,28],done:[0,16,6,27,1],accbba:4,stdlib:[25,13,2],stabl:16,miss:[7,11],differ:[16,17,11,1,12,2,26,13,15],ingular:[25,13,2],j87:1,atomic_basis_odd:15,exterior_algebra_basi:11,least:[25,15],expand:[0,26,4],is_zero:27,store:[26,7],option:[0,16,19,11,1,24,12,2,25,26,27,15,6,13],groebner:[25,13,26,2],exterior_algebra:7,jordan:[],std:[25,13,2],king:[0,2,25,26,13,15],cyclic:24,withbasi:5,annihil:6,"81y5x11":[25,13,2],bialgebra:18,str:[6,15],cbacab:4,comput:[0,16,19,1,20,2,25,26,27,15,6,7,13],polynomial_r:28,convert_from_milnor_matrix:15,packag:[0,15],lie:[16,1,26,4,5,7],graded_commutative_algebra:11,equival:[0,6,18,20],antipode_on_basi:[16,7,20,12],violat:25,h22:20,also:[0,16,23,18,19,1,11,20,2,25,4,27,5,15,6,7,14,13,28],analogu:24,left_id:6,albert:5,previou:[16,18,15],most:[16,17,9,19,1,20,11,24,12,15,25,26,4,27,5,18,6,7,13],plai:7,larg:15,wall_height:16,alpha:[6,26],cbaacb:4,clear:[16,19,1],roughli:0,part:[17,7,18,15,24],uniquerepresent:[17,11,1,5,7,28],combinatorialfreemodule_with_categori:16,change_basi:16,wood____i:16,superalgebra:7,affin:[],penalti:17,coerc:[25,6,7,4,12],indexerror:[17,4],solut:[6,12],unique_nam:[25,13,2],factor:[16,27,6,26],abelian:[12,11],bruhat_l:1,leading_coeffici:16,express:[16,1,2,25,4,13],"1x2y2z2":[25,13,2],rest:[16,7,15],arxiv:[20,1],basis_nam:[16,19],statist:1,multinomial_odd:0,set:[16,23,18,19,1,20,2,25,4,5,15,6,7,13],quotient_map:[27,23],dump:[17,18,20,12,21,26,6,13],decompos:16,emac:[25,13,2],sec:[25,13,2],arg:[25,6,27,13,2],analog:15,chose:26,comm_revz_long:19,someth:[7,15],smallest:[6,7],volume_form:7,nontrivi:[16,15,12,2],sl2z:12,subscript:16,ihalgebra:1,signatur:19,letterplac:[],numer:6,induc:[6,12],moyal:28,fgh:4,ringhomomorphism_im_gen:23,distinguish:[18,1],vectorspac:27,both:[0,16,11,1,12,6],last:[16,17,9,19,1,11,24,12,15,25,26,4,5,27,6,13],set_verbos:15,lusztig:1,whole:[16,19],quaternion_algebra:6,load:[17,18,20,12,21,26,6,13],point:[16,6,11,1],residu:7,linux:[25,13,2],b_1:13,b_2:13,to_t_basi:1,cbba:4,due:7,calculu:9,pbw_basi:26,far:16,chevallei:1,neglex:25,imag:[23,7,11],convert:[0,16,19,11,20,12,2,25,26,13,15],coordin:[7,14],differential_geometri:7,partli:6,repetit:[15,19],multiply_by_conjug:6,homogeneous_compon:16,bcba:4,dynkin:24,term_order_of_block:13,batch:[25,13,2],ramif:6,"while":[5,16,15,19],behavior:[16,25,13,19,2],error:[0,16,19,11,1,6,15],scrimshaw:[5,7,28,20,1],propag:27,vol:5,echelon:[6,10],itself:11,letterplaceid:25,quadrat:[6,7,24,1],is_freealgebraquotientel:3,minim:[16,1,2,25,13,14],belong:[27,6,26,1],subalgebra:[5,13,7],cocycl:11,is_exact:[6,12],e_ij:18,optim:16,comm_mono_to_str:19,sym:20,covari:7,moment:15,"0x7f2713950140":6,user:[0,16,11,1,2,25,13,15],specialis:16,typic:5,recent:[16,17,9,19,1,11,24,12,25,26,4,5,27,6,13],coboundari:[7,11],lib:[25,13,2],entri:[0,16,18,19,11,1,6,7,15],noncommut:[6,7,24],pickl:6,self:[16,23,18,10,1,11,20,12,2,21,4,27,5,26,6,7,14,28],construct:[16,23,17,9,19,11,24,12,25,26,5,13,7,15,28],a_2:13,a_1:13,combinat:[16,9,1,20,12,21,26,4,18,7],truncation_typ:[16,15,19],voevodski:16,unit_id:6,shortcut:1,theorem:[16,4],hall_polynomi:20,input:[0,1,2,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,23,24,25,26,27,28],bin:[25,13,2],marco:11,stein:[6,26,3],format:[0,6,19,28],big:6,multidegre:11,comm_long_mono_to_str:19,finite_dimensional_algebra_el:14,bit:[16,6],differentialweylalgebra:28,collect:0,princip:7,"boolean":[16,23,19,11,27,14,15],bruin:1,bacb:4,often:[5,7],some:[0,16,17,1,11,2,25,26,4,15,6,7,13],back:[16,7,1],exterioralgebra:7,scale:6,per:[9,12,2,25,4,13],substitut:1,mathemat:[0,5,1],quaternionalgebraelement_gener:6,recognis:1,ternary_quadratic_form:6,mr2642451:1,proc:16,run:[17,11,20,3,2,25,26,27,13,7],shufflealgebra:4,step:[0,16,28],"_reductor_":2,automorph:[7,20,1],impos:11,idx:[16,25,13,2],transpos:[7,20],novikov:16,primary_decomposit:27,block:[25,13,2],primarili:11,hall_algebra:20,to_cp_basi:1,contributor:[25,13,2],cho:5,kohel:[6,26,3,21],inclus:[6,7,12],span:[0,16,6],element_class:[16,11],question:7,"long":[16,19,1,20,12,13,6,15],arithmet:[16,17,11,26,6,13],includ:[6,15,11],suit:16,chu:5,iwahoriheckealgebra:[24,1],properli:7,margoli:16,sqrt2:6,to_pbw_basi:21,"_latex_":[19,11],decomposit:27,link:[25,13,2,1],sdb:[25,13,2],atom:[6,15],groebnerbasi:2,line:[25,13,15,19,2],info:[25,13,2],concaten:[0,19],consist:[16,18,11,27,6,15],index_cmp:1,similar:[16,7,15,19,1],mccrimmon78:5,constant:[25,13,7,2],"_steenrod_milnor_basis_nam":19,total_degre:11,doesn:[16,19,11,26,7,15],lectur:[0,20],steenrod_algebra_el:19,"3x2yz3":[25,13,2],bracket:[7,11],invalid:[17,19],additive_ord:16,setenv:[25,13,2],transport:20,quaternionord:6,"7y4x2":[25,13,2],assertionerror:[9,24],create_object:[6,26],parentmethod:[9,4,12],mprsh:[25,13,2],william:[6,26,3],meaning:[18,14],eval:6,schiffmann:20,algorithm:[0,16,6,12],vice:[25,13,2],evenli:11,discrimin:6,xx4711:[25,13,2],hall_littlewood:20,finite_dimensional_algebra:[27,23,14,10],hello:19,steenrodalgebra_mod_two:16,code:[13,19,1,2,25,6,15],partial:[20,28],scratch:[25,13,2],edu:0,degree_neg:7,simon:[0,2,25,26,13,15],send:[16,19,1,20,12,25,7],sens:[16,7,15],sent:[25,13,7,2],is_invert:14,note_:[25,13,2],additiveabeliangroup:11,uniquefactori:[6,26],volum:7,free_modul:[16,9,1,20,12,21,26,4,18,6,7],relev:16,tri:16,z_1:2,z_3:2,pullback:7,epstein:[0,16],dealt:28,impli:[5,1],smaller:[25,18],natur:[7,18,20,12,11],c_0:7,fold:[16,18],"3z8":[25,13,2],odd:[0,16,19,11,6,7,15],append:[16,15,19],compat:25,index:[0,8,17,9,1,16,11,24,12,20,26,4,18,6,7,28],hodge_du:7,compar:[16,6,11,20,1],find:[0,6],access:[22,13,25,2],niltemperlei:[],left_ord:6,deduc:16,can:[0,16,18,19,1,11,20,12,2,25,26,4,5,6,7,13,28],involv:6,matrix_express:[25,13,2],is_finit:[16,27,6,12],consolid:15,hkp:1,groebner_basi:[25,13,26,2],len:[6,17,15,19],jordanalgebra:5,let:[0,16,18,1,5,22,6,7,28],cab:4,lex:[16,25,13,20,2],shuffle_product:4,sinc:[0,16,17,11,20,12,2,25,26,6,7,13],remark:[16,17],convers:[16,20,19,4,1],"2x2":6,poincare_birkhoff_witt_basi:26,steenrod_algebra_mult:[0,16,15],chang:[16,11,1,27,7,15],steenrodalgebra_generic_with_categori:16,coercibl:7,degrevlex:26,abcd:[7,4],firefox:[25,13,2],appli:[0,16,18,1],submodul:[25,13,2],"_mul_":1,binomial_mod2:0,from:[0,1,24,4,5,6,7,11,12,13,14,15,16,18,19,2,23,20,25,26,27,28],abcb:4,zip:16,next:[5,28,1],"7x2y4":[25,13,2],usr:[25,13,2],cacbba:4,commut:[],remaind:[25,13,2],sort:[16,11,2,25,6,13],babc:4,given_by_matrix:[27,10],group_algebra:12,"__call__":[26,18,20],"0x7f8fce1fb2a8":[],iii:20,binomial_modp:0,augment:16,alia:[27,17,7,26,28],cambridg:[5,16],jacobson71:5,codomain:[23,7],is_unitari:27,obvious:12,squarefre:6,proof:[0,16,6,26,12],control:[16,26],cbacba:4,finitedimensionalalgebraswithbasi:27,process:[0,25,13,19,2],high:25,tab:22,onlin:[25,13,2],dualiz:18,"3z3yx2":[25,13,2],degre:[16,23,18,10,11,12,2,25,26,27,15,6,7,13],occur:1,lifted_bilinear_form:7,revz:[16,19],comm_revz:[16,15,19],instead:[0,16,11,1,27,6,7],pst_basi:15,sin:11,frac:[6,28,1],overridden:16,singular:[],inst:16,modulemorphismbylinear:7,bockstein:[0,16],gcalgebra_multigrad:11,honestli:11,chu2012:5,issb:[25,13,2],llex:[16,19],lift_morph:7,element:[],issu:6,gradedcommutativealgebra:11,allow:[16,19,1,2,25,26,6,13],fallback:20,move:[19,1],additive_abelian_group:11,comma:11,x__2:2,x__1:2,cohomolog:[0,16,7,11],x__4:2,x__5:2,outer:1,chosen:13,therefor:[0,16,18,1,26,28],fourth:[25,13,2],nonneg:[0,7],python:[6,11],auto:[16,15,19],extra_arg:6,maxord_solve_aux_eq:6,e_kl:18,padicr:12,trac:[0,16,11,20,12,2,25,26,6,7,13],anyth:16,a_pst:16,subset:7,weyl:[],bump:1,combinatorialfreemoduleel:[16,18,1,20,21,26,4,7],hlp:20,combinatori:[26,18,20],our:[26,20,4,1],hallalgebra:20,special:[5,20,1],out:[16,1,2,25,6,7,13],variabl:[18,19,1,24,2,25,21,4,26,6,7,13,28],theta_seri:6,matrix:[0,23,9,10,1,11,24,2,25,27,5,15,6,7,14,13,28],rep:[6,19,11],coproduct:[16,18,20,12,4,7],categori:[16,23,11,1,20,12,26,5,27,7],suitabl:[19,1],stud:16,lattic:6,thieri:1,matric:[0,17,1,26,27,6,15],common:0,random_el:[27,6,14,12],insid:[6,24,1],manipul:[4,11],york:5,dictionari:[0,16,11,2,25,13,7,28],unwieldi:19,quo:26,s_1:16,s_2:16,transposit:7,s_8:16,could:[25,13,11,15,2],"_long":[16,15],timer:[25,13,2],keep:[0,20],length:[0,16,18,19,1,24,6,7,15],outsid:16,geometri:5,quaternionalgebra_ab:6,is_matrix_r:6,softwar:0,scene:1,echo:[25,13,2],unpickle_quaternionalgebra_v0:6,suffic:12,lift_isometri:7,unknown:5,"2_2":16,system:[25,13,2,1],wrapper:[25,13,26,2],attach:19,appl:[16,15],zxy:4,termin:[0,25,13,2],"final":0,pizer:6,shell:[25,13,2],travi:[5,7,28,20,1],aabb:4,essenti:19,iwahori:[],exactli:[6,15,11],steen:0,slack:2,see:[0,16,17,18,19,1,11,20,12,2,25,26,4,22,15,6,7,13],structur:[16,17,18,1,11,20,12,2,21,3,5,26,6,7,14,28],charact:18,subcoalgebra:18,hodg:7,serre_cartan_basi:15,julian:6,correspond:[0,16,18,19,1,11,24,12,20,26,4,6,7,13,28],have:[0,16,18,19,1,11,20,12,2,25,26,27,15,6,7,13],need:[16,6,7,17,11],border:7,iwahoriheckealgebra_nonstandard:1,mil:[0,16],min:[25,13,2],jacobson:5,modp_splitting_map:6,mix:[16,19],builtin:[25,13,2],which:[0,16,17,9,19,1,18,11,12,2,25,26,4,27,5,15,6,7,14,13,28],singl:[16,25,6,15,11],heisenberg:28,unless:[16,23,12,2],who:[25,13,2],discov:[16,22],singular_system:[25,13,2],free_algebra:[26,17],clifford_algebra:7,comparison:1,"class":[1,24,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,21,2,23,20,25,26,27,28],pushout:12,homogen:[],laurent:[20,1],dens:15,request:[16,25,26,17,11],inde:7,univari:[6,20],determin:[16,19,11,1,2,25,6,7,13],occasion:16,fact:[0,16,7,11],homogeneous_noncommutative_vari:24,verbos:15,tty:[25,13,2],"1_2":16,"1_1":16,"1_0":16,zero_id:[27,23],trivial:[2,12,1],homomorph:[27,23,7],highest:16,should:[0,16,18,19,11,1,20,15,26,27,6,7,13],lemma:[20,1],baser:[25,13,2],suppos:7,s_12:16,local:[25,6,27,13,2],hopf:[16,7,19,12,20],meant:[16,1],next_prim:6,abbc:4,contribut:[16,25,13,2],abba:4,pull:7,familiar:15,increas:[0,18,19,13,7,15],freealgebrafactori:26,triangl:[25,13,2],y_5:2,y_2:2,y_1:2,integr:[16,12,2,25,26,6,13],partit:[20,18,15,24],contain:[0,16,9,11,1,2,25,26,15,6,13],voi2012:6,view:[0,16,19,11,24,6],altern:[16,19,11,1,26,7],modulo:[7,9,12],is_integral_domain:[16,6,12],endomorph:[5,7,18],kazhdan_lusztig:1,mpmode:[25,13,2],mr0165016:1,still:[7,11],twosid:[25,13,17,26,2],zba:26,correctli:[18,12],pattern:19,boundari:7,restricted_partit:15,favor:7,written:[0,5,1],reduced_trac:6,crude:15,theta:6,neither:6,bunch:6,kei:[0,16,11,26,4,22,6,7,13],notion:7,entir:[16,15],amer:[5,24],embed:[6,7],jon:6,addit:[16,11,1,12,2,25,13,6,28],inverse_imag:23,equal:[0,16,7,18],etc:[0,16,19,11,12,6],differential_matrix_multigrad:11,instanc:[0,16,19,12,11],acbacb:4,wall:[16,15,19],arguement:24,respect:[16,23,19,11,1,2,25,27,15,6,7,14,13],string_express:[25,13,2],evalu:11,normalform:[25,13,2],bba:4,compon:[16,7,19,11],treat:15,long_el:1,ecart:[25,13,2],inverse_gener:1,meaningless:15,assert:[16,6],x_3:2,x_1:2,hecke_algebra:1,finitedimensionalalgebramorph:[27,23],present:[0,15,19,1],multi:[11,1],a_real:1,from_reduced_word:1,defin:[0,16,23,17,18,19,1,11,24,20,26,4,5,6,7,15,28],inner_product_matrix:6,observ:1,irreduc:18,motiv:[16,7],dual:[0,16,7,18,4],revis:0,noetherian:[16,6],is_squarefre:6,product_by_gener:1,uniti:[5,20,28],cross:7,sqrt:[6,28],handl:[6,26],whenev:1,largest:7,antideriv:7,infer:[5,7],dualpbwbasi:4,transpose_cmp:20,phi:7,http:[0,16,7],again:[5,25,6],groebneer:2,expans:[0,26,4],effect:[25,15,19,1],cyclicpermutationgroup:12,off:[6,1],center:7,philo:16,serre_cartan_mono_to_str:19,well:[16,24,7,11,1],latexexpr:28,exampl:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],command:[16,25,13,2],choos:[0,16,13,7],zyx:4,usual:[16,11,24,5,13,7],p_mono:0,affine_nil_temperley_lieb:9,less:[16,19],is_freealgebra:26,free_algebra_el:21,obtain:[16,6,7,18],detail:[16,20,15,1],simultan:18,get_basis_nam:[16,15,19],web:[25,13,2],preprint:15,shuffle_algebra:4,add:[0,16,11,26,13,7,15],match:[16,19],haut:16,piec:16,freealgebraquoti:[17,3],realiz:[7,1],know:12,knot:1,press:[0,16,2,25,4,5,22,13],tick:[25,13,2],recurs:[0,4],is_unit:16,normalized_laurent_polynomi:1,loss:6,like:[16,19,7,15,12],martin:12,steenrod:[],page:[8,13,25,2],revers:[16,6,13,15],hain:1,pbw_element:26,i64:1,pariti:7,center_basi:7,proper:6,guarante:25,librari:[25,13,2],tmp:[25,13,2],lead:[16,25,13,28,2],avoid:[5,13],antipod:[16,7,20,12],aab:4,summand:[0,16,6,12],"_group":12,expansion_on_basi:4,is_division_algebra:[16,6],interior_product_on_basi:7,imaginari:6,although:[7,11],kd4:12,to_c_basi:1,continu:5,about:[16,19,2,25,26,13,15],actual:[0,6,7,20],quadraticform:[6,7,28],testsuit:[17,11,3,26,13,7],column:[0,7],ramified_prim:6,statement:1,abab:4,constructor:[6,26],piz1980:6,kra:16,devid:2,q_0:16,automat:[16,25,13,12,2],diagon:[0,6],right_ord:6,lie_polynomi:26,empti:[19,15,4],ea2:16,involut:[5,7,1],macdonald1995:20,"81y11x5":[25,13,2],renorm:20,product_by_generator_on_basi:1,much:[16,26,17],inner:6,arg1:[6,26],"var":6,individu:1,"function":[],triangular:1,basis_for_quaternion_lattic:6,getenv:[25,13,2],brant:1,leading_term:16,bug:[0,16,6],filtrat:[16,7],made:[16,15],"\u00e9tude":16,ramifi:6,whether:[0,16,23,9,10,19,11,2,6,13],unshuffl:7,displai:[25,13,2],scranton:0,below:[16,19,11,2,25,6,13],arnona_mono_to_str:19,otherwis:[0,16,19,11,26,6,7,15,28],problem:[15,12,1],albert47:5,surrpris:2,"int":[25,6,11,13,2],dure:[25,13,2],pid:[25,13,2],with_basi:7,poly_express:[25,13,2],implement:[],permutationgroupel:6,eric:18,inc:5,mutual:20,kl79:1,p2005:9,other:[16,18,19,1,11,12,2,25,5,15,6,7,13],bool:[6,15],kazhdanlusztigpolynomi:1,wall_long:[16,15,19],repeat:[0,18,15],q_6:16,q_4:16,q_3:16,q_2:[16,1],q_1:[16,1],singularlib:[25,13,2],homolog:7,stai:13,schur_representative_indic:18,dihedralgroup:12,pbwbasisoffreealgebra:26,bca:4,comm_long:16,preimag:20,magmat:5,decemb:16,invari:[6,14,1],quaternion_algebra_el:6},objtypes:{"0":"py:module","1":"py:method","2":"py:class","3":"py:function","4":"py:attribute"},objnames:{"0":["py","module","Python module"],"1":["py","method","Python method"],"2":["py","class","Python class"],"3":["py","function","Python function"],"4":["py","attribute","Python attribute"]},filenames:["sage/algebras/steenrod/steenrod_algebra_mult","sage/algebras/iwahori_hecke_algebra","sage/algebras/letterplace/free_algebra_element_letterplace","sage/algebras/free_algebra_quotient_element","sage/algebras/shuffle_algebra","sage/algebras/jordan_algebra","sage/algebras/quatalg/quaternion_algebra","sage/algebras/clifford_algebra","index","sage/algebras/affine_nil_temperley_lieb","sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_ideal","sage/algebras/commutative_dga","sage/algebras/group_algebra","sage/algebras/letterplace/free_algebra_letterplace","sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_element","sage/algebras/steenrod/steenrod_algebra_bases","sage/algebras/steenrod/steenrod_algebra","sage/algebras/free_algebra_quotient","sage/algebras/schur_algebra","sage/algebras/steenrod/steenrod_algebra_misc","sage/algebras/hall_algebra","sage/algebras/free_algebra_element","sage/algebras/catalog","sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_morphism","sage/algebras/nil_coxeter_algebra","sage/algebras/letterplace/letterplace_ideal","sage/algebras/free_algebra","sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra","sage/algebras/weyl_algebra"],titles:["Multiplication for elements of the Steenrod algebra","Iwahori-Hecke Algebras","Weighted homogeneous elements of free algebras, in letterplace implementation.","Free algebra quotient elements","Shuffle algebras","Jordan Algebras","Quaternion Algebras","Clifford Algebras","Algebras","Affine nilTemperley Lieb Algebra of type A","Ideals of Finite Algebras","Commutative Differential Graded Algebras","Group algebras","Free associative unital algebras, implemented via Singular’s letterplace rings","Elements of Finite Algebras","Steenrod algebra bases","The Steenrod algebra","Finite dimensional free algebra quotients","Schur algebras for <span class=\"math\">\\(GL_n\\)</span>","Miscellaneous functions for the Steenrod algebra and its elements","Hall Algebras","Free algebra elements","Catalog of Algebras","Morphisms Between Finite Algebras","Nil-Coxeter Algebra","Homogeneous ideals of free algebras.","Free algebras","Finite-Dimensional Algebras","Weyl Algebras"],objects:{"sage.algebras.steenrod.steenrod_algebra.SteenrodAlgebra_generic.Element":{prime:[16,1,1,""],is_decomposable:[16,1,1,""],milnor:[16,1,1,""],degree:[16,1,1,""],basis:[16,1,1,""],is_nilpotent:[16,1,1,""],additive_order:[16,1,1,""],coproduct:[16,1,1,""],change_basis:[16,1,1,""],is_homogeneous:[16,1,1,""],excess:[16,1,1,""],wall_height:[16,1,1,""],basis_name:[16,1,1,""],may_weight:[16,1,1,""],is_unit:[16,1,1,""]},"sage.algebras.hall_algebra.HallAlgebra.Element":{scalar:[20,1,1,""]},"sage.algebras.quatalg.quaternion_algebra.QuaternionOrder":{right_ideal:[6,1,1,""],quadratic_form:[6,1,1,""],discriminant:[6,1,1,""],basis:[6,1,1,""],gens:[6,1,1,""],random_element:[6,1,1,""],left_ideal:[6,1,1,""],ngens:[6,1,1,""],unit_ideal:[6,1,1,""],ternary_quadratic_form:[6,1,1,""],intersection:[6,1,1,""],gen:[6,1,1,""],free_module:[6,1,1,""],quaternion_algebra:[6,1,1,""]},"sage.algebras.quatalg":{quaternion_algebra:[6,0,0,"-"]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element.FiniteDimensionalAlgebraElement":{characteristic_polynomial:[14,1,1,""],inverse:[14,1,1,""],minimal_polynomial:[14,1,1,""],matrix:[14,1,1,""],is_zerodivisor:[14,1,1,""],is_nilpotent:[14,1,1,""],is_invertible:[14,1,1,""],vector:[14,1,1,""],left_matrix:[14,1,1,""]},"sage.algebras.free_algebra.PBWBasisOfFreeAlgebra.Element":{expand:[26,1,1,""]},"sage.algebras.clifford_algebra.ExteriorAlgebraBoundary":{chain_complex:[7,1,1,""]},"sage.algebras.steenrod.steenrod_algebra_mult":{binomial_mod2:[0,3,1,""],multinomial_odd:[0,3,1,""],binomial_modp:[0,3,1,""],multinomial:[0,3,1,""],make_mono_admissible:[0,3,1,""],milnor_multiplication:[0,3,1,""],milnor_multiplication_odd:[0,3,1,""],adem:[0,3,1,""]},"sage.algebras.schur_algebra.SchurTensorModule":{Element:[18,2,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element":{FiniteDimensionalAlgebraElement:[14,2,1,""]},"sage.algebras.iwahori_hecke_algebra":{index_cmp:[1,3,1,""],IwahoriHeckeAlgebra:[1,2,1,""],normalized_laurent_polynomial:[1,3,1,""],IwahoriHeckeAlgebra_nonstandard:[1,2,1,""]},"sage.algebras.quatalg.quaternion_algebra.QuaternionFractionalIdeal_rational":{theta_series_vector:[6,1,1,""],scale:[6,1,1,""],gram_matrix:[6,1,1,""],quadratic_form:[6,1,1,""],multiply_by_conjugate:[6,1,1,""],basis:[6,1,1,""],theta_series:[6,1,1,""],left_order:[6,1,1,""],gens:[6,1,1,""],quaternion_order:[6,1,1,""],cyclic_right_subideals:[6,1,1,""],free_module:[6,1,1,""],basis_matrix:[6,1,1,""],conjugate:[6,1,1,""],right_order:[6,1,1,""],is_equivalent:[6,1,1,""],intersection:[6,1,1,""],ring:[6,1,1,""],norm:[6,1,1,""],quaternion_algebra:[6,1,1,""]},"sage.algebras.shuffle_algebra":{DualPBWBasis:[4,2,1,""],ShuffleAlgebra:[4,2,1,""]},"sage.algebras.shuffle_algebra.DualPBWBasis.Element":{expand:[4,1,1,""]},"sage.algebras.jordan_algebra.JordanAlgebraSymmetricBilinear":{basis:[5,1,1,""],algebra_generators:[5,1,1,""],gens:[5,1,1,""],one:[5,1,1,""],zero:[5,1,1,""],Element:[5,2,1,""]},"sage.algebras.jordan_algebra":{SpecialJordanAlgebra:[5,2,1,""],JordanAlgebraSymmetricBilinear:[5,2,1,""],JordanAlgebra:[5,2,1,""]},"sage.algebras.letterplace.free_algebra_element_letterplace.FreeAlgebraElement_letterplace":{lc:[2,1,1,""],degree:[2,1,1,""],letterplace_polynomial:[2,1,1,""],reduce:[2,1,1,""],lm:[2,1,1,""],lm_divides:[2,1,1,""],normal_form:[2,1,1,""],lt:[2,1,1,""]},"sage.algebras.group_algebra":{GroupAlgebra:[12,2,1,""],GroupAlgebraFunctor:[12,2,1,""]},"sage.algebras.clifford_algebra":{ExteriorAlgebra:[7,2,1,""],CliffordAlgebra:[7,2,1,""],ExteriorAlgebraBoundary:[7,2,1,""],ExteriorAlgebraCoboundary:[7,2,1,""],CliffordAlgebraElement:[7,2,1,""],ExteriorAlgebraDifferential:[7,2,1,""]},"sage.algebras.steenrod.steenrod_algebra_misc":{arnonA_mono_to_string:[19,3,1,""],comm_mono_to_string:[19,3,1,""],arnonA_long_mono_to_string:[19,3,1,""],wall_mono_to_string:[19,3,1,""],pst_mono_to_string:[19,3,1,""],milnor_mono_to_string:[19,3,1,""],is_valid_profile:[19,3,1,""],wood_mono_to_string:[19,3,1,""],normalize_profile:[19,3,1,""],comm_long_mono_to_string:[19,3,1,""],convert_perm:[19,3,1,""],wall_long_mono_to_string:[19,3,1,""],serre_cartan_mono_to_string:[19,3,1,""],get_basis_name:[19,3,1,""]},"sage.algebras.free_algebra.PBWBasisOfFreeAlgebra":{product:[26,1,1,""],algebra_generators:[26,1,1,""],gens:[26,1,1,""],expansion:[26,1,1,""],Element:[26,2,1,""],one_basis:[26,1,1,""],free_algebra:[26,1,1,""],gen:[26,1,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_ideal.FiniteDimensionalAlgebraIdeal":{vector_space:[10,1,1,""],basis_matrix:[10,1,1,""]},"sage.algebras.clifford_algebra.ExteriorAlgebra":{degree_on_basis:[7,1,1,""],counit:[7,1,1,""],lift_morphism:[7,1,1,""],antipode_on_basis:[7,1,1,""],Element:[7,2,1,""],lifted_bilinear_form:[7,1,1,""],coboundary:[7,1,1,""],coproduct_on_basis:[7,1,1,""],volume_form:[7,1,1,""],boundary:[7,1,1,""],interior_product_on_basis:[7,1,1,""]},"sage.algebras.letterplace.letterplace_ideal":{poly_reduce:[25,3,1,""],singular_system:[25,3,1,""],LetterplaceIdeal:[25,2,1,""]},"sage.algebras.free_algebra_quotient_element":{FreeAlgebraQuotientElement:[3,2,1,""],is_FreeAlgebraQuotientElement:[3,3,1,""]},"sage.algebras.letterplace.free_algebra_letterplace.FreeAlgebra_letterplace":{ideal_monoid:[13,1,1,""],current_ring:[13,1,1,""],set_degbound:[13,1,1,""],degbound:[13,1,1,""],term_order_of_block:[13,1,1,""],is_commutative:[13,1,1,""],ngens:[13,1,1,""],generator_degrees:[13,1,1,""],is_field:[13,1,1,""],commutative_ring:[13,1,1,""],gen:[13,1,1,""]},"sage.algebras.quatalg.quaternion_algebra.QuaternionAlgebra_abstract":{is_matrix_ring:[6,1,1,""],is_division_algebra:[6,1,1,""],basis:[6,1,1,""],is_finite:[6,1,1,""],is_integral_domain:[6,1,1,""],is_commutative:[6,1,1,""],ngens:[6,1,1,""],is_noetherian:[6,1,1,""],vector_space:[6,1,1,""],random_element:[6,1,1,""],is_exact:[6,1,1,""],inner_product_matrix:[6,1,1,""],order:[6,1,1,""],is_field:[6,1,1,""]},"sage.algebras.quatalg.quaternion_algebra.QuaternionAlgebra_ab":{modp_splitting_data:[6,1,1,""],ramified_primes:[6,1,1,""],invariants:[6,1,1,""],discriminant:[6,1,1,""],quaternion_order:[6,1,1,""],maximal_order:[6,1,1,""],modp_splitting_map:[6,1,1,""],ideal:[6,1,1,""],inner_product_matrix:[6,1,1,""],gen:[6,1,1,""]},"sage.algebras.free_algebra_element":{FreeAlgebraElement:[21,2,1,""]},"sage.algebras.shuffle_algebra.DualPBWBasis":{product:[4,1,1,""],shuffle_algebra:[4,1,1,""],algebra_generators:[4,1,1,""],gens:[4,1,1,""],expansion:[4,1,1,""],Element:[4,2,1,""],one_basis:[4,1,1,""],expansion_on_basis:[4,1,1,""],gen:[4,1,1,""]},"sage.algebras.hall_algebra.HallAlgebraMonomials.Element":{scalar:[20,1,1,""]},"sage.algebras.schur_algebra":{SchurAlgebra:[18,2,1,""],schur_representative_from_index:[18,3,1,""],GL_irreducible_character:[18,3,1,""],SchurTensorModule:[18,2,1,""],schur_representative_indices:[18,3,1,""]},"sage.algebras.free_algebra_quotient.FreeAlgebraQuotient":{rank:[17,1,1,""],monoid:[17,1,1,""],monomial_basis:[17,1,1,""],dimension:[17,1,1,""],module:[17,1,1,""],gen:[17,1,1,""],free_algebra:[17,1,1,""],ngens:[17,1,1,""],Element:[17,4,1,""],matrix_action:[17,1,1,""]},"sage.algebras.weyl_algebra":{DifferentialWeylAlgebraElement:[28,2,1,""],DifferentialWeylAlgebra:[28,2,1,""],repr_from_monomials:[28,3,1,""]},"sage.algebras.free_algebra_quotient_element.FreeAlgebraQuotientElement":{vector:[3,1,1,""]},"sage.algebras.free_algebra_element.FreeAlgebraElement":{variables:[21,1,1,""],to_pbw_basis:[21,1,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism.FiniteDimensionalAlgebraMorphism":{matrix:[23,1,1,""],inverse_image:[23,1,1,""]},"sage.algebras.steenrod.steenrod_algebra_bases":{convert_to_milnor_matrix:[15,3,1,""],atomic_basis:[15,3,1,""],restricted_partitions:[15,3,1,""],steenrod_basis_error_check:[15,3,1,""],serre_cartan_basis:[15,3,1,""],convert_from_milnor_matrix:[15,3,1,""],milnor_basis:[15,3,1,""],xi_degrees:[15,3,1,""],arnonC_basis:[15,3,1,""],atomic_basis_odd:[15,3,1,""],steenrod_algebra_basis:[15,3,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra_nonstandard":{C:[1,2,1,""],Cp:[1,2,1,""],T:[1,2,1,""]},"sage.algebras.clifford_algebra.ExteriorAlgebraDifferential":{homology:[7,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra.T.Element":{inverse:[1,1,1,""]},"sage.algebras.free_algebra.FreeAlgebra_generic":{pbw_basis:[26,1,1,""],monoid:[26,1,1,""],ngens:[26,1,1,""],algebra_generators:[26,1,1,""],is_commutative:[26,1,1,""],gens:[26,1,1,""],pbw_element:[26,1,1,""],one_basis:[26,1,1,""],poincare_birkhoff_witt_basis:[26,1,1,""],is_field:[26,1,1,""],product_on_basis:[26,1,1,""],lie_polynomial:[26,1,1,""],g_algebra:[26,1,1,""],Element:[26,4,1,""],gen:[26,1,1,""],quo:[26,1,1,""],quotient:[26,1,1,""]},"sage.algebras.commutative_dga.DifferentialGCAlgebra.Element":{differential:[11,1,1,""],is_coboundary:[11,1,1,""],is_cohomologous_to:[11,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra_nonstandard.C":{to_T_basis:[1,1,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra":{FiniteDimensionalAlgebra:[27,2,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra_nonstandard.Cp":{to_T_basis:[1,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra_nonstandard.T":{to_Cp_basis:[1,1,1,""],to_C_basis:[1,1,1,""]},"sage.algebras.letterplace.free_algebra_element_letterplace":{poly_reduce:[2,3,1,""],singular_system:[2,3,1,""],FreeAlgebraElement_letterplace:[2,2,1,""]},"sage.algebras.commutative_dga.DifferentialGCAlgebra":{cohomology_raw:[11,1,1,""],cocycles:[11,1,1,""],coboundaries:[11,1,1,""],differential:[11,1,1,""],cohomology:[11,1,1,""],Element:[11,2,1,""],graded_commutative_algebra:[11,1,1,""],quotient:[11,1,1,""]},"sage.algebras.commutative_dga.GCAlgebra":{quotient:[11,1,1,""],Element:[11,2,1,""],differential:[11,1,1,""],cdg_algebra:[11,1,1,""],basis:[11,1,1,""]},"sage.algebras.free_algebra_quotient":{hamilton_quatalg:[17,3,1,""],FreeAlgebraQuotient:[17,2,1,""]},"sage.algebras.shuffle_algebra.ShuffleAlgebra":{dual_pbw_basis:[4,1,1,""],coproduct:[4,1,1,""],algebra_generators:[4,1,1,""],is_commutative:[4,1,1,""],to_dual_pbw_element:[4,1,1,""],gens:[4,1,1,""],one_basis:[4,1,1,""],variable_names:[4,1,1,""],coproduct_on_basis:[4,1,1,""],product_on_basis:[4,1,1,""],counit:[4,1,1,""],gen:[4,1,1,""]},"sage.algebras.commutative_dga.GCAlgebra.Element":{is_homogeneous:[11,1,1,""],dict:[11,1,1,""],basis_coefficients:[11,1,1,""],degree:[11,1,1,""]},"sage.algebras.nil_coxeter_algebra":{NilCoxeterAlgebra:[24,2,1,""]},"sage.algebras":{group_algebra:[12,0,0,"-"],affine_nil_temperley_lieb:[9,0,0,"-"],free_algebra_quotient:[17,0,0,"-"],shuffle_algebra:[4,0,0,"-"],hall_algebra:[20,0,0,"-"],free_algebra_quotient_element:[3,0,0,"-"],commutative_dga:[11,0,0,"-"],catalog:[22,0,0,"-"],free_algebra_element:[21,0,0,"-"],jordan_algebra:[5,0,0,"-"],nil_coxeter_algebra:[24,0,0,"-"],free_algebra:[26,0,0,"-"],weyl_algebra:[28,0,0,"-"],schur_algebra:[18,0,0,"-"],iwahori_hecke_algebra:[1,0,0,"-"],clifford_algebra:[7,0,0,"-"]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra.FiniteDimensionalAlgebra":{maximal_ideals:[27,1,1,""],quotient_map:[27,1,1,""],is_commutative:[27,1,1,""],one:[27,1,1,""],primary_decomposition:[27,1,1,""],is_associative:[27,1,1,""],maximal_ideal:[27,1,1,""],table:[27,1,1,""],basis:[27,1,1,""],left_table:[27,1,1,""],ideal:[27,1,1,""],is_zero:[27,1,1,""],from_base_ring:[27,1,1,""],degree:[27,1,1,""],is_finite:[27,1,1,""],random_element:[27,1,1,""],Element:[27,4,1,""],cardinality:[27,1,1,""],gen:[27,1,1,""],is_unitary:[27,1,1,""],ngens:[27,1,1,""],base_extend:[27,1,1,""]},"sage.algebras.commutative_dga":{DifferentialGCAlgebra:[11,2,1,""],GCAlgebra_multigraded:[11,2,1,""],CohomologyClass:[11,2,1,""],Differential:[11,2,1,""],exterior_algebra_basis:[11,3,1,""],GCAlgebra:[11,2,1,""],Differential_multigraded:[11,2,1,""],GradedCommutativeAlgebra:[11,3,1,""],DifferentialGCAlgebra_multigraded:[11,2,1,""],total_degree:[11,3,1,""]},"sage.algebras.commutative_dga.GCAlgebra_multigraded":{differential:[11,1,1,""],basis:[11,1,1,""],Element:[11,2,1,""],cdg_algebra:[11,1,1,""],quotient:[11,1,1,""]},"sage.algebras.quatalg.quaternion_algebra":{is_QuaternionAlgebra:[6,3,1,""],QuaternionAlgebra_abstract:[6,2,1,""],basis_for_quaternion_lattice:[6,3,1,""],QuaternionAlgebraFactory:[6,2,1,""],unpickle_QuaternionAlgebra_v0:[6,3,1,""],maxord_solve_aux_eq:[6,3,1,""],intersection_of_row_modules_over_ZZ:[6,3,1,""],QuaternionFractionalIdeal:[6,2,1,""],QuaternionAlgebra_ab:[6,2,1,""],QuaternionFractionalIdeal_rational:[6,2,1,""],normalize_basis_at_p:[6,3,1,""],QuaternionOrder:[6,2,1,""]},"sage.algebras.quatalg.quaternion_algebra.QuaternionAlgebraFactory":{create_key:[6,1,1,""],create_object:[6,1,1,""]},"sage.algebras.group_algebra.GroupAlgebra":{is_finite:[12,1,1,""],group:[12,1,1,""],ngens:[12,1,1,""],algebra_generators:[12,1,1,""],is_integral_domain:[12,1,1,""],gens:[12,1,1,""],random_element:[12,1,1,""],is_commutative:[12,1,1,""],construction:[12,1,1,""],is_field:[12,1,1,""],is_exact:[12,1,1,""],gen:[12,1,1,""]},"sage.algebras.clifford_algebra.ExteriorAlgebraCoboundary":{chain_complex:[7,1,1,""]},"sage.algebras.commutative_dga.CohomologyClass":{representative:[11,1,1,""]},"sage.algebras.weyl_algebra.DifferentialWeylAlgebra":{polynomial_ring:[28,1,1,""],algebra_generators:[28,1,1,""],basis:[28,1,1,""],variables:[28,1,1,""],differentials:[28,1,1,""],ngens:[28,1,1,""],one:[28,1,1,""],zero:[28,1,1,""],Element:[28,4,1,""],gen:[28,1,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_ideal":{FiniteDimensionalAlgebraIdeal:[10,2,1,""]},"sage.algebras.jordan_algebra.SpecialJordanAlgebra":{basis:[5,1,1,""],algebra_generators:[5,1,1,""],gens:[5,1,1,""],one:[5,1,1,""],zero:[5,1,1,""],Element:[5,2,1,""]},"sage.algebras.jordan_algebra.JordanAlgebraSymmetricBilinear.Element":{bar:[5,1,1,""],trace:[5,1,1,""],norm:[5,1,1,""]},"sage.algebras.free_algebra":{PBWBasisOfFreeAlgebra:[26,2,1,""],is_FreeAlgebra:[26,3,1,""],FreeAlgebraFactory:[26,2,1,""],FreeAlgebra_generic:[26,2,1,""]},"sage.algebras.free_algebra.FreeAlgebraFactory":{create_key:[26,1,1,""],create_object:[26,1,1,""]},"sage.algebras.steenrod.steenrod_algebra.SteenrodAlgebra_mod_two":{Sq:[16,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra":{q1:[1,1,1,""],C:[1,2,1,""],q2:[1,1,1,""],coxeter_group:[1,1,1,""],T:[1,2,1,""],Cp:[1,2,1,""],cartan_type:[1,1,1,""],a_realization:[1,1,1,""]},"sage.algebras.clifford_algebra.ExteriorAlgebra.Element":{hodge_dual:[7,1,1,""],scalar:[7,1,1,""],interior_product:[7,1,1,""],constant_coefficient:[7,1,1,""],antiderivation:[7,1,1,""]},"sage.algebras.clifford_algebra.CliffordAlgebraElement":{supercommutator:[7,1,1,""],reflection:[7,1,1,""],degree_negation:[7,1,1,""],support:[7,1,1,""],transpose:[7,1,1,""],list:[7,1,1,""],clifford_conjugate:[7,1,1,""],conjugate:[7,1,1,""]},"sage.algebras.commutative_dga.Differential":{coboundaries:[11,1,1,""],differential_matrix:[11,1,1,""],cohomology_raw:[11,1,1,""],cohomology:[11,1,1,""],cocycles:[11,1,1,""]},"sage.algebras.weyl_algebra.DifferentialWeylAlgebraElement":{list:[28,1,1,""]},"sage.algebras.steenrod.steenrod_algebra":{AA:[16,3,1,""],Sq:[16,3,1,""],SteenrodAlgebra_generic:[16,2,1,""],SteenrodAlgebra:[16,3,1,""],SteenrodAlgebra_mod_two:[16,2,1,""]},"sage.algebras.clifford_algebra.CliffordAlgebra":{supercenter_basis:[7,1,1,""],quadratic_form:[7,1,1,""],gens:[7,1,1,""],algebra_generators:[7,1,1,""],is_commutative:[7,1,1,""],ngens:[7,1,1,""],Element:[7,4,1,""],degree_on_basis:[7,1,1,""],one_basis:[7,1,1,""],lift_isometry:[7,1,1,""],center_basis:[7,1,1,""],free_module:[7,1,1,""],lift_module_morphism:[7,1,1,""],gen:[7,1,1,""],dimension:[7,1,1,""],pseudoscalar:[7,1,1,""]},"sage.algebras.steenrod.steenrod_algebra.SteenrodAlgebra_generic":{milnor:[16,1,1,""],is_integral_domain:[16,1,1,""],is_commutative:[16,1,1,""],degree_on_basis:[16,1,1,""],is_noetherian:[16,1,1,""],is_generic:[16,1,1,""],basis_name:[16,1,1,""],Q_exp:[16,1,1,""],homogeneous_component:[16,1,1,""],basis:[16,1,1,""],coproduct:[16,1,1,""],is_field:[16,1,1,""],counit_on_basis:[16,1,1,""],profile:[16,1,1,""],algebra_generators:[16,1,1,""],is_division_algebra:[16,1,1,""],top_class:[16,1,1,""],an_element:[16,1,1,""],is_finite:[16,1,1,""],antipode_on_basis:[16,1,1,""],Element:[16,2,1,""],Q:[16,1,1,""],P:[16,1,1,""],gen:[16,1,1,""],pst:[16,1,1,""],prime:[16,1,1,""],gens:[16,1,1,""],ngens:[16,1,1,""],order:[16,1,1,""],one_basis:[16,1,1,""],coproduct_on_basis:[16,1,1,""],product_on_basis:[16,1,1,""],dimension:[16,1,1,""]},"sage.algebras.nil_coxeter_algebra.NilCoxeterAlgebra":{homogeneous_noncommutative_variables:[24,1,1,""],k_schur_noncommutative_variables:[24,1,1,""],homogeneous_generator_noncommutative_variables:[24,1,1,""]},"sage.algebras.hall_algebra":{transpose_cmp:[20,3,1,""],HallAlgebra:[20,2,1,""],HallAlgebraMonomials:[20,2,1,""]},"sage.algebras.group_algebra.GroupAlgebraFunctor":{group:[12,1,1,""]},"sage.algebras.hall_algebra.HallAlgebraMonomials":{antipode_on_basis:[20,1,1,""],Element:[20,2,1,""],one_basis:[20,1,1,""],coproduct_on_basis:[20,1,1,""],product_on_basis:[20,1,1,""],counit:[20,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra.T":{hash_involution_on_basis:[1,1,1,""],bar_on_basis:[1,1,1,""],product_by_generator_on_basis:[1,1,1,""],Element:[1,2,1,""],to_Cp_basis:[1,1,1,""],product_on_basis:[1,1,1,""],inverse_generator:[1,1,1,""],to_C_basis:[1,1,1,""],product_by_generator:[1,1,1,""],inverse_generators:[1,1,1,""]},"sage.algebras.steenrod":{steenrod_algebra_mult:[0,0,0,"-"],steenrod_algebra_misc:[19,0,0,"-"],steenrod_algebra_bases:[15,0,0,"-"],steenrod_algebra:[16,0,0,"-"]},"sage.algebras.finite_dimensional_algebras":{finite_dimensional_algebra_ideal:[10,0,0,"-"],finite_dimensional_algebra_element:[14,0,0,"-"],finite_dimensional_algebra:[27,0,0,"-"],finite_dimensional_algebra_morphism:[23,0,0,"-"]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism.FiniteDimensionalAlgebraHomset":{zero:[23,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra.C":{hash_involution_on_basis:[1,1,1,""]},"sage.algebras.commutative_dga.DifferentialGCAlgebra_multigraded":{coboundaries:[11,1,1,""],cohomology_raw:[11,1,1,""],cohomology:[11,1,1,""],Element:[11,2,1,""],cocycles:[11,1,1,""]},"sage.algebras.affine_nil_temperley_lieb":{AffineNilTemperleyLiebTypeA:[9,2,1,""]},"sage.algebras.schur_algebra.SchurAlgebra":{product_on_basis:[18,1,1,""],dimension:[18,1,1,""],one:[18,1,1,""]},"sage.algebras.iwahori_hecke_algebra.IwahoriHeckeAlgebra.Cp":{hash_involution_on_basis:[1,1,1,""]},"sage.algebras.affine_nil_temperley_lieb.AffineNilTemperleyLiebTypeA":{has_no_braid_relation:[9,1,1,""],algebra_generators:[9,1,1,""],index_set:[9,1,1,""],weyl_group:[9,1,1,""],one_basis:[9,1,1,""],product_on_basis:[9,1,1,""],algebra_generator:[9,1,1,""]},"sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphism":{FiniteDimensionalAlgebraHomset:[23,2,1,""],FiniteDimensionalAlgebraMorphism:[23,2,1,""]},"sage.algebras.commutative_dga.GCAlgebra_multigraded.Element":{degree:[11,1,1,""]},"sage.algebras.letterplace":{free_algebra_element_letterplace:[2,0,0,"-"],letterplace_ideal:[25,0,0,"-"],free_algebra_letterplace:[13,0,0,"-"]},"sage.algebras.letterplace.free_algebra_letterplace":{singular_system:[13,3,1,""],poly_reduce:[13,3,1,""],FreeAlgebra_letterplace:[13,2,1,""]},"sage.algebras.commutative_dga.Differential_multigraded":{coboundaries:[11,1,1,""],cohomology_raw:[11,1,1,""],cohomology:[11,1,1,""],differential_matrix_multigraded:[11,1,1,""],cocycles:[11,1,1,""]},"sage.algebras.letterplace.letterplace_ideal.LetterplaceIdeal":{reduce:[25,1,1,""],groebner_basis:[25,1,1,""]},"sage.algebras.hall_algebra.HallAlgebra":{monomial_basis:[20,1,1,""],antipode_on_basis:[20,1,1,""],Element:[20,2,1,""],one_basis:[20,1,1,""],coproduct_on_basis:[20,1,1,""],product_on_basis:[20,1,1,""],counit:[20,1,1,""]}},titleterms:{lieb:9,schur:18,via:13,weight:2,grade:11,multipl:0,indic:8,weyl:28,tabl:8,ring:13,todo:[26,23,7,11,1],affin:9,unit:13,clifford:7,coxet:24,differenti:11,group:12,nil:24,singular:13,ideal:[25,10],between:23,type:9,commut:11,"function":19,steenrod:[0,16,15,19],letterplac:[13,2],algebra:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28],niltemperlei:9,finit:[27,23,17,14,10],free:[17,3,21,25,26,13,2],catalog:22,base:15,jordan:5,shuffl:4,iwahori:1,associ:13,hall:20,miscellan:19,homogen:[25,2],quaternion:6,element:[0,19,3,21,2,14],heck:1,implement:[13,2],morphism:23,dimension:[27,17],quotient:[17,3]}})
