Script Reference

K_Nilpotent.at

Lines:
838
Definitions:
101
Dependencies:
basic.atnilpotent_orbits.atK_norm.atprint_K_types.at
Source:
GitHub

Definitions

NameSignatureDescription
kn_verbose
vectorbasis,ParamPol P) = Maybe<vec>:
vectorbasis,KTypePol P) = Maybe<vec>:
Vectorbasis,KTypePol P)=vec:requisition(vector(basis,P))
Vectorbasis,ParamPol P)=vec:requisition(vector(basis,P))
root_datumd)=RootDatum: d.real_form.root_datum
Q_matricesd)=[mat]:for (,,Q,) in d.Q_and_P_X_matrices do Q od
P_X_matricesd)=[mat]:for (,,,P_X) in d.Q_and_P_X_matrices do P_X od
complex_orbit_numberd,ComplexNilpotent OC)=int:find(d.complex_orbits,OC)
real_orbit_numberd,RealNilpotent O)=int:find(d.real_orbits,O)
complex_orbit_numberd,RealNilpotent O) =int:complex_orbit_number(d,complex_orbit(O))
complex_orbit_numberd,int real_orbit) =int:complex_orbit_number(d,d.real_orbits[real_orbit])
real_forms_ofd,int complex_orbit)=[int]:
other_real_formsd,int real_orbit)=[int]:real_forms_of(d,complex_orbit_number(d,real_orbit))
closured,int complex_nilpotent)=[int]:
closure_reald,int complex_orbit)=[int]:
closure_of_real_orbitd,int real_nilpotent)=[int]:
smaller_orbitsd,int real_orbit)=[int]:
K_basis= monomials@KTypePol
K_basis= monomials@[KTypePol]
K_basis(KNilpotentData data, int real_orbit) = [KType]:
K_basisdata, [int] real_orbits)=[KType]:
K_basis_closuredata,int complex_orbit)=[KType]:
K_basis_closure_of_real_orbitdata,int real_orbit)=[KType]:
K_basisdata)=[KType]:
change_basisK_basis, [KType] K_basis_new,mat M)=mat:
L_cap_K_basisd,int real_orbit)=[KType]:
L_cap_K_basisd,[int] real_orbits)=[KType]:
L_cap_K_basisd)=[KType]:L_cap_K_basis(d,#(#d.real_orbits))
L_cap_K_basis_oppd)=[KType]:L_cap_K_basis(d,reverse(#(#d.real_orbits)))
T_matrix(KType,KTypePol) ] pairs)=([KType],[KType],mat):
merge_matrices([KType],[KType],mat) ] matrices)=([KType],[KType],mat):
merge_T_matricesd,[int] real_orbits)=([KType],[KType],mat):
merge_P_X_matricesd,[int] real_orbits)=([KType],[KType],mat):
compute_Y_matrixd,int complex_orbit)=([KType],[KType],mat):
theta_orbit_repsx, [vec] roots)=[vec]:
s_one_rootsO,KGBElt x)=[vec]:
s_one_roots_restrictedO,KGBElt x)=[vec]:
s_one_nc_cx_restricted_rootsO,KGBElt x)=[vec]:
subsets_of_s_one_nc_cx_restricted_rootsO,KGBElt x)=[[vec]]:
rho_shiftsO,KGBElt x_G)=[(vec,int)]:
twist_by_minus_2rho_u_cap_sP,KTypePol K_type_formula)=KTypePol:
twist_by_minus_2rho_u_cap_sP,KType mu)=KType:
Phi(RealNilpotent O,int kgb_number_L, ratvec lambda_L) = KTypePol:
PhiO,Param p_L)=KTypePol:Phi(O,#x(p_L),lambda(p_L))
PhiO,KType mu_L)=KTypePol:Phi(O,#x(mu_L),lambda(mu_L))
PhiO,KTypePol mu_L)=KTypePol:
functions_on_real_orbitO_in)=KTypePol:
in_spanlist,KTypePol P)=([KType],mat,vec,bool):
in_spanlist_of_lists,KTypePol P)=([KType],mat,vec,bool):
Phi_uptoO,int N, ratvec v)=[(KType,KTypePol)]:
Phi_uptox_K,[RealNilpotent] orbits, int N, ratvec v)=[(RealNilpotent,[(KType,KTypePol)])]:
initialize_KNilpotentG, int N,ratvec v, bool include_Q_and_P_X_matrices)=KNilpotentData:
initialize_KNilpotentG, int N,bool compute)=KNilpotentData:initialize_KNilpotent(G,N,rho_check(G),compute)
initialize_KNilpotentG, int N)=KNilpotentData:initialize_KNilpotent(G,N,rho_check(G),true)
initialize_KNilpotentG, ratvec v, int N)=KNilpotentData:initialize_KNilpotent(G,N,v,true)
potential_real_nilpotent_orbitsG,[ComplexNilpotent] complex_orbits)=[RealNilpotent]:
potential_real_nilpotent_orbitsG)=[RealNilpotent]:
update_pairspairs,int j,[(KType,KTypePol)] new_pairs)=[[(KType,KTypePol)]]:
update_T_matrices] T_matrices,int j, ([KType],[KType],mat) new_matrices)=[([KType],[KType],m
update_Y_matrices] Y_matrices,int j, ([KType],[KType],mat) new_matrices)=[([KType],[KType],m
update_Q_and_P_X_matrices] Q_and_P_X__matrices,int j, ([KType],[KType],mat,mat) new_matr
fill_one_stepd, int complex_orbit)={KNilpotentData:}KNilpotentData:
filld,int n)=KNilpotentData:
filld)=KNilpotentData:
failed([KType]:[],[KType]:[], null(0,0),null(0),null(0),false)
failed_av_annnull(0,0),null(0),null(0),false)
failed_av([KType]:[],[KType]:[],[int]:[],null(0,0),null(0),null(0),false)
searchd,[int] real_orbits,KTypePol P)=([KType],[KType],mat,vec,vec,bool):
searchd,int real_orbit,[int] real_orbits,KType mu_L)=([KType],[KType],mat,vec,vec,bool):
searchd,int complex_orbit,KTypePol P)=([KType],[KType],mat,vec,vec,bool):
av_annd,KTypePol P)=([KType],[KType],int,mat,vec,vec,bool):
av_annd,Param p)=([KType],[KType],int,mat,vec,vec,bool):
projectorv, int i)=
av_from_av_annd,int complex_orbit,KTypePol P)=vec:
av_from_av_annd,int complex_orbit,Param p)=
avd, KTypePol P)=vec:
avd, Param p)=
avd,[Param] params)=[(Param,vec)]:
av_ann_elem_longd,KTypePol P)=([KType],[KType],int,mat,vec,vec,bool):
av_ann_elem_longd,Param p)=([KType],[KType],int,mat,vec,vec,bool):
av_from_av_ann_elem_longd,int complex_orbit,KTypePol P)=([KType],[KType],[int],mat,vec,vec,bool):
av_from_av_ann_elem_longd,int complex_orbit,Param p)=([KType],[KType],[int],mat,vec,vec,bool):
av_elem_longd,KTypePol P)=([KType],[KType],[int],mat,vec,vec,bool):
av_elem_longd,Param p)=([KType],[KType],[int],mat,vec,vec,bool):
av_ann_elemd,KTypePol P)=int:let (,,av,,,,)=av_ann_elem_long(d,P) in av
av_ann_elemd,Param p)=int:let (,,av,,,,)=av_ann_elem_long(d,p) in av
av_from_av_ann_elemd,int complex_orbit,KTypePol P)=[int]:let (,,av,,,,)=av_from_av_ann_elem_long(d,c
av_from_av_ann_elemd,int complex_orbit,Param p)=[int]:let (,,av,,,,)=av_from_av_ann_elem_long(d,comp
av_elemd,KTypePol P)=[int]:let (,,av,,,,)=av_elem_long(d,P) in av
av_elemd,Param p)=[int]:let (,,av,,,,)=av_elem_long(d,p) in av
KNilpotent_real_orbitsG,int N, ratvec v)=
KNilpotent_real_orbitsG,int N)=KNilpotent_real_orbits(G,N,rho_check(G))
KNilpotent_real_orbitsG)=KNilpotent_real_orbits(G,K_norm(trivial(G).K_type_pol)+3) {in SU(2,1) need +3}in SU(2,1) need +3
stringifya,int b))="(" + a.to_string + "," + b.to_string + ")"
display_stringO)=string:
showd)=void:
test_minimal_orbitsG, int N)=void:
test_minimal_orbitsG, int N, void flag)=void:
test_all_orbitsG, int N)=void:
test_all_orbitsG, int N, void flag)=void: