Script Reference

tits_centralizer.at

Lines:
718
Definitions:
72
Dependencies:
tits.atstructure_constants.atcyclotomic_Gaussian_elim.atcyclotomic_Lie_algebra.atcyclotomicMat.at
Source:
GitHub

Definitions

NameSignatureDescription
to_base(int n, (int->string) digit) = (int->string):
permutation_of_root_vectorsw)=mat:
all_root_indexrd,vec alpha)=int:
all_root_indexrd)=(vec->int):
simple_reflection_on_root_vectorrd, int i, int j)=
simple_reflection_on_root_vectorsrd,int i,ratvec v)=ratvec:
simple_reflection_on_root_vectorsrd,int i,CyclotomicVec v)=CyclotomicVec:
action_on_root_vectorsrd,[int] S,ratvec v)=ratvec:
action_on_root_vectorsrd,[int] S,CyclotomicVec v)=CyclotomicVec:
action_on_root_vectorsw,ratvec v)=ratvec:
action_on_root_vectorsw,CyclotomicVec v)=CyclotomicVec:
signw,vec alpha)=
tits_actionw,LieAlgebraElement X)=LieAlgebraElement:
tits_actionw,CFLieAlgebraElement X)=CFLieAlgebraElement:
torus_actionv,CFLieAlgebraElement X)=CFLieAlgebraElement:
*w,CFLieAlgebraElement X)=CFLieAlgebraElement:
tits_centralizes_weakw,[vec] S)=bool:
tits_centralizes_weakw,LieAlgebraElement X)=bool:
tits_centralizes_weakw,CFLieAlgebraElement X)=bool:
tits_centralizer_weakws,[vec] S)=[WeylElt]:
tits_centralizer_weakS,LieAlgebraElement X)=[WeylElt]:
tits_centralizer_weakX)=tits_centralizer_weak(W(X.root_datum),X)
tits_centralizer_weakS,CFLieAlgebraElement X)=[WeylElt]:
tits_centralizer_weakX)=tits_centralizer_weak(W(X.root_datum),X)
tits_centralizer_weakH,LieAlgebraElement X)=
tits_centralizer_weakH,CFLieAlgebraElement X)=
tits_centralizer_weakH,[vec] S)=
tits_centralizer_weakrd,ratvec H,[vec] S)=
tits_centralizer_weakt,ComplexNilpotent O)=
tits_centralizer_weakO)=
spanning_subsetM)=(mat,[int],[int]):
map_root_of_unityz)=CyclotomicFieldElement:
map_root_of_unityv)=CyclotomicVec:
promotev)=CyclotomicVec:
promoteX)=CFLieAlgebraElement:
is_solvable_for_torus_elementM,CyclotomicVec v)=bool:
solve_for_torus_elementM, CyclotomicVec v)=(bool,ratvec):
solve_for_torus_element_oldM, CyclotomicVec v)=
JM_triplet,vec H,[vec] S_roots,CyclotomicField F)=(bool,(CFLieAlgebraElement,CFLieAlgebraEle
JM_triplet,ComplexNilpotent O,CyclotomicField F)=
JM_triple_onet,vec H,[vec] S_roots,[int] coeff,CyclotomicField F)=
JM_triplest,vec H,[vec] S_roots,CyclotomicField F,int number, int start)={(bool,(CFLieAlgebr(bool,(CFLieAlgebraElement,CFLieAlgebraElement,CFLieAlgebraElement)):
JM_triplet,vec H,CyclotomicField F)=
JM_triplest,vec H,CyclotomicField F,int number,int start)=
solve_for_tits_elementw,CFLieAlgebraElement X)=
make_coordsN, int modulus, int size)=
inverse_make_coordsv,int modulus)=
JM_triple_strongt,vec H,[vec] S_roots,CyclotomicField F,WeylElt w,[int] start_vec, int tries
JM_triple_strongt,ComplexNilpotent O,CyclotomicField F,WeylElt w,int tries)=
JM_triple_strongt,vec H,[vec] S_roots,CyclotomicField F,[WeylElt] ws,[int] start_vec, int tr
JM_triples_strong_oldt,vec H,[vec] S,CyclotomicField F,WeylElt w,[int] start_vec, int tries)(bool,(CFLieAlgebraElement,CFLieAlgebraElement,CFLieAlgebraElement)):
jump
JM_triples_strongt,vec H,[vec] S_roots,CyclotomicField F,[WeylElt] ws,[int] start_vec, int t(bool,(CFLieAlgebraElement,CFLieAlgebraElement,CFLieAlgebraElement)):
new_orderg)=int:
basis_dual_latticeM)=ratmat:right_inverse(^M)
basis_dual_latticeM)=ratmat:basis_dual_lattice(mat_as_ratmat(M))
tits_centralizer_generatorsH,LieAlgebraElement X)=
findS,Tits_elt g)=first(#S,(int i)bool:S[i]=g)
tits_subgroupS)=[Tits_elt]:
tits_centralizerH,LieAlgebraElement X)=
tits_centralizert,ComplexNilpotent O)=
findS,vec alpha)=first(for i:#S do alpha=S[i] od)
orbitsS,WeylElt w)=[[vec]]:
choicesS,WeylElt w)=[[vec]]:orbits(S,w)
choicesH,WeylElt w)=[[vec]]:
make_vectors_from_choicesw, [[vec]] choices)=
combine_vectors_from_choicesvectors)=
make_choicesH,WeylElt w)=
listS,WeylElt w)=void:
listX,WeylElt w)=void:list(X.support,w)
good_rootsS,WeylElt w)=
good_rootsH,WeylElt w)=