Script Reference

cyclotomic_field_bracket.at

Lines:
216
Definitions:
46
Dependencies:
structure_constants.atratmat.atnilpotent_orbits.atcyclotomicMat.atcyclotomic_Gaussian_elim.at
Source:
GitHub

Definitions

NameSignatureDescription
FX)=CyclotomicField:let (,(v,))=X in v.F
root_datum(t,))=RootDatum:t.root_datum
root_part
semisimple_part
HX)=CyclotomicVec:X.semisimple_part
=X,CFLieAlgebraElement Y)=bool:
nullt,CyclotomicField F)=CFLieAlgebraElement:(t,(null(#t.root_datum.roots,F),null(t.root_dat
=X)=bool:X=null(X.t,X.F)
+X,CFLieAlgebraElement Y)=CFLieAlgebraElement:
*c,CFLieAlgebraElement X)=CFLieAlgebraElement:
*c,CFLieAlgebraElement X)=CFLieAlgebraElement:embed(c,X.F)*X
embedX,CyclotomicField F)=(X.t,(embed(X.root_part,F),embed(X.H,F)))
coordinatesX)=CyclotomicVec:X.root_part##X.H
supportX)=[vec]:
CF_lie_algebra_elementt,CyclotomicVec v)=CFLieAlgebraElement:
CF_lie_algebra_element_semisimplet,CyclotomicVec v)=CF_lie_algebra_element(t,(null(#t.root_d
CF_lie_algebra_element_root_vectorst,CyclotomicVec v)=CF_lie_algebra_element(t,v##(null(t.ro
X_alphat,int i, CyclotomicField F)=CFLieAlgebraElement:embed(X_alpha(t,i),F)
X_alphat,vec alpha, CyclotomicField F)=CFLieAlgebraElement:embed(X_alpha(t,alpha),F)
Ht,vec h,CyclotomicField F)=CFLieAlgebraElement:embed(H(t,h),F)
Xt,(vec alpha,vec h),CyclotomicField F)=CFLieAlgebraElement:embed(X(t,(alpha,h)),F)
Xt,vec alpha,vec h,CyclotomicField F)=CFLieAlgebraElement:embed(X(t,(alpha,h)),F)
lie_algebra_elementt,CyclotomicVec v)=CFLieAlgebraElement:
lie_algebra_element_semisimplet,CyclotomicVec v)=lie_algebra_element(t,(null(#t.root_datum.r
lie_algebra_element_root_vectorst,CyclotomicVec v)=lie_algebra_element(t,v##(null(t.root_dat
CFbasist,int i,CyclotomicField F)=CFLieAlgebraElement:
to_stringsX)=string:
root_part_arrayX)=[(CyclotomicFieldElement,vec)]:
show_longX)=void:prints(X.to_string)
bracket_root_termX,CFLieAlgebraElement Y)=CFLieAlgebraElement:
sumS)=CyclotomicVec:
bracket_torus_termX,CFLieAlgebraElement Y)=CFLieAlgebraElement:
*v,CyclotomicVec w)=CyclotomicFieldElement:
bracket_off_diagonal_termsX,CFLieAlgebraElement Y)=CFLieAlgebraElement:
bracketX,CFLieAlgebraElement Y)=CFLieAlgebraElement:
adX)=CyclotomicMat:
solve_adX,CFLieAlgebraElement Z)=full_solve(ad(X),coordinates(Z))
any(CF_lin_solution x) = bool: case x | affine_space: true | no_Cyclotomic_solution: false esac
a_solution((CyclotomicMat,CyclotomicVec)system) = CyclotomicVec:
jacobi_formulaX,LieAlgebraElement Y,LieAlgebraElement Z)=LieAlgebraElement:
jacobi_identitiest)=bool:
jacobi_identities_longt)=void:
jacobi_identitiesrd)=bool:jacobi_identities(rd.structure_constant_table)
jacobi_identities_longrd)=void:jacobi_identities_long(rd.structure_constant_table)
centralizerX,LieAlgebraElement Y))=
showv)=void: