Script Reference
all_finite_order.at
Definitions
| Name | Signature | Description |
|---|---|---|
| bounded_lists | ([int] limits,[int] labels, int order) = [ [int] ]: | |
| get_subsets_given_order | rd, int order) = [ [int] ]: | |
| get_subsets | rd, int max_order) = [[ [int] ]]: | |
| null | rd)=([int],RootDatum,int):([],GL(1),0) | |
| get_raw_data | rd,[[[int]]] S)=[[([int],RootDatum,int)]]: | |
| mysort | = ([([int],RootDatum,int)] -> [([int],RootDatum,int)]): | |
| refine_raw_data | data)=[[([int],RootDatum,int)]]:for a in data do mysort(a) od | |
| get_data | rd,[[[int]]] S)=[[([int],RootDatum,int)]]:refine_raw_data(get_raw_data(rd,S)) | |
| get_data | rd,int n)=[[([int],RootDatum,int)]]:refine_raw_data(get_raw_data(rd,get_subsets(rd,n))) | |
| nice_classes | rd, int n)= | |
| info | data, int j)=void: | |
| info_reduced | data, int j)=void: | |
| info | data, int j, int bound)=void: | |
| cox | rd,int n)=void:let v=rho(rd)/n then | |
| test | data, int n)=void: | |
| find | data, int n)=void: | |
| find_short | data, int n)=void: | |
| table | data)=void: | |
| table | data,int bound)=void: | |
| table_reduced | data)=void: | |
| Kac_diags_given_order | rd, int order)=[[int]]: | Given a positive integer m, (r+1)-tuples of integers a_i so that sum_i(a_i m_i)=m, with a_i's relatively prime. The last entry corresponds to the lowest root. These are essentially Kac diagrams. |
| Kac_diags_up_to_order | rd, int max_order)=[[[int]]]: | |
| Kac_x | (RootDatum rd, vec v)=ratvec: let labels=simple_root_labels(rd)#1 | Given a Kac diagram, compute the corresponding element of the Lie algebra. |
| order | (RootDatum rd, vec v)=int: denom(Kac_x(rd,v)) | Given a Kac diagram, compute the order of the corresponding element of G. |
| Kac_diags_of_identity | (RootDatum rd)=[[int]]: | List the Kac diagrams for the identity element of a complex group G (unique if G is simply connected). |
| identity_in_fund_domain | (RootDatum rd)=[ratvec]: | List the elements in the fundamental domain for the affine Weyl Group that exponentiate to the identity element. |
| is_conjugate | (ratvec v,ratvec w,RootDatum rd)=bool: | Given two ratvecs representing elements of T, decide whether they are conjugate in G. |
| is_conjugate_Kac | ([int] v,[int] w, RootDatum rd)=bool: | |
| Kac_classes_given_order_crude | = Kac_diags_given_order@(RootDatum,int) | crude listing. } set Kac_classes_given_order_crude = Kac_diags_given_order@(RootDatum,int) |
| Kac_classes_given_order | (RootDatum rd,int order)=[[int]]: | List all Kac elements of a given order, up to conjugacy of the corresponding group element. |
| zero_roots | rd,[int] Kac)=[int]: | |
| complex_pseudo_Levi | rd, [int] S)= RootDatum: | |
| centralizer_of_Kac | (RootDatum rd, [int] Kac)=RootDatum: |