atlas Library · Script File

`diagram.at`

Functionality related to Lie types, Dynkin diagrams, and their automorphisms

Source

atlas-scripts/diagram.at (158 lines)

Definitions

Loads

<basic.at
<generics.at { for |foldr| }
<sort.at { for |partition_by| }
<combinatorics.at { for |compose_permutation| }

Loaded by

subgroups.at conjugate.at

Definitions in source order

Computing diagram automorphismes for a Lie type:
For a Lie type, generate all diagram automorphisms as permutation vectors,
whose positions correspond to nodes of the diagram, so size is semisimple rank.

`simple_automorphisms`

L13simple_automorphisms (string simple_type, int rank) = [Permutation]

`permutable_types`

L37permutable_types ([string,int] simple_factors) = [[int]]

Find groups of equal simple factors, presumably produced by |simple_factors|.
This uses plain equality of strings and numbers, so if one wishes to allow
permuting factors B2 and C2, give them the same name before calling
|permutable_types| (and make arragements to do the permutation correctly).

Example: permutable_types(simple_factors("A2D4A2A1D4A2")) = [[3],[0,2,5],[1,4]]

`diagram_automorphism_iterator`

L43diagram_automorphism_iterator (LieType t) = Iterator<vec>

Prepare for iterating over diagram autormorphisms (a laborious enterprise)

also in this file at line 129

`sanitize`

L113sanitize (bool to_C) = ((LieType,[int])->LieType,[int])

`diagram_automorphism_iterator`

L129diagram_automorphism_iterator (RootDatum rd) = Iterator<mat>

also in this file at line 43

Generated from atlas-scripts at commit 648506c (2026-10-13).