DynkinDiagram -- the class of Dynkin diagrams

Description

A Dynkin diagram contains lists representing vertices of the Dynkin diagram (in other words a simple root). Each of these lists contains sublists of end points of an edge from the vertex. There are in this order, the simple edges, double edge to a smaller root, double edge to a larger root, triple edge to a smaller root, triple edge to a larger root. If there is no such edge, we have an empty sublist.

i1 : dynkinDiagram(rootSystemB(4))

o1 = DynkinDiagram{{{2}, {}, {}, {}, {}}, {{1, 3}, {}, {}, {}, {}}, {{2}, {4}, {}, {}, {}}, {{}, {}, {3}, {}, {}}}

o1 : DynkinDiagram

i2 : dynkinDiagram(rootSystemD(4))

o2 = DynkinDiagram{{{2}, {}, {}, {}, {}}, {{1, 3, 4}, {}, {}, {}, {}}, {{2}, {}, {}, {}, {}}, {{2}, {}, {}, {}, {}}}

o2 : DynkinDiagram

Methods that use an object of class DynkinDiagram:

connectedComponents(DynkinDiagram) -- the connected components of a Dynkin diagram
dynkinDiagram(DynkinDiagram,Parabolic) -- the Dynkin diagram of the Levy subgroup of a parabolic
dynkinType(DynkinDiagram) -- the Dynkin type of a Dynkin diagram
endVertices(DynkinDiagram) -- the vertices of a Dynkin diagram with at most one neighbor
rank(DynkinDiagram) -- the rank of a Dynkin diagram
rootSystem(DynkinDiagram) -- the root system corresponding to a Dynkin diagram

For the programmer

The object DynkinDiagram is a type, with ancestor classes BasicList < Thing.