Finite Coxeter Groups¶
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sage.categories.finite_coxeter_groups.
FiniteCoxeterGroups
¶ The category of finite Coxeter groups.
EXAMPLES:
sage: CoxeterGroups.Finite() Category of finite coxeter groups sage: FiniteCoxeterGroups().super_categories() [Category of finite generalized coxeter groups, Category of coxeter groups] sage: G = CoxeterGroups().Finite().example() sage: G.cayley_graph(side = "right").plot() Graphics object consisting of 40 graphics primitives
Here are some further examples:
sage: WeylGroups().Finite().example() The symmetric group on {0, ..., 3} sage: WeylGroup(["B", 3]) Weyl Group of type ['B', 3] (as a matrix group acting on the ambient space)
Those other examples will eventually be also in this category:
sage: SymmetricGroup(4) Symmetric group of order 4! as a permutation group sage: DihedralGroup(5) Dihedral group of order 10 as a permutation group