Weyl Groups

class sage.categories.weyl_groups.WeylGroups(s=None)

Bases: sage.categories.category.Category

The category of Weyl groups

See: http://en.wikipedia.org/wiki/Weyl_groups

EXAMPLES:

sage: WeylGroups()                      # todo: uppercase for Weyl
Category of weyl groups
sage: WeylGroups().super_categories()
[Category of coxeter groups]

Here are some examples:

sage: WeylGroups().example()            # todo: not implemented
sage: FiniteWeylGroups().example()
The symmetric group on {0, ..., 3}
sage: AffineWeylGroups().example()      # todo: not implemented
sage: WeylGroup(["B", 3])
Weyl Group of type ['B', 3] (as a matrix group acting on the ambient space)

This one will eventually be also in this category:

sage: SymmetricGroup(4)
Symmetric group of order 4! as a permutation group

TESTS:

sage: C = WeylGroups()
sage: TestSuite(C).run()

class ElementMethods

class WeylGroups.ParentMethods

WeylGroups.super_categories(*args, **kwds)

EXAMPLES:

sage: WeylGroups().super_categories()
[Category of coxeter groups]