Finite Weyl Groups

class sage.categories.finite_weyl_groups.FiniteWeylGroups(s=None)

Bases: sage.categories.category.Category

The category of finite Weyl groups.

EXAMPLES:

sage: C = FiniteWeylGroups()
sage: C
Category of finite weyl groups
sage: C.super_categories()
[Category of weyl groups, Category of finite coxeter groups]
sage: C.example()
The symmetric group on {0, ..., 3}

TESTS:

sage: W = FiniteWeylGroups().example()
sage: TestSuite(W).run(verbose = "True")
running ._test_an_element() . . . pass
running ._test_associativity() . . . pass
running ._test_category() . . . pass
running ._test_elements() . . .
  Running the test suite of self.an_element()
  running ._test_category() . . . pass
  running ._test_eq() . . . pass
  running ._test_not_implemented_methods() . . . pass
  running ._test_pickling() . . . pass
  pass
running ._test_elements_eq_reflexive() . . . pass
running ._test_elements_eq_symmetric() . . . pass
running ._test_elements_eq_transitive() . . . pass
running ._test_elements_neq() . . . pass
running ._test_enumerated_set_contains() . . . pass
running ._test_enumerated_set_iter_cardinality() . . . pass
running ._test_enumerated_set_iter_list() . . . pass
running ._test_eq() . . . pass
running ._test_has_descent() . . . pass
running ._test_inverse() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_one() . . . pass
running ._test_pickling() . . . pass
running ._test_prod() . . . pass
running ._test_reduced_word() . . . pass
running ._test_simple_projections() . . . pass
running ._test_some_elements() . . . pass
class ElementMethods
class FiniteWeylGroups.ParentMethods
FiniteWeylGroups.super_categories()

EXAMPLES:

sage: FiniteWeylGroups().super_categories()
[Category of weyl groups, Category of finite coxeter groups]

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