Finite Crystals

class sage.categories.finite_crystals.FiniteCrystals(base_category)

Bases: sage.categories.category_with_axiom.CategoryWithAxiom

The category of finite crystals.

EXAMPLES:

sage: C = FiniteCrystals()
sage: C
Category of finite crystals
sage: C.super_categories()
[Category of crystals, Category of finite enumerated sets]
sage: C.example()
Highest weight crystal of type A_3 of highest weight omega_1

TESTS:

sage: TestSuite(C).run()
sage: B = FiniteCrystals().example()
sage: TestSuite(B).run(verbose = True)
running ._test_an_element() . . . 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
  running ._test_stembridge_local_axioms() . . . 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_fast_iter() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
running ._test_some_elements() . . . pass
running ._test_stembridge_local_axioms() . . . pass
class TensorProducts(category, *args)

Bases: sage.categories.tensor.TensorProductsCategory

The category of finite crystals constructed by tensor product of finite crystals.

extra_super_categories()

EXAMPLES:

sage: FiniteCrystals().TensorProducts().extra_super_categories()
[Category of finite crystals]
FiniteCrystals.example(n=3)

Returns an example of highest weight crystals, as per Category.example().

EXAMPLES:

sage: B = FiniteCrystals().example(); B
Highest weight crystal of type A_3 of highest weight omega_1
FiniteCrystals.extra_super_categories()

EXAMPLES:

sage: FiniteCrystals().extra_super_categories()
[Category of finite enumerated sets]

Previous topic

Finite Coxeter Groups

Next topic

Finite dimensional algebras with basis

This Page