Finite Crystals¶
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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_cardinality() . . . 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
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class
TensorProducts
(category, *args)¶ Bases:
sage.categories.tensor.TensorProductsCategory
The category of finite crystals constructed by tensor product of finite crystals.
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extra_super_categories
()¶ EXAMPLES:
sage: FiniteCrystals().TensorProducts().extra_super_categories() [Category of finite crystals]
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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
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FiniteCrystals.
extra_super_categories
()¶ EXAMPLES:
sage: FiniteCrystals().extra_super_categories() [Category of finite enumerated sets]
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class