Coverage for local/lib/python2.7/site-packages/sage/categories/finite_crystals.py : 31%
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r""" Finite Crystals """ #***************************************************************************** # Copyright (C) 2010 Anne Schilling <anne at math.ucdavis.edu> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from sage.misc.cachefunc import cached_method from sage.categories.category_with_axiom import CategoryWithAxiom from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets from sage.categories.tensor import TensorProductsCategory
class FiniteCrystals(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_new() . . . 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_new() . . . pass running ._test_not_implemented_methods() . . . pass running ._test_pickling() . . . pass running ._test_some_elements() . . . pass running ._test_stembridge_local_axioms() . . . pass """
@cached_method def extra_super_categories(self): r""" EXAMPLES::
sage: FiniteCrystals().extra_super_categories() [Category of finite enumerated sets] """
def example(self, n = 3): """ Returns an example of highest weight crystals, as per :meth:`Category.example`.
EXAMPLES::
sage: B = FiniteCrystals().example(); B Highest weight crystal of type A_3 of highest weight omega_1 """
class TensorProducts(TensorProductsCategory): """ The category of finite crystals constructed by tensor product of finite crystals. """ @cached_method def extra_super_categories(self): """ EXAMPLES::
sage: FiniteCrystals().TensorProducts().extra_super_categories() [Category of finite crystals] """
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