def __init__(self, n=None):
r"""
EXAMPLES::
sage: from sage.combinat.baxter_permutations import BaxterPermutations_all
sage: BaxterPermutations_all()
Baxter permutations
"""
self.element_class = Permutations().element_class
from sage.categories.examples.infinite_enumerated_sets import NonNegativeIntegers
from sage.sets.family import Family
DisjointUnionEnumeratedSets.__init__(self,
Family(NonNegativeIntegers(),
BaxterPermutations_size),
facade=False, keepkey=False)
def __init__(self, enumset):
"""
EXAMPLES::
sage: from sage.sets.family import EnumeratedFamily
sage: f = EnumeratedFamily(Permutations(3))
sage: TestSuite(f).run()
sage: from sage.categories.examples.infinite_enumerated_sets import NonNegativeIntegers
sage: f = Family(NonNegativeIntegers())
sage: TestSuite(f).run()
"""
if enumset.cardinality() == Infinity:
baseset = NonNegativeIntegers()
else:
baseset = xrange(enumset.cardinality())
LazyFamily.__init__(self, baseset, enumset.unrank)
self.enumset = enumset
def __init__(self, R, k, t=None):
"""
EXAMPLES::
sage: kSchurFunctions(QQ, 3).base_ring()
Univariate Polynomial Ring in t over Rational Field
sage: kSchurFunctions(QQ, 3, t=1).base_ring()
Rational Field
sage: ks3 = kSchurFunctions(QQ, 3)
sage: ks3 == loads(dumps(ks3))
True
"""
self.k = k
self._name = "k-Schur Functions at level %s"%k
self._prefix = "ks%s"%k
self._element_class = kSchurFunctions_t.Element
if t is None:
R = R['t']
self.t = R.gen()
elif t not in R:
raise ValueError, "t (=%s) must be in R (=%s)"%(t,R)
else:
self.t = R(t)
if str(t) != 't':
self._name += " with t=%s"%self.t
self._s_to_self_cache = s_to_k_cache.get(k, {})
self._self_to_s_cache = k_to_s_cache.get(k, {})
# This is an abuse, since kschur functions do not form a basis of Sym
sfa.SymmetricFunctionAlgebra_generic.__init__(self, R)
# so we need to take some counter measures
self._basis_keys = sage.combinat.partition.Partitions(NonNegativeIntegers(), max_part=k)
self._s = sfa.SFASchur(self.base_ring())
# temporary until Hom(GradedHopfAlgebrasWithBasis work better)
category = sage.categories.all.ModulesWithBasis(self.base_ring())
# This really should be a conversion, not a coercion (it can fail)
self .register_coercion(SetMorphism(Hom(self._s, self, category), self._s_to_self))
self._s.register_coercion(SetMorphism(Hom(self, self._s, category), self._self_to_s))