def __init__(self, base): r""" Initialize the hyperbolic models of hyperbolic space. INPUT: - ``base`` -- a hyperbolic space TESTS:: sage: from sage.geometry.hyperbolic_space.hyperbolic_interface import HyperbolicModels sage: H = HyperbolicPlane() sage: models = HyperbolicModels(H) sage: H.UHP() in models True """ Category_realization_of_parent.__init__(self, base)
def __init__(self, base): r""" Initialize the bases of a free Lie algebra. INPUT: - ``base`` -- a free Lie algebra TESTS:: sage: from sage.algebras.lie_algebras.free_lie_algebra import FreeLieAlgebraBases sage: L.<x, y> = LieAlgebra(QQ) sage: bases = FreeLieAlgebraBases(L) sage: L.Hall() in bases True """ Category_realization_of_parent.__init__(self, base)
def __init__(self, base): r""" Initialize the bases of a descent algebra. INPUT: - ``base`` -- a descent algebra TESTS:: sage: from sage.combinat.descent_algebra import DescentAlgebraBases sage: DA = DescentAlgebra(QQ, 4) sage: bases = DescentAlgebraBases(DA) sage: DA.B() in bases True """ Category_realization_of_parent.__init__(self, base)
def __init__(self, base): r""" Initialize the bases of an `FQSym` INPUT: - ``base`` -- an instance of `FQSym` TESTS:: sage: from sage.combinat.fqsym import FQSymBases sage: FQSym = algebras.FQSym(ZZ) sage: bases = FQSymBases(FQSym) sage: FQSym.F() in bases True """ Category_realization_of_parent.__init__(self, base)
def __init__(self, base, t='t'): """ Initialization of the bases of the `k`-bounded subspace INPUT: - ``base`` -- a basis in the `k`-bounded subspace - ``t` -- a parameter (default: 't') TESTS:: sage: Sym = SymmetricFunctions(QQ['t']) sage: from sage.combinat.sf.new_kschur import KBoundedSubspaceBases sage: KB = Sym.kBoundedSubspace(3) sage: ks = KB.kschur() sage: KBB = KBoundedSubspaceBases(ks); KBB Category of k bounded subspace bases of 3-bounded Symmetric Functions over Univariate Polynomial Ring in t over Rational Field in the 3-Schur basis """ self.t = t Category_realization_of_parent.__init__(self, base)