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 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 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):
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):
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, 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)
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)
