def __init__(self, Sym, pfix):
r"""
Initialize the basis and register coercions.
The coercions are set up between the ``other_basis``
INPUT:
- ``Sym`` -- an instance of the symmetric function algebra
- ``pfix`` -- a prefix to use for the basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: ht = SymmetricFunctions(QQ).ht(); ht
Symmetric Functions over Rational Field in the induced trivial
symmetric group character basis
sage: st = SymmetricFunctions(QQ).st(); st
Symmetric Functions over Rational Field in the irreducible
symmetric group character basis
"""
SFA_generic.__init__(
self,
Sym,
basis_name="irreducible symmetric group character",
prefix=pfix,
graded=False)
self._other = Sym.Schur()
self._p = Sym.powersum()
self.module_morphism(self._self_to_power_on_basis,
codomain=Sym.powersum()).register_as_coercion()
self.register_coercion(
SetMorphism(Hom(self._other, self), self._other_to_self))
def __init__(self, Sym, other_basis, bname, pfix):
r"""
Initialize the basis and register coercions.
The coercions are set up between the ``other_basis``.
INPUT:
- ``Sym`` -- an instance of the symmetric function algebra
- ``other_basis`` -- a basis of Sym
- ``bname`` -- the name for this basis (convention: ends in "character")
- ``pfix`` -- a prefix to use for the basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: ht = SymmetricFunctions(QQ).ht(); ht
Symmetric Functions over Rational Field in the induced trivial character basis
sage: st = SymmetricFunctions(QQ).st(); st
Symmetric Functions over Rational Field in the irreducible symmetric group character basis
sage: TestSuite(ht).run()
"""
SFA_generic.__init__(self, Sym, basis_name=bname, prefix=pfix, graded=False)
self._other = other_basis
self.module_morphism(self._self_to_other_on_basis,
codomain=self._other).register_as_coercion()
self.register_coercion(SetMorphism(Hom(self._other, self),
self._other_to_self))
def __init__(self, Sym, pfix):
r"""
Initialize the basis and register coercions.
The coercions are set up between the ``other_basis``
INPUT:
- ``Sym`` -- an instance of the symmetric function algebra
- ``pfix`` -- a prefix to use for the basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: ht = SymmetricFunctions(QQ).ht(); ht
Symmetric Functions over Rational Field in the induced trivial
character basis
sage: st = SymmetricFunctions(QQ).st(); st
Symmetric Functions over Rational Field in the irreducible
symmetric group character basis
"""
SFA_generic.__init__(self, Sym,
basis_name="irreducible symmetric group character",
prefix=pfix, graded=False)
self._other = Sym.Schur()
self._p = Sym.powersum()
self.module_morphism(self._self_to_power_on_basis,
codomain=Sym.powersum()).register_as_coercion()
from sage.categories.morphism import SetMorphism
self.register_coercion(SetMorphism(Hom(self._other, self),
self._other_to_self))
def __init__(self, Sym, other_basis, bname, pfix):
r"""
Initialize the basis and register coercions.
The coercions are set up between the ``other_basis``.
INPUT:
- ``Sym`` -- an instance of the symmetric function algebra
- ``other_basis`` -- a basis of Sym
- ``bname`` -- the name for this basis (convention: ends in "character")
- ``pfix`` -- a prefix to use for the basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: ht = SymmetricFunctions(QQ).ht(); ht
Symmetric Functions over Rational Field in the induced trivial character basis
sage: st = SymmetricFunctions(QQ).st(); st
Symmetric Functions over Rational Field in the irreducible symmetric group character basis
sage: TestSuite(ht).run()
"""
SFA_generic.__init__(self,
Sym,
basis_name=bname,
prefix=pfix,
graded=False)
self._other = other_basis
self.module_morphism(self._self_to_other_on_basis,
codomain=self._other).register_as_coercion()
self.register_coercion(
SetMorphism(Hom(self._other, self), self._other_to_self))
