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))