def coproduct_on_basis(self, mu):
r"""
Returns the coproduct of ``self(mu)``.
Here ``self`` is the basis of Schur functions in the ring of symmetric functions.
INPUT:
- ``self`` -- a Schur symmetric function basis
- ``mu`` -- a partition
OUTPUT:
- an element of the tensor square of the Schur basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: s.coproduct_on_basis([2])
s[] # s[2] + s[1] # s[1] + s[2] # s[]
"""
import sage.libs.lrcalc.lrcalc as lrcalc
T = self.tensor_square()
return T._from_dict(lrcalc.coprod(mu, all=1))
def coproduct_on_basis(self, mu):
r"""
Returns the coproduct of ``self(mu)``.
Here ``self`` is the basis of Schur functions in the ring of symmetric functions.
INPUT:
- ``self`` -- a Schur symmetric function basis
- ``mu`` -- a partition
OUTPUT:
- the image of the ``mu``-th Schur function under the comultiplication of
the Hopf algebra of symmetric functions; this is an element of the
tensor square of the Schur basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: s.coproduct_on_basis([2])
s[] # s[2] + s[1] # s[1] + s[2] # s[]
"""
T = self.tensor_square()
return T._from_dict( lrcalc.coprod(mu, all=1) )
def coproduct_on_basis(self, mu):
r"""
Returns the coproduct of ``self(mu)``.
Here ``self`` is the basis of Schur functions in the ring of symmetric functions.
INPUT:
- ``self`` -- a Schur symmetric function basis
- ``mu`` -- a partition
OUTPUT:
- an element of the tensor square of the Schur basis
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: s.coproduct_on_basis([2])
s[] # s[2] + s[1] # s[1] + s[2] # s[]
"""
import sage.libs.lrcalc.lrcalc as lrcalc
T = self.tensor_square()
return T._from_dict( lrcalc.coprod(mu, all=1) )
