Classical symmetric functions.

class sage.combinat.sf.classical.SymmetricFunctionAlgebra_classical(R, basis_name=None, prefix=None)

Bases: sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic

TESTS:

sage: TestSuite(SymmetricFunctions(QQ).s()).run()

class Element(M, x)

Bases: sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic_Element

A symmetric function.

SymmetricFunctionAlgebra_classical.is_commutative()

Return True if this symmetric function algebra is commutative.

EXAMPLES:

sage: s = SFASchur(QQ)
sage: s.is_commutative()
True

SymmetricFunctionAlgebra_classical.is_field(proof=True)

EXAMPLES:

sage: s = SFASchur(QQ)
sage: s.is_field()
False

sage.combinat.sf.classical.init()

Set up the conversion functions between the classical bases.

EXAMPLES:

sage: from sage.combinat.sf.classical import init
sage: sage.combinat.sf.classical.conversion_functions = {}
sage: init()
sage: sage.combinat.sf.classical.conversion_functions[('schur', 'power')]
<built-in function t_SCHUR_POWSYM_symmetrica>