Classical symmetric functions.

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

Bases: sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic

The class of classical symmetric functions.

Todo

delete this class once all coercions will be handled by Sage’s coercion model

TESTS:

sage: TestSuite(SymmetricFunctions(QQ).s()).run()
sage: TestSuite(SymmetricFunctions(QQ).h()).run()
sage: TestSuite(SymmetricFunctions(QQ).m()).run()
sage: TestSuite(SymmetricFunctions(QQ).e()).run()
sage: TestSuite(SymmetricFunctions(QQ).p()).run()
class Element(M, x)

Bases: sage.combinat.sf.sfa.SymmetricFunctionAlgebra_generic_Element

A symmetric function.

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', 'powersum')]
<built-in function t_SCHUR_POWSYM_symmetrica>

The following checks if the bug described in trac ticket #15312 is fixed.:

sage: change = sage.combinat.sf.classical.conversion_functions[('powersum', 'Schur')]
sage: hideme = change({Partition([1]*47):ZZ(1)}) # long time
sage: change({Partition([2,2]):QQ(1)})
s[1, 1, 1, 1] - s[2, 1, 1] + 2*s[2, 2] - s[3, 1] + s[4]

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