Bases for \(NCSym\).¶
AUTHORS:
- Travis Scrimshaw (08-04-2013): Initial version
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sage.combinat.ncsym.bases.
MultiplicativeNCSymBases
¶ Category of multiplicative bases of symmetric functions in non-commuting variables.
A multiplicative basis is one for which \(\mathbf{b}_A \mathbf{b}_B = \mathbf{b}_{A|B}\) where \(A|B\) is the
pipe()
operation on set partitions.EXAMPLES:
sage: from sage.combinat.ncsym.bases import MultiplicativeNCSymBases sage: NCSym = SymmetricFunctionsNonCommutingVariables(QQ) sage: MultiplicativeNCSymBases(NCSym) Category of multiplicative bases of symmetric functions in non-commuting variables over the Rational Field
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sage.combinat.ncsym.bases.
NCSymBases
¶ Category of bases of symmetric functions in non-commuting variables.
EXAMPLES:
sage: from sage.combinat.ncsym.bases import NCSymBases sage: NCSym = SymmetricFunctionsNonCommutingVariables(QQ) sage: NCSymBases(NCSym) Category of bases of symmetric functions in non-commuting variables over the Rational Field
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sage.combinat.ncsym.bases.
NCSymBasis_abstract
¶ Abstract base class for a basis of \(NCSym\) or its dual.
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sage.combinat.ncsym.bases.
NCSymDualBases
¶ Category of bases of dual symmetric functions in non-commuting variables.
EXAMPLES:
sage: from sage.combinat.ncsym.bases import NCSymDualBases sage: DNCSym = SymmetricFunctionsNonCommutingVariables(QQ).dual() sage: NCSymDualBases(DNCSym) Category of bases of dual symmetric functions in non-commuting variables over the Rational Field
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sage.combinat.ncsym.bases.
NCSymOrNCSymDualBases
¶ Base category for the category of bases of symmetric functions in non-commuting variables or its Hopf dual for the common code.