examples::SymmetricFunctions

examples::SymmetricFunctions(R) creates a domain for the symmetric functions over the ground ring .

Details:

Entries

"powersum"
"p"	The domain of symmetric functions expanded on the powersums basis
"Schur"
"s"	The domain of symmetric functions expanded on the Schur basis
"elementary"
"e"	The domain of symmetric functions expanded on the elementary basis
"complete"
"h"	The domain of symmetric functions expanded on the complete basis
"monomial"
"m"	The domain of symmetric functions expanded on the monomial basis

antipode – antipode of symmetric functions

()::antipode(symmetric function f)

Returns the antipode of the symmetric function f; the result need not be expressed in the same basis as f.

omega – omega operator on symmetric function

()::omega(symmetric function f)

Returns the image of the symmetric function f by the omega operator; the result need not be expressed in the same basis as f.

omega is an algebra homomorphism and an involution. For any homogeneous symmetric function , and alphabet , one has omega f(X) = (-1)^deg(f) f(-X).

fromPoly – conversion from symmetric polynomials

()::fromPoly(symmetric polynomial (in \Mex{DOM_POLY}) f)

Express the symmetric polynomial in the monomial basis.

The polynomial is assumed to be symmetric; no check is done.