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SYMF::SfEval -- realizes the action of symmetric functions on polynomials

Call(s)


SYMF::SfEval(sf,expr)

Parameters

sf- any symmetric function
expr- any expression depending on some variables

Introduction

Symmetric functions can be considered as operators on polynomials (lambda-ring structure of the ring of polynomials). Let sf be a power sum p[k], then

SYMF::SfEval(p[k],  c_u u  +  c_v v  +  ...) =
         c_u u^k + c_v v^k + ...,
where u, v, ... are monomials and c_u, c_v, ... are scalars.

For a product of power-sums sf=p[i,j,...], SYMF::SfEval(sf, expr) is set to be equal to the product SYMF::SfEval(p[i], expr) x SYMF::SfEval(p[j], expr) x...

The definition is extended by linearity to any symmetric function sf.

Example 1

>> muEC::SYMF::SfEval( p[2], 3*x*y + 2*z );
                                 2  2      2
                              3 x  y  + 2 z
>> muEC::SYMF::SfEval( p[4,3] + q*p[2], 2*x + 3*y );
                     2      2        3      3      4      4
               q (2 x  + 3 y ) + (2 x  + 3 y ) (2 x  + 3 y )

Related Functions

SfAExpand, SfPlethysm

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MuPAD Combinat, an open source algebraic combinatorics package