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SYMF::Sf2Table -- converts a symmetric function into a table

Call(s)


SYMF::Sf2Table(sf,b)

Parameters

sf- any symmetric function
b- any name of known basis

Introduction

The SYMF::Sf2Table function converts a symmetric function into a table. The table is indexed by partitions (possibly empty) and each entry that corresponds to a partition part is interpreted as the coefficient of b[part] in the expression of the symmetric function in the basis b.

This function can be useful if one wants to act either on coefficients or on partitions. For instance, one can use the map function to act on coefficients.

Example 1

>> muEC::SYMF::Sf2Table( q^2*s[3,1,1] + q*s[4,2] + q + s[4,2], s );
                             table(
                               [] = q,
                                            2
                               [3, 1, 1] = q ,
                               [4, 2] = q + 1
                             )
>> map( %, coefficient -> coefficient - 1 );
                           table(
                             [] = q - 1,
                                          2
                             [3, 1, 1] = q  - 1,
                             [4, 2] = q
                           )
>> muEC::SYMF::Table2Sf( %, s );
                 2
               (q  - 1) s[3, 1, 1] + q s[4, 2] + s[] (q - 1)

Related Functions

Sf2TableVar, Table2Sf

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MuPAD Combinat, an open source algebraic combinatorics package