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TYP::SfA -- how symmetric functions are encoded in SFA

Introduction

This part describes how symmetric functions are represented in SFA.

Symmetric function names are compatible with Macdonald's conventions.

The bases that are considered in SFA are the same as in SYMF.

All symmetric functions in SFA must have as alphabet a valid formal alphabet expression.

Allowed alphabet expressions are linear combinations of formal alphabets A1, A2, A3, ..., for instance 3/2*A1 - A3 + 3/4 is valid.

One can also introduce variables in alphabets through the instruction SfAVars( {{x}, {y}, z1, z2 }). Here, z1, z2, all xi's and yi's will be held as variables and not constants, although z3 for instance is a constant, and so is B1: both of them are interpretated as formal reals.

Example 1

>> muEC::TYP::IseA( e[3,3,1](2/3*A3) );
                                   TRUE

Related Functions

IseA, IshA, IsmA, IspA, IssA, IsPart, Sf

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MuPAD Combinat, an open source algebraic combinatorics package