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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 `x`i's and `y`i'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