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## `SFA::SfA2Sf` -- from `SFA` objects to `SYMF` objects

#### Call(s)

`SFA::SfA2Sf(sf <,alist>)`

#### Parameters

`sf` | - | any valid expression in `SYMF`
`alist` | - | a list of alphabets

#### Introduction

The `SFA::SfA2Sf` function transforms any symmetric function of the `SFA` package into an object of ``SFA`` for a given list of alphabets (by default all alphabets).

Valid bases for symmetric functions are `e, h, p, s, m`.

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

The inverse function is `Sf2SfA`.

#### Example 1

    >> sfa :=  7/5*s[2,2](2*A3) + s[3,1](A2)*p[2](A2) - q*e[2,1](A2);

              7 s[2, 2](2 A3)
              --------------- - q e[2, 1](A2) + p[2](A2) s[3, 1](A2)
                     5

    >> muEC::SFA::SfA2Sf( sfa );

                                                  7 s[2, 2]
                       p[2] s[3, 1] - q e[2, 1] + ---------
                                                      5

    >> muEC::SFA::SfA2Sf( sfa, [ A2, A3 ] );

                    7 s[2, 2](2 A3)
                    --------------- - q e[2, 1] + p[2] s[3, 1]
                           5

    >> muEC::SFA::SfA2Sf( sfa, [ A2, 2*A3 ] );

                                                  7 s[2, 2]
                       p[2] s[3, 1] - q e[2, 1] + ---------
                                                      5

#### Related Functions

`Sf2SfA`, `TYP::Sf`, `TYP::SfA`

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MuPAD Combinat, an open source algebraic combinatorics package