HELP FOR: how symmetric functions are represented in the SFA package.

SYNOPSIS:

• This section describes how symmetric functions are represented in the SFA package.

• Symmetric function names are compatible with Macdonald's conventions, as well as the conventions used in the SYMF package of ACE and also those adopted in the SF package of Stembridge.

• SFA provides the different bases e, h, p, s, m, which are indexed objects: one writes p[3,3,1](A1) instead of p3^2*p1 as in SYMF or SF. Informations on SYMF can be obtained by typing either ?SYMF or ?TYP[Sf].

• The indexing lists must be partitions in the sense of the PART package.

• 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 declaration 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.

• The bases declared by default are the following: e : products of elementary symmetric functions. h : products of complete symmetric functions. m : basis of monomial symmetric functions. p : products of power sum symmetric functions. s : Schur functions.

EXAMPLES:

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