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

SYNOPSIS:

• This part describes how symmetric functions are represented in the SYMF package.

• Symmetric function names are compatible with Macdonald's conventions, as well as the conventions used in the SF package of Stembridge.

• First of all, one may consider two types of bases: multiplicative bases and non-multiplicative ones.

• The bases declared by default are the following: e : multiplicative basis of elementary symmetric functions. The generators of such a basis are e0, e1, e2, ..., and the elements of the basis are the monomials in these variables. h : multiplicative basis of complete homogeneous symmetric functions. The generators of such a basis are h0, h1, h2, ..., and the elements of the basis are the monomials in these variables. m : non-multiplicative basis of monomial symmetric functions. The elements of such a basis are indexed by partitions. For instance, m[3,3,1] and m[] are elements of the m-basis. p : multiplicative basis of power sum symmetric functions. The generators of such a basis are p0, p1, p2, ..., and the elements of the basis are the monomials in these variables. s : non-multiplicative basis of Schur functions. The elements of such a basis are indexed by partitions. For instance, s[3,3,1] and s[] are elements of the s-basis. c : non-multiplicative basis of cycle indices. The elements of such a basis are indexed by partitions. For instance, c[3,3,1] and c[] are elements of the c-basis.

EXAMPLES:

> with(TYP):
> Ish(h3);
 
                                      true
 
> Iss(s[2,1]);
 
                                      true