muEC::TYP::Sf

This part describes how symmetric functions are represented in SYMF.

Call:

Related Functions:

Details:

Symmetric function names are compatible with Macdonald's conventions.

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

The bases declared by default are the following:

multiplicative basis of elementary symmetric functions. The generators of such a basis are e[], e[1], e[2], ..., and the elements of the basis are the monomials in these variables, which are denoted by e[i1,i2,...,ik], the indexing vector being a partition.
multiplicative basis of complete homogeneous symmetric functions. The generators of such a basis are h[], h[1], h[2], ..., and the elements of the basis are the monomials in these variables, which are denoted by h[i1,i2,...,ik], the indexing vector being a partition.
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.
multiplicative basis of power sum symmetric functions. The generators of such a basis are p[1], p[2], ..., and the elements of the basis are the monomials in these variables, which are denoted by p[i1,i2,...,ik], the indexing vector being a partition.
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.

muEC::TYP::Ish( h[3,1] );

muEC::TYP::Iss( s[2,2,1] );