TYP::Sf --
how symmetric functions are encoded in SYMF
Introduction
This part describes how symmetric functions are represented in SYMF.
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:
e: 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.
h: 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.
m: m[3,3,1] and m[] are elements of
the m-basis.
p: 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.
s: s[3,3,1] and s[] are elements of the s-basis.
Example 1>> muEC::TYP::Ish( h[3,1] );
TRUE
>> muEC::TYP::Iss( s[2,2,1] );
TRUE
Related FunctionsIse, Ish, Ism, Isp, Iss, IsPart, SfA
MuPAD Combinat, an open source algebraic combinatorics package