TYP::Sf
--
how symmetric functions are encoded in SYMF
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.
>> muEC::TYP::Ish( h[3,1] );
TRUE
>> muEC::TYP::Iss( s[2,2,1] );
TRUE
Ise
, Ish
, Ism
, Isp
, Iss
, IsPart
, SfA
MuPAD Combinat, an open source algebraic combinatorics package