SYMF::Sf2Table --
converts a symmetric function into a table
Call(s)
SYMF::Sf2Table(sf,b)
Parameterssf | - | any symmetric function |
b | - | any name of known basis |
Introduction
The SYMF::Sf2Table function converts a symmetric function into a table.
The table is indexed by partitions (possibly empty) and each entry that
corresponds to a partition part is interpreted as the coefficient of
b[part] in the expression of the symmetric function in the basis
b.
This function can be useful if one wants to act either on coefficients
or on partitions.
For instance, one can use the map function to act on coefficients.
Example 1>> muEC::SYMF::Sf2Table( q^2*s[3,1,1] + q*s[4,2] + q + s[4,2], s );
table(
[] = q,
2
[3, 1, 1] = q ,
[4, 2] = q + 1
)
>> map( %, coefficient -> coefficient - 1 );
table(
[] = q - 1,
2
[3, 1, 1] = q - 1,
[4, 2] = q
)
>> muEC::SYMF::Table2Sf( %, s );
2
(q - 1) s[3, 1, 1] + q s[4, 2] + s[] (q - 1)
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package