SYMF::SfInternal
--
computes the inner tensor product of symmetric functions
SYMF::SfInternal(sf1, sf2)
The SYMF::SfInternal
function computes the inner tensor product of symmetric
functions sf1
and sf2
.
This operation is also called the internal product.
Since sf1
and sf2
may be seen as virtual characters,
SYMF::SfInternal
computes the symmetric function associated with the product
(Kronecker product) of these two virtual characters.
For the basis of products of power-sums,
SYMF::SfInternal
(p[part], p[part']
) = 0 if
part
<>part'
,
= SfZee(part) x p[part]
otherwise.
The result is expressed in the product of power-sums basis.
>> muEC::SYMF::SfInternal( p[3,3,2,1,1], p[3,3,2,1,1] );
72 p[3, 3, 2, 1, 1]
>> muEC::SYMF::SfZee( [3,3,2,1,1] );
72
>> muEC::SYMF::SfInternal( s[3,2,1], p[3]*h[3] );
2 p[3, 3] p[3, 1, 1, 1] - --------- - ------------- 3 3
Char2Sf
, SfPlethysm
, Sf2Char
, SfZee
MuPAD Combinat, an open source algebraic combinatorics package