muEC::SYMF::SfPlethysm – plethysm of symmetric functions
computes the plethysm of symmetric functions
Call:
muEC::SYMF::SfPlethysm(sf1, sf2, <b1, b2>)
Parameters:
|
sf1, sf2: |
any symmetric functions |
|
b1, b2: |
any known bases |
Related Functions:
Details:
The muEC::SYMF::SfPlethysm function computes the plethysm sf1[sf2].
One may specify that sf1 and sf2 are expressed on the bases b1 and b2 by using either muEC::SYMF::SfPlethysm(sf1, sf2, b1), muEC::SYMF::SfPlethysm(sf1, sf2, b1, b2).
The plethysm operation is defined as follows: let p[i] be the i-th power-sum symmetric function and sf1, sf2, sf3 be any symmetric functions, then,
The default is to compute plethysms on the p-basis and return the result expressed on the p-basis.
Special algorithms have been included to compute plethysms. In particular, the result is expressed on the basis of Schur functions when:
b1=e, b2=e,h,s,
b1=h, b2=e,h,s,
b1=s, b2=e,h,s,
b1=p, b2=e,h,p,s,m,
b1=m, b2=e,h,p,s,m.
muEC::SYMF::SfPlethysm( p[1]*s[2], h[1] );
muEC::SYMF::SfPlethysm( e[3], s[2,1], e, s );
