SYMF::SfEval
--
realizes the action of symmetric functions on polynomials
SYMF::SfEval(sf,expr)
sf | - | any symmetric function |
expr | - | any expression depending on some variables |
Symmetric functions can be considered as operators on polynomials
(lambda-ring structure of the ring of polynomials).
Let sf
be a power sum p
[k], then
where u, v, ... are monomials and c_u, c_v, ... are scalars.SYMF::SfEval
(p
[k], c_u u + c_v v + ...) = c_u u^k + c_v v^k + ...,
For a product of power-sums sf=p[i,j,...]
, SYMF::SfEval
(sf, expr)
is set
to be equal to the product
SYMF::SfEval
(p[i], expr)
x SYMF::SfEval
(p[j], expr)
x...
The definition is extended by linearity to any symmetric function sf
.
>> muEC::SYMF::SfEval( p[2], 3*x*y + 2*z );
2 2 2 3 x y + 2 z
>> muEC::SYMF::SfEval( p[4,3] + q*p[2], 2*x + 3*y );
2 2 3 3 4 4 q (2 x + 3 y ) + (2 x + 3 y ) (2 x + 3 y )
MuPAD Combinat, an open source algebraic combinatorics package