SYMF::SfEval --
realizes the action of symmetric functions on polynomials
Call(s)
SYMF::SfEval(sf,expr)
Parameterssf | - | any symmetric function |
expr | - | any expression depending on some variables |
Introduction
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.
Example 1>> 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 )
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package