Maxima Function
multsym (ppart_1, ppart_2, n)
returns the product of the two symmetric polynomials in n variables by working only modulo the action of the symmetric group of order n. The polynomials are in their partitioned form.
Given the 2 symmetric polynomials in x, y: 3*(x + y)+ 2*x*y
and 5*(x^2 + y^2)
whose partitioned forms are [[3,1], [2, 1, 1]]
and [[5, 2]]
, their product will be
(%i1) multsym ([[3, 1], [2, 1, 1]], [[5, 2]], 2); (%o1) [[10, 3, 1], [15, 3, 0], [15, 2, 1]]
that is 10*(x^3*y + y^3*x) + 15*(x^2*y + y^2*x) + 15*(x^3 + y^3)
.
Functions for changing the representations of a symmetric polynomial:
contract
, cont2part
, explose
, part2cont
,
partpol
, tcontract
, tpartpol
.