# Singular          #### D.15.4.9 powSumSym

Procedure from library `chern.lib` (see chern_lib).

Usage:
powSumSym(l [,N]); l a list of polynomials, N integer

Return:
list of polynomials

Purpose:
computes the expressions for the sums of powers [up to degree N] in terms of the elementary symmetric polynomials (entries of l),

Note:
returns the terms of the Chern character
multiplied by the correspoding factorials

Example:
 ```LIB "chern.lib"; // the expressions of the first 3 sums of powers of 3 variables a(1), a(2), a(3) // in terms of the elementary symmetric polynomials c(1), c(2), c(3): ring r = 0, (c(1..3)), dp; list l=(c(1..3)); print(powSumSym(l)); ==> : ==> c(1) ==> : ==> c(1)^2-2*c(2) ==> : ==> c(1)^3-3*c(1)*c(2)+3*c(3) // The first 5 sums in the same situation print(powSumSym(l, 5)); ==> : ==> c(1) ==> : ==> c(1)^2-2*c(2) ==> : ==> c(1)^3-3*c(1)*c(2)+3*c(3) ==> : ==> c(1)^4-4*c(1)^2*c(2)+2*c(2)^2+4*c(1)*c(3) ==> : ==> c(1)^5-5*c(1)^3*c(2)+5*c(1)*c(2)^2+5*c(1)^2*c(3)-5*c(2)*c(3) ```

### Misc 