# Singular

#### D.15.4.1 symm

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

Usage:
symm(l [,n]); l a list of polynomials, n integer

Return:
list of polynomials

Purpose:
computes the list of elementary symmetric functions in the entries of l

Note:
makes sense only for a list of polynomials

Example:
 ```LIB "chern.lib"; // elementary symmetric functions in x, y, z: ring r = 0, (x, y, z), dp; list l=(x, y, z); print(symm(l)); ==> [1]: ==> x+y+z ==> [2]: ==> xy+xz+yz ==> [3]: ==> xyz //now let us compute only the first two symmetric polynomials in a(1), ... , a(10) ring q= 0,(a(1..10)), dp; list l=a(1..10); print(symm(l, 2)); ==> [1]: ==> a(1)+a(2)+a(3)+a(4)+a(5)+a(6)+a(7)+a(8)+a(9)+a(10) ==> [2]: ==> a(1)*a(2)+a(1)*a(3)+a(2)*a(3)+a(1)*a(4)+a(2)*a(4)+a(3)*a(4)+a(1)*a(5)+\ a(2)*a(5)+a(3)*a(5)+a(4)*a(5)+a(1)*a(6)+a(2)*a(6)+a(3)*a(6)+a(4)*a(6)+a(5\ )*a(6)+a(1)*a(7)+a(2)*a(7)+a(3)*a(7)+a(4)*a(7)+a(5)*a(7)+a(6)*a(7)+a(1)*a\ (8)+a(2)*a(8)+a(3)*a(8)+a(4)*a(8)+a(5)*a(8)+a(6)*a(8)+a(7)*a(8)+a(1)*a(9)\ +a(2)*a(9)+a(3)*a(9)+a(4)*a(9)+a(5)*a(9)+a(6)*a(9)+a(7)*a(9)+a(8)*a(9)+a(\ 1)*a(10)+a(2)*a(10)+a(3)*a(10)+a(4)*a(10)+a(5)*a(10)+a(6)*a(10)+a(7)*a(10\ )+a(8)*a(10)+a(9)*a(10) ```