Singular

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));
==> [1]:
==>    c(1)
==> [2]:
==>    c(1)^2-2*c(2)
==> [3]:
==>    c(1)^3-3*c(1)*c(2)+3*c(3)
// The first 5 sums in the same situation
print(powSumSym(l, 5));
==> [1]:
==>    c(1)
==> [2]:
==>    c(1)^2-2*c(2)
==> [3]:
==>    c(1)^3-3*c(1)*c(2)+3*c(3)
==> [4]:
==>    c(1)^4-4*c(1)^2*c(2)+2*c(2)^2+4*c(1)*c(3)
==> [5]:
==>    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)