Singular Manual: powSumSym

| #### D.5.2.9 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 corresponding 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));
    ==> [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)

User manual for Singular version 4.4.1, 2025, generated by texi2html.