Singular Manual: symNsym

| #### D.15.3.2 symNsym Procedure from library `chern.lib` (see chern_lib). Usage: symNsym(f, c); f polynomial; c list of polynomials Return: list with 2 poly entries Purpose: computes a symmetric and a non-symmetric part of f in terms of the elementary symmetric functions from c as well a non-symmetric remainder Note: constants are not considered symmetric Example:
    LIB "chern.lib";
    ring r=0, (x,y,z, c(1..3)), dp;
    list l=c(1..3);
    // The symmetric part of f = 3x2 + 3y2 + 3z2 + 7xyz + y
    // in terms of the elemenatary symmetric functions c(1), c(2), c(3)
    // and the remainder
    poly f = 3x2 + 3y2 + 3z2 + 7xyz + y;
    print( symNsym(f, l) );
    ==> [1]:
    ==>    3*c(1)^2-6*c(2)+7*c(3)
    ==> [2]:
    ==>    y
    // Take a symmetrix polynomial in variables x and z
    f=x2+xz+z2;
    // Express it in terms of the elementary the symmetric functions
    print( symNsym(f, l)[1]);
    ==> c(1)^2-c(2)

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