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This relates to question "Expressing a symmetric polynomial in terms of elementary symmetric polynomials using computer?"

I would like to try absolute resolvent for group $C_5$ in $S_5$. For example $(r_1-r_2)(r_2-r_3)(r_3-r_4)(r_4-r_5)(r_5-r_1)$ should work. Coefficinets of polynomial are symmetric functions, so absolute resolvent should be expressable by function of coefficients.

But how to calculate resolvent? There is a part for symmetric polynomials in manual of Maxima, but I just don't understand it. Can Sage do this, or Pari/GP or some other free software?

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