Muirhead's Inequality (software?)

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I just started learning about inequalities: Schur's, Karamata's, Muirhead's, etc... They are beautiful but it seems that in the case of more than two variables, some of the computations become a nightmare. If you work with inequalities, do you suggest any particular software package? I looked at Maple and Mathematica but was not able to find an implementation of the symmetric sum (perhaps the nomenclature is different?)