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Symmetric polynomials


Dear All,

   Is the possibility in "Mathematica" express symmetric functions, for
example:

P=y1^2 y2 y3 + y1 y2^2 y3 + y1 y2 y3^2 + y1^2 y2 y4 +
y1 y2^2 y4 + y1^2 y3 y4 + y2^2 y3 y4 + y1 y3^2 y4 +
y2 y3^2 y4 + y1 y2 y4^2 + y1 y3 y4^2 + y2 y3 y4^2;

by the standard symmetric polynomials:
S1=y1+y2+y3+y4;
S2=y1^2+y2^2+y3^2+y4^2;
S3=y1^3+y2^3+y3^3+y4^3;
      . . .

Best regards
                      Nodar Shubitidze
                      Joint Institute for Nuclear Research
                      Dubna, Moscow region, Russia


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