Managing combinatorial explosion

• Elementary symmetric functions can be expressed in terms of power sums,
  • e.g. ?2(y) = y1y2 + y1y3 .. + ym-1 ym

= 1/2((? yi)2 - (? yi2))

- Expand in terms of power sums

- compute modulo w.r.t. a high degree

polynomial, e.g., y7

P = ?1(y)q1 ?2(y)q2 ?3(y)q3 . . . ?k(y)qk

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