From: On algorithms testing positivity of real symmetric polynomials
Restrictions defining \(Z_{i}\) | Input n:= | Input (r,s):= |
---|---|---|
r + s = n, \(r\ge r_{0}\), \(s\ge s_{0}\) | r + s | \((p+r_{0},q+r_{0})\) |
r + s = n, \(r_{0}\le r\le r_{1}\), \(s_{0}\le s\le s_{1}\) | r + s | \((\frac{p\cdot r_{0}+r_{1}}{p+1},\frac{q\cdot s_{0}+s_{1}}{q+1} )\) |
r + s = n, r ≥ 1, s ≥ φ(r) | r + s | (p + 1,φ(r)+q) |
r + s = n, φ(r)≤s ≤ ψ(r) | r + s | \((p+1,\frac{q\cdot \varphi (r)+\psi (r)}{q+1} )\) |
r + s = n, \((r,s)\in \mbox{quadrilateral region with vertices }V_{i}=(r_{i},s_{i})\) | r + s | \(\frac{p\cdot q\cdot V_{1}+p\cdot V_{2}+q\cdot V_{3}+V_{4}}{(p+1)\cdot (q+1)}\) |
r = 1, 1 ≤ s ≤ n − 1 | r + s + p | (1,q + 1) |