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Table 1 Input coding for inequalities

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)