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A good practical test of the constraint is obtained by restricting ui to a one-parameter family ui = ai z+ bi for some fixed sets of real numbers ai and bi with the condition that all ai ≥ 0 (nothing is assumed about bi). Then the equation χ (z) =0 must either have only real roots z or be identically satisfied for all z. This form of the constraint is convenient for numerical tests by using a large number of randomly chosen vectors ai and bi.
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A good practical test of the constraint is obtained by restricting u i to a one-parameter family u i = a i z + b i for some fixed sets of real numbers a i and b i with the condition that all a i ≥ 0 (nothing is assumed about b i). Then the equation χ (z) = 0 must either have only real roots z or be identically satisfied for all z. This form of the constraint is convenient for numerical tests by using a large number of randomly chosen vectors a i and b i.
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