Abstract
All zeroes of inequations have to be removed from the solution set. This requires them to be treated similarly to the equations. For example, consider the system S := {p = 0, q 6= 0} = {x − x + 1 = 0, x + a 6= 0}. For almost all values a, S|a=a has two distinct zeroes, exceptions determined by r(a) = 0, where r = res(p, q, x) = a + a + 1. Use r to decompose S into the simple systems {p = 0, r 6= 0} and {x − a − 1 = 0, r = 0}.
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