We study polynomials of degree up to 4 over the rationals or a computable real subfield. Our motivation comes from the need to evaluate predicates in nonlinear computational geometry efficiently and exactly. We show a new method to compare real algebraic numbers by precomputing generalized Sturm sequences, thus avoiding iterative methods; the method, moreover handles all degenerate cases. Our f...

data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified.hspace{.1cm}often the underlying imprecision can be suitably described in terms of fuzzy numbers/values. for these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accura...

The articles [8], [11], [10], [5], [1], [7], [12], [4], [3], [2], [9], and [6] provide the notation and terminology for this paper. In this paper i, j, k, k1, k2, n, m, i1, i2, j1, j2 are natural numbers. Let us consider i1, i2. We say that i1 and i2 are adjacent if and only if: (Def. 1) i2 = i1 + 1 or i1 = i2 + 1. One can prove the following propositions: (1) For all i1, i2 such that i1 and i2...