Real intersection points of piecewise algebraic curves

Numerical Method for Real Root Isolation of Semi-Algebraic System and Its Applications

“…Example 4.4. This example for computing the real roots of piecewise algebraic curve is modified from [3]. Suppose that f, g ∈ S 1 3 (∆) and on cell a :…”

“…Hence, f and g have 5 real points. Methods given by Wang, et al, based on interval method, Groebner basis in [1,2,3,4,5] can also find the commom points of piecewise algebraic curve, but they did not consider these points which lie in the boundary.…”

“…The problem of counting and isolating real solutions of nonlinear system is an important topic in computing geometry and many other applications in various fields, e.g., the real intersection points for piecewise algebraic curve [1,2,3,4,5], the stability of a large class of biological networks [6,7], discovering non-linear ranking functions of loop programs in [8,9], automated proving inequality type theorem [10] and so on.…”

“…This example for computing the real roots of piecewise algebraic curve is modified from[3].Let ∆ = {a, b, c, d}be a regular triangulation of rectangular domain ABCD in R 2 , where a = [AOB], b = [BOC], c = [COD] and d = [AOD], where A = (−3, 0), B = (0, −3), C = (3, 0) D = (0, 3) and O = (0, 0), f and g are algebraic curves (See…”