Solving Parametric Semi-Algebraic Systems
نویسندگان
چکیده
Let Q be the field of rational numbers and Q[u1, ..., ud, x1, ..., xs] the ring of polynomials in n indeterminates with coefficients in Q and d + s = n (0 ≤ d < n). The indeterminates are divided into two groups: u = (u1, ..., ud) and x = (x1, ..., xs), which are called parameters and variables, respectively. A polynomial set is a finite set of nonzero polynomials in Q[u,x]. The following system is called a parametric semi-algebraic system (SAS for short). p1(u,x) = 0, ..., pr(u,x) = 0, g1(u,x) ≥ 0, ..., gk(u,x) ≥ 0, gk+1(u,x) > 0, ..., gt(u,x) > 0, h1(u,x) 6= 0, ..., hm(u,x) 6= 0, (1)
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