Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
The complete root classification of a parametric polynomial on an interval
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Automatic computation of the complete root classification for a parametric polynomial
Journal of Symbolic Computation
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The problem of localizing real zeros of polynomials with parametric coefficients is considered.An informative solution to this problem is proposed and an algorithm based on a generalization of Sturm's method for univariate polynomials over the reals is presented. Thus, given a polynomial P(x,y), where x is the variable and y a parameter, and a real interval Ix for the variable x, the algorithm furnishes a list (eventually empty) of real intervals Iiy for the parameter y, such that there exist i real simple zeros of P(x,y) in the two dimension interval determined by Ix and Iiy.