Zero-nonzero and real-nonreal sign determination.

PERRUCCI, DANIEL ; ROY, MARIE-FRANCOISE

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Lugar: Oxford; Año: 2013 vol. 439 p. 3016 - 3030

0024-3795

We consider first the zero-nonzero determination problem, which consists in determining the listof zero-nonzero conditions realized by a finite list of polynomials on a finite set Z ⊂ Ck with C analgebraic closed field. We describe an algorithm to solve the zero-nonzero determination problem andwe perform its bit complexity analysis. This algorithm, which is in many ways an adaptation of themethods used to solve the more classical sign determination problem, presents also new ideas whichcan be used to improve sign determination. Then, we consider the real-nonreal sign determinationproblem, which deals with both the sign determination and the zero-nonzero determination problem.We describe an algorithm to solve the real-nonreal sign determination problem, we perform its bitcomplexity analysis and we discuss this problem in a parametric context.