Abstract

Let W ⊂ Rn be a semialgebraic set defined by a quantifier-free formula with k atomic polynomials of the kind f ∈ Z[X1, . , Xn] such that degX1, . , Xn(f) < d and the absolute values of coefficients of f are less than 2M for some positive integers d, M. An algorithm is proposed for producing the complexification, Zariski closure, and also for finding all irreducible components of W. The running time of the algorithm is bounded from above by MO(1)(kd)nO(1). The procedure is applied to computing a Whitney system for a semialgebraic set and the real radical of a polynomial ideal.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.