Paper Info
Title
Validating the Completeness of the Real Solution Set of a System of Polynomial Equations.
Abstract
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares programming to test whether a given set is \"complete\" with respect to the real solution set. Specifically, we test whether the Zariski closure of that set is indeed equal to the solution set of the real radical of the ideal generated by the given polynomials. Examples with finitely and infinitely many real solutions are provided, along with an example having polynomial inequalities.
Year
DOI
Venue
2016
10.1145/2930889.2930910
ISSAC
Field
DocType
Citations 
Discrete mathematics,Combinatorics,Algebra,Polynomial,Computer science,System of polynomial equations,Algebraic variety,Solution set,Reciprocal polynomial,Gröbner basis,Matrix polynomial,Real algebraic geometry
Conference
2
PageRank 
References 
Authors
0.39
28
3
Name
Order
Citations
PageRank
Daniel A. Brake1173.56
Jonathan D. Hauenstein226937.65
Alan C. Liddell Jr.3182.88