Name
Abstract | ||
|---|---|---|
We present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely: the number n of variables, and some upper bound for the geometric degree of its zero set in K-n, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1145/3208976.3208981 | ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION |
Keywords | Field | DocType |
zero-test, polynomial ideals, Schwartz-Zippel Lemma, automated reasoning in geometry, proving by examples, GeoGebra | Zero element,Discrete mathematics,Schwartz–Zippel lemma,Finite set,Polynomial,Computer science,Upper and lower bounds,Zero set,Deterministic algorithm,Algebraically closed field | Conference |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tomás Recio | 1 | 307 | 42.06 |
| J. Rafael Sendra | 2 | 621 | 68.33 |
| Carlos Villarino | 3 | 55 | 8.42 |