RT info:eu-repo/semantics/conferenceObject
T1 The importance of being zero
A1 Recio, Tomás
A1 Sendra Pons, Juan Rafael
A1 Villarino Cabellos, Carlos
K1 Zero-test
K1 Polynomial ideals
K1 Schwartz-Zippel Lemma
K1 Automated reasoning in geometry
K1 Proving by examples
K1 GeoGebra
K1 Matemáticas
K1 Mathematics
AB 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 Kn, 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 somevariables 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.
PB ACM Press
SN 978-1-4503-5550-6
YR 2018
FD 2018-07
LK http://hdl.handle.net/10017/45788
UL http://hdl.handle.net/10017/45788
LA eng
NO 2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United States
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 05-jun-2023