2021/12/28 by Zoltán Kovács, Róbert Vajda
Computer Science · Mathematics · #Algebra over a field #Algorithm #Basis (linear algebra) #Computation #Computer science #Gröbner basis #Mathematics #Mathematics and Applications #Numerical Methods and Algorithms #Parametric statistics #Polynomial and algebraic computation #Programming language #Pure mathematics #Quantifier elimination #Theoretical computer science #cs.MS #math.AG
paper · pdf · doi:10.4204/eptcs.352.19
published in Electronic Proceedings in Theoretical Computer Science 352, 167-172 (Open Publishing Association) · In Proceedings ADG 2021, arXiv:2112.14770
openalex publication_date 2021/12/28 · openalex created_date 2021/12/31 · arxiv created 2022/01/03 · arxiv updated 2022/01/04 · openalex updated_date 2026/08/08
We introduced the package/subsystem GeoGebra Discovery to GeoGebra which supports the automated proving or discovering of elementary geometry inequalities. In this case study, for inequality exploration problems related to isosceles and right angle triangle subclasses, we demonstrate how our general real quantifier elimination (RQE) approach could be replaced by a parametric root finding (PRF) algorithm. The general RQE requires the full cell decomposition of a high dimensional space, while the new method can avoid this expensive computation and can lead to practical speedups. To obtain a solution for a 1D-exploration problem, we compute a Groebner basis for the discriminant variety of the 1-dimensional parametric system and solve finitely many nonlinear real (NRA) satisfiability (SAT) problems. We illustrate the needed computations by examples. Since Groebner basis algorithms are available in Giac (the underlying free computer algebra system in GeoGebra) and freely available efficient NRA-SAT solvers (SMT-RAT, Tarski, Z3, etc.) can be linked to GeoGebra, we hope that the method could be easily added to the existing reasoning tool set for educational purposes.