Mechanical geometry theorem proving based on Gröbner bases
type: Item
instance of: scholarly article
title: Mechanical geometry theorem proving based on Gröbner bases
zbMATH Open document ID: 0882.13029
DOI: 10.1007/BF02943140
author: Jinzhao Wu
published in: Journal of Computer Science and Technology
publication date: 1998-02-17T00:00:00Z
review text: The paper proposes a method for mechanical elementary geometry theorem proving. In more details, suppose a geometric statement is described by some polynomials \[ h_1,\ldots,h_m \in {\mathbb{Q}}[x_1,\ldots,x_n] \] and suppose the conclusion is expressed by a polynomial \(g\in {\mathbb{Q}}[x_1,\ldots,x_n]\); assume the ideal \(J=(h_1,\ldots,h_m)\) is zero-dimensional. The statement is said generally true if \(g\in \sqrt J\) and, if \({\mathcal M}\) is a minimal prime over \(J\), is said generally true on the component \(\mathcal M\) if \(g\in {\mathcal M}\). The paper gives an algorithm which computes, from the Gröbner basis of \(J\) with respect to a pure lexicographic order, the minimal primes over \(J\). In this way the author gives a method which allows to verify if a statement is generally true or generally true on some components of the ideal \(J\).
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 993814
zbMATH Keywords: Gröbner bases
zbMATH Keywords: mechanical theorem proving
reviewed by: Alessandro Logar
MaRDI profile type: Publication
cites work: Proving geometry theorems with rewrite rules
cites work: Solving systems of algebraic equations by using gröbner bases
cites work: On radical zero-dimensional ideals
cites work: A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
cites work: Q4848888
full work available at URL: https://doi.org/10.1007/bf02943140
OpenAlex ID: W2083042137
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description: scientific article; zbMATH DE number 993814