Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Gröbner Systems

DOI10.1007/978-3-540-77356-6_8zbMath1195.68093arXivmath/0703483OpenAlexW2104693850MaRDI QIDQ5453488

Antonio Montes, Tomás Recio

Publication date: 1 April 2008

Published in: Automated Deduction in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703483

zbMATH Keywords

automatic theorem provingcomprehensive Gröbner systemautomatic discoveringcanonical Gröbner system

Mathematics Subject Classification ID

Related Items (12)

On protocols for the automated discovery of theorems in elementary geometry ⋮ Gröbner bases for polynomial systems with parameters ⋮ Automatic deduction in (dynamic) geometry: Loci computation ⋮ Detecting truth, just on parts ⋮ Generic regular decompositions for parametric polynomial systems ⋮ Automated reducible geometric theorem proving and discovery by Gröbner basis method ⋮ A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases ⋮ Generalizing the Steiner-Lehmus theorem using the Gröbner cover ⋮ Cylinders Through Five Points: Complex and Real Enumerative Geometry ⋮ Minimal canonical comprehensive Gröbner systems ⋮ Generic regular decompositions for generic zero-dimensional systems ⋮ Automated generation of geometric theorems from images of diagrams

Uses Software

• CoCoA

Cites Work

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• On protocols for the automated discovery of theorems in elementary geometry
• Minimal canonical comprehensive Gröbner systems
• Using Gröbner bases to reason about geometry problems
• A method for the mechanical derivation of formulas in elementary geometry
• Wu's method and its application to perspective viewing
• Comprehensive Gröbner bases
• A new approach for automatic theorem proving in real geometry
• Some features of \(CoCoA 3\)
• A new algorithm for discussing Gröbner bases with parameters.
• Automatic discovery of theorems in elementary geometry
• Improving the DISPGB algorithm using the discriminant ideal
• Gröbner bases for families of affine or projective schemes
• Artificial Intelligence and Symbolic Computation
• Automated Deduction in Geometry
• Automated Deduction in Geometry

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