Related papers: Automatic Discovery of Geometry Theorems Using Min…
This is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters". In this paper we define the Minimal Canonical Comprehensive Groebner System (MCCGS) of a parametric ideal and fix under which…
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Groebner bases depending on the values of the parameters,…
We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary…
We describe a prototype of a new experimental GeoGebra command and tool Discover that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary planar…
In 1992, V. Weispfenning proved the existence of Comprehensive Groebner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or…
We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to…
We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the…
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…
For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…