Related papers: Using the Regular Chains Library to build cylindri…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…
This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is based at Coventry University and the University of Bath, in the United Kingdom. The project seeks to push back the Doubly Exponential Wall of Cylindrical…
A new projection operator based on cylindrical algebraic decomposition (CAD) is proposed. The new operator computes the intersection of projection factor sets produced by different CAD projection orders. In other words, it computes the gcd…
Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and…
McCallum-style Cylindrical Algebra Decomposition (CAD) is a major improvement on the original Collins version, and has had many subsequent advances, notably for total or partial equational constraints. But it suffers from a problem with…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a…
Representing a 3D shape with a set of primitives can aid perception of structure, improve robotic object manipulation, and enable editing, stylization, and compression of 3D shapes. Existing methods either use simple parametric primitives…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to…
The maintenance, archiving and usage of the design drawings is cumbersome in physical form in different industries for longer period. It is hard to extract information by simple scanning of drawing sheets. Converting them to their digital…
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
In product design, a decomposition of the overall product function into a set of smaller, interacting functions is usually considered a crucial first step for any computer-supported design tool. Here, we propose a new approach for the…
We present a novel AI-assisted method for decomposing (segmenting) planar CAD (computer-aided design) models into well shaped rectangular blocks as a proof-of-principle of a general decomposition method applicable to complex 2D and 3D CAD…