14 Result(s)
within
**angbo Chen
English
Discrete Mathematics in Computer Science
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Chapter and Conference Paper
Comprehensive Triangular Decomposition
We introduce the concept of comprehensive triangular decomposition (CTD) for a parametric polynomial system F with coefficients in a field. In broad words, this is a finite partition of the the parameter space in...
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Chapter and Conference Paper
Semi-algebraic Description of the Equilibria of Dynamical Systems
We study continuous dynamical systems defined by autonomous ordinary differential equations, themselves given by parametric rational functions. For such systems, we provide semi-algebraic descriptions of their...
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Chapter and Conference Paper
Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One
For a regular chain R in dimension one, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of R, that is, the set ...
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Chapter and Conference Paper
Solving Parametric Polynomial Systems by RealComprehensiveTriangularize
In the authors’ previous work, the concept of comprehensive triangular decomposition of parametric semi-algebraic systems (RCTD for short) was introduced. For a given parametric semi-algebraic system, say S, a...
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Chapter and Conference Paper
The Basic Polynomial Algebra Subprograms
The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coeffi...
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Chapter and Conference Paper
Cylindrical Algebraic Decomposition in the RegularChains Library
Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry and has been implemented in several software. While existing implementations are all based on Collins’ p...
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Chapter and Conference Paper
Doing Algebraic Geometry with the RegularChains Library
Traditionally, Groebner bases and cylindrical algebraic decomposition are the fundamental tools of computational algebraic geometry. Recent progress in the theory of regular chains has exhibited efficient algo...
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Chapter and Conference Paper
Real Quantifier Elimination in the RegularChains Library
Quantifier elimination (QE) over real closed fields has found numerous applications. Cylindrical algebraic decomposition (CAD) is one of the main tools for handling quantifier elimination of nonlinear input fo...
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Chapter and Conference Paper
Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constan...
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Chapter and Conference Paper
Regular Chains under Linear Changes of Coordinates and Applications
Given a regular chain, we are interested in questions like computing the limit points of its quasi-component, or equivalently, computing the variety of its saturated ideal. We propose techniques relying on lin...
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Chapter and Conference Paper
Simplification of Cylindrical Algebraic Formulas
For a set S of cells in a cylindrical algebraic decomposition of ℝ n , we introduce the notion of generalized cylindrical algebraic formula (GCAF) associated with S. We propose a...
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Chapter and Conference Paper
A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications
For a bi-parametric real polynomial system with parameter values restricted to a finite rectangular region, under certain assumptions, we introduce the notion of border curve. We propose a numerical method to ...
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Chapter and Conference Paper
Chordality Preserving Incremental Triangular Decomposition and Its Implementation
In this paper, we first prove that the incremental algorithm for computing triangular decompositions proposed by Chen and Moreno Maza in ISSAC’ 2011 in its original form preserves chordality, which is an impo...
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Chapter and Conference Paper
Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks
Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heu...
