10 Result(s)
within
**angbo Chen
Numeric Computing
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Chapter and Conference Paper
Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library
We present new functionalities that we have added to the RegularChains library in Maple to efficiently compute irredundant triangular decompositions. We report on the implementation of different strategies. Our e...
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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
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 ...
