8 Result(s)
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Chapter and Conference Paper
Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically
Understanding the mechanisms of the brain is a common theme for both computational neuroscience and artificial intelligence. Machine learning technique, like artificial neural network, has been benefiting from...
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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
Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, ...
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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...
