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Synopsis
Polynomial systems arise in many applications:robotics, kinematics, chemical kinetics, computer vision, truss design, geometric modeling, and many others. Many polynomial systems have solutions sets, called algebraic varieties, having several irreducible components. A fundamental problem of the numerical algebraic geometry is to decompose such an algebraic variety into its irreducible components. The witness point sets are the natural numerical data structure to encode irreducible algebraic varieties. Sommese, Verschelde and Wampler represented the irreducible algebraic decomposition of an algebraic variety as a union of finite disjoint sets called numerical irreducible decomposition. The sets present the irreducible components. The numerical irreducible decomposition is implemented in Bertini . We modify this concept using partially Groebner bases, triangular sets, local dimension, and the so-called zero sum relation. We present in the second chapter the corresponding algorithms and their implementations in SINGULAR. We give some examples and timings, which show that the modified algorithms are more efficient if the number of variables is not too large.
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About the Author
2004 Bachelor of Science in Mathematics at the University of Damascus, Syria.2005-2007 Study of Mathematics at the University of Kaiserslautern, Germany.2007 Master of Science in Mathematics at the University of Kaiserslautern, Germany.2011 Doctor rerum naturalium, Dr. rer. nat. University of Kaiserslautern.
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Numerical Algorithms in Algebraic Geometry
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Numerical Algorithms in Algebraic Geometry
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Polynomial systems arise in many applications:robotics, kinematics, chemical kinetics, computer vision, truss design, geometric modeling, and many others. Many polynomial systems have solutions sets, called algebraic varieties, having several irreducible components. A fundamental problem of the numerical algebraic geometry is to decompose such an algebraic variety into its irreducible components. The witness point sets are the natural numerical data structure to encode irreducible algebraic varieties. Sommese, Verschelde and Wampler represented the irreducible algebraic decomposition of an algebraic variety as a union of finite disjoint sets called numerical irreducible decomposition. The sets present the irreducible components. The numerical irreducible decomposition is implemented in Bertini . We modify this concept using partially Groebner bases, triangular sets, local dimension, and the so-called zero sum relation. We present in the second chapter the corresponding algorithms and their implementations in SINGULAR. We give some examples and timings, which show that the modified algorithms are more efficient if the number of variables is not too large. 152 pp. Englisch. Seller Inventory # 9783838113500
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Numerical Algorithms in Algebraic Geometry
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Polynomial systems arise in many applications:robotics, kinematics, chemical kinetics, computer vision, truss design, geometric modeling, and many others. Many polynomial systems have solutions sets, called algebraic varieties, having several irreducible components. A fundamental problem of the numerical algebraic geometry is to decompose such an algebraic variety into its irreducible components. The witness point sets are the natural numerical data structure to encode irreducible algebraic varieties. Sommese, Verschelde and Wampler represented the irreducible algebraic decomposition of an algebraic variety as a union of finite disjoint sets called numerical irreducible decomposition. The sets present the irreducible components. The numerical irreducible decomposition is implemented in Bertini . We modify this concept using partially Groebner bases, triangular sets, local dimension, and the so-called zero sum relation. We present in the second chapter the corresponding algorithms and their implementations in SINGULAR. We give some examples and timings, which show that the modified algorithms are more efficient if the number of variables is not too large. Seller Inventory # 9783838113500
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Numerical Algorithms in Algebraic Geometry
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Al Rashed Shwki2004 Bachelor of Science in Mathematics at the University of Damascus, Syria.2005-2007 Study of Mathematics at the University of Kaiserslautern, Germany.2007 Master of Science in Mathematics at the University of Kaiser. Seller Inventory # 5405726
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Numerical Algorithms in Algebraic Geometry
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