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Elimination Methods [electronic resource] /
The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.
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| Language: | eng |
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Vienna : Springer Vienna : Imprint: Springer,
2001
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| Subjects: | Mathematics., Computer science, Algebra., Geometry., Convex geometry., Discrete geometry., Topology., Manifolds (Mathematics)., Complex manifolds., Symbolic and Algebraic Manipulation., Convex and Discrete Geometry., Manifolds and Cell Complexes (incl. Diff.Topology)., |
| Online Access: | http://dx.doi.org/10.1007/978-3-7091-6202-6 |
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Mathematics. Computer science Algebra. Geometry. Convex geometry. Discrete geometry. Topology. Manifolds (Mathematics). Complex manifolds. Mathematics. Algebra. Geometry. Topology. Symbolic and Algebraic Manipulation. Convex and Discrete Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). Mathematics. Computer science Algebra. Geometry. Convex geometry. Discrete geometry. Topology. Manifolds (Mathematics). Complex manifolds. Mathematics. Algebra. Geometry. Topology. Symbolic and Algebraic Manipulation. Convex and Discrete Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). |
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Mathematics. Computer science Algebra. Geometry. Convex geometry. Discrete geometry. Topology. Manifolds (Mathematics). Complex manifolds. Mathematics. Algebra. Geometry. Topology. Symbolic and Algebraic Manipulation. Convex and Discrete Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). Mathematics. Computer science Algebra. Geometry. Convex geometry. Discrete geometry. Topology. Manifolds (Mathematics). Complex manifolds. Mathematics. Algebra. Geometry. Topology. Symbolic and Algebraic Manipulation. Convex and Discrete Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). Wang, Dongming. author. SpringerLink (Online service) Elimination Methods [electronic resource] / |
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The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics. |
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Texto |
| topic_facet |
Mathematics. Computer science Algebra. Geometry. Convex geometry. Discrete geometry. Topology. Manifolds (Mathematics). Complex manifolds. Mathematics. Algebra. Geometry. Topology. Symbolic and Algebraic Manipulation. Convex and Discrete Geometry. Manifolds and Cell Complexes (incl. Diff.Topology). |
| author |
Wang, Dongming. author. SpringerLink (Online service) |
| author_facet |
Wang, Dongming. author. SpringerLink (Online service) |
| author_sort |
Wang, Dongming. author. |
| title |
Elimination Methods [electronic resource] / |
| title_short |
Elimination Methods [electronic resource] / |
| title_full |
Elimination Methods [electronic resource] / |
| title_fullStr |
Elimination Methods [electronic resource] / |
| title_full_unstemmed |
Elimination Methods [electronic resource] / |
| title_sort |
elimination methods [electronic resource] / |
| publisher |
Vienna : Springer Vienna : Imprint: Springer, |
| publishDate |
2001 |
| url |
http://dx.doi.org/10.1007/978-3-7091-6202-6 |
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AT wangdongmingauthor eliminationmethodselectronicresource AT springerlinkonlineservice eliminationmethodselectronicresource |
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1756266677068103680 |
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KOHA-OAI-TEST:1949602018-07-30T23:20:19ZElimination Methods [electronic resource] / Wang, Dongming. author. SpringerLink (Online service) textVienna : Springer Vienna : Imprint: Springer,2001.engThe development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.Polynomial arithmetic and zeros -- 1.1 Polynomials -- 1.2 Greatest common divisor, pseudo-division, and polynomial remainder sequences -- 1.3 Resultants and subresultants -- 1.4 Field extension and factorization -- 1.5 Zeros and ideals -- 1.6 Hilbert’s Nullstellensatz -- Zero decomposition of polynomial systems -- 2.1 Triangular systems -- 2.2 Characteristic-set-based algorithm -- 2.3 Seidenberg’s algorithm refined -- 2.4 Subresultant-based algorithm -- Projection and simple systems -- 3.1 Projection -- 3.2 Zero decomposition with projection -- 3.3 Decomposition into simple systems -- 3.4 Properties of simple systems -- Irreducible zero decomposition -- 4.1 Irreducibility of triangular sets -- 4.2 Decomposition into irreducible triangular systems -- 4.3 Properties of irreducible triangular systems -- 4.4 Irreducible simple systems -- Various elimination algorithms -- 5.1 Regular systems -- 5.2 Canonical triangular sets -- 5.3 Gröbner bases -- 5.4 Resultant elimination -- Computational algebraic geometry and polynomial-ideal theory -- 6.1 Dimension -- 6.2 Decomposition of algebraic varieties -- 6.3 Ideal and radical ideal membership -- 6.4 Primary decomposition of ideals -- Applications -- 7.1 Solving polynomial systems -- 7.2 Automated geometry theorem proving -- 7.3 Automatic derivation of unknown relations -- 7.4 Other geometric applications -- 7.5 Algebraic factorization -- 7.6 Center conditions for certain differential systems -- Bibliographic notes -- References.The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.Mathematics.Computer scienceAlgebra.Geometry.Convex geometry.Discrete geometry.Topology.Manifolds (Mathematics).Complex manifolds.Mathematics.Algebra.Geometry.Topology.Symbolic and Algebraic Manipulation.Convex and Discrete Geometry.Manifolds and Cell Complexes (incl. Diff.Topology).Springer eBookshttp://dx.doi.org/10.1007/978-3-7091-6202-6URN:ISBN:9783709162026 |