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Título : Algorithms in Real Algebraic Geometry Tipo de documento: documento electrónico Autores: Saugata Basu ; SpringerLink (Online service) ; Pollack, Richard ; Roy, Marie-Françoise Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 10 Número de páginas: X, 662 p Il.: online resource ISBN/ISSN/DL: 978-3-540-33099-8 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Algebraic geometry Algorithms Geometry Symbolic and Manipulation Clasificación: 51 Matemáticas Resumen: The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added Nota de contenido: Algebraically Closed Fields -- Real Closed Fields -- Semi-Algebraic Sets -- Algebra -- Decomposition of Semi-Algebraic Sets -- Elements of Topology -- Quantitative Semi-algebraic Geometry -- Complexity of Basic Algorithms -- Cauchy Index and Applications -- Real Roots -- Cylindrical Decomposition Algorithm -- Polynomial System Solving -- Existential Theory of the Reals -- Quantifier Elimination -- Computing Roadmaps and Connected Components of Algebraic Sets -- Computing Roadmaps and Connected Components of Semi-algebraic Sets En línea: http://dx.doi.org/10.1007/3-540-33099-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34952 Algorithms in Real Algebraic Geometry [documento electrónico] / Saugata Basu ; SpringerLink (Online service) ; Pollack, Richard ; Roy, Marie-Françoise . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - X, 662 p : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 10) .
ISBN : 978-3-540-33099-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Algebraic geometry Algorithms Geometry Symbolic and Manipulation Clasificación: 51 Matemáticas Resumen: The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added Nota de contenido: Algebraically Closed Fields -- Real Closed Fields -- Semi-Algebraic Sets -- Algebra -- Decomposition of Semi-Algebraic Sets -- Elements of Topology -- Quantitative Semi-algebraic Geometry -- Complexity of Basic Algorithms -- Cauchy Index and Applications -- Real Roots -- Cylindrical Decomposition Algorithm -- Polynomial System Solving -- Existential Theory of the Reals -- Quantifier Elimination -- Computing Roadmaps and Connected Components of Algebraic Sets -- Computing Roadmaps and Connected Components of Semi-algebraic Sets En línea: http://dx.doi.org/10.1007/3-540-33099-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34952 Ejemplares
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Título : Algorithms and Programming : Problems and Solutions Tipo de documento: documento electrónico Autores: Shen, Alexander ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Otro editor: Imprint: Springer Colección: Springer Undergraduate Texts in Mathematics and Technology, ISSN 1867-5506 Número de páginas: XII, 272 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-1748-5 Idioma : Inglés (eng) Palabras clave: Mathematics Computer programming Algorithms mathematics Numerical analysis Analysis Programming Techniques Computational and Algorithm Problem Complexity Clasificación: 51 Matemáticas Resumen: "Algorithms and Programming" is primarily intended for a first year undergraduate course in programming. Structured in a problem-solution format, the text motivates the student to think through the programming process, thus developing a firm understanding of the underlying theory. Although a moderate familiarity with programming is assumed, the book is easily utilized by students new to computer science. The more advanced chapters make the book useful for a graduate course in the analysis of algorithms and/or compiler construction. New to the second edition are added chapters on suffix trees, games and strategies, and Huffman coding as well as an appendix illustrating the ease of conversion from Pascal to C. The material covers such topics as combinatorics, sorting, searching, queues, grammar and parsing, selected well-known algorithms, and much more. Reviews of the 1st Edition: "The book is addressed both to ambitious students and instructors looking for interesting problems [and] fulfills this task perfectly, especially if the reader has a good mathematical background." — Zentralblatt MATH "This book is intended for students, engineers, and other people who want to improve their computer skills.... The chapters can be read independently. Throughout the book, useful exercises give readers a feeling for how to apply the theory." — Computing Reviews "Overall...the book is well done. I recommend it to teachers and those wishing to sharpen their data structure and compiler skills." — SIGACT News Nota de contenido: Variables, expressions, assignments -- Generation of combinatorial objects -- Tree traversal (backtracking) -- Sorting -- Finite-state algorithms in text processing -- Data types -- Recursion -- Recursive and non-recursive programs -- Graph algorithms -- Pattern matching -- Games analysis -- Optimal coding -- Set representation. Hashing -- Sets, trees, and balanced trees -- Context-free grammars -- Left-to-right parsing (LR) En línea: http://dx.doi.org/10.1007/978-1-4419-1748-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33609 Algorithms and Programming : Problems and Solutions [documento electrónico] / Shen, Alexander ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2010 . - XII, 272 p : online resource. - (Springer Undergraduate Texts in Mathematics and Technology, ISSN 1867-5506) .
ISBN : 978-1-4419-1748-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer programming Algorithms mathematics Numerical analysis Analysis Programming Techniques Computational and Algorithm Problem Complexity Clasificación: 51 Matemáticas Resumen: "Algorithms and Programming" is primarily intended for a first year undergraduate course in programming. Structured in a problem-solution format, the text motivates the student to think through the programming process, thus developing a firm understanding of the underlying theory. Although a moderate familiarity with programming is assumed, the book is easily utilized by students new to computer science. The more advanced chapters make the book useful for a graduate course in the analysis of algorithms and/or compiler construction. New to the second edition are added chapters on suffix trees, games and strategies, and Huffman coding as well as an appendix illustrating the ease of conversion from Pascal to C. The material covers such topics as combinatorics, sorting, searching, queues, grammar and parsing, selected well-known algorithms, and much more. Reviews of the 1st Edition: "The book is addressed both to ambitious students and instructors looking for interesting problems [and] fulfills this task perfectly, especially if the reader has a good mathematical background." — Zentralblatt MATH "This book is intended for students, engineers, and other people who want to improve their computer skills.... The chapters can be read independently. Throughout the book, useful exercises give readers a feeling for how to apply the theory." — Computing Reviews "Overall...the book is well done. I recommend it to teachers and those wishing to sharpen their data structure and compiler skills." — SIGACT News Nota de contenido: Variables, expressions, assignments -- Generation of combinatorial objects -- Tree traversal (backtracking) -- Sorting -- Finite-state algorithms in text processing -- Data types -- Recursion -- Recursive and non-recursive programs -- Graph algorithms -- Pattern matching -- Games analysis -- Optimal coding -- Set representation. Hashing -- Sets, trees, and balanced trees -- Context-free grammars -- Left-to-right parsing (LR) En línea: http://dx.doi.org/10.1007/978-1-4419-1748-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33609 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar Algorithms in Algebraic Geometry / SpringerLink (Online service) ; Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J (2008)
Título : Algorithms in Algebraic Geometry Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: The IMA Volumes in Mathematics and its Applications, ISSN 0940-6573 num. 146 Número de páginas: XII, 162 p Il.: online resource ISBN/ISSN/DL: 978-0-387-75155-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Applied mathematics Engineering Algorithms Geometry Applications of Clasificación: 51 Matemáticas Resumen: In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric compuation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 18-22, 2006 at the University of Minnesota is one tangible indication of the interest. One hundred ten participants from eleven countries and twenty states came to listen to the many talks; discuss mathematics; and pursue collaborative work on the many faceted problems and the algorithms, both symbolic and numberic, that illuminate them. This volume of articles captures some of the spirit of the IMA workshop Nota de contenido: Application of a Numerical Version of Terr Acini’s Lemma for Secants and Joins -- On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces -- Intersections of Schubert varieties and other permutation array schemes -- Efficient Inversion of Rational Maps Over Finite Fields -- Higher-Order Deflation for Polynomial Systems With Isolated Singular Solutions -- Polars of Real Singular Plane Curves -- Semidefinite Representation of the k-Ellipse -- Solving Polynomial Systems Equation by Equation En línea: http://dx.doi.org/10.1007/978-0-387-75155-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34204 Algorithms in Algebraic Geometry [documento electrónico] / SpringerLink (Online service) ; Dickenstein, Alicia ; Schreyer, Frank-Olaf ; Sommese, Andrew J . - New York, NY : Springer New York, 2008 . - XII, 162 p : online resource. - (The IMA Volumes in Mathematics and its Applications, ISSN 0940-6573; 146) .
ISBN : 978-0-387-75155-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Applied mathematics Engineering Algorithms Geometry Applications of Clasificación: 51 Matemáticas Resumen: In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric compuation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 18-22, 2006 at the University of Minnesota is one tangible indication of the interest. One hundred ten participants from eleven countries and twenty states came to listen to the many talks; discuss mathematics; and pursue collaborative work on the many faceted problems and the algorithms, both symbolic and numberic, that illuminate them. This volume of articles captures some of the spirit of the IMA workshop Nota de contenido: Application of a Numerical Version of Terr Acini’s Lemma for Secants and Joins -- On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces -- Intersections of Schubert varieties and other permutation array schemes -- Efficient Inversion of Rational Maps Over Finite Fields -- Higher-Order Deflation for Polynomial Systems With Isolated Singular Solutions -- Polars of Real Singular Plane Curves -- Semidefinite Representation of the k-Ellipse -- Solving Polynomial Systems Equation by Equation En línea: http://dx.doi.org/10.1007/978-0-387-75155-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34204 Ejemplares
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Título : Solving Polynomial Equations : Foundations, Algorithms, and Applications Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Bronstein, Manuel ; Cohen, Arjeh M ; Cohen, Henri ; Eisenbud, David ; Sturmfels, Bernd ; Dickenstein, Alicia ; Emiris, Ioannis Z Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 14 Número de páginas: XIV, 426 p. 44 illus., 11 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-27357-8 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Algebra Algorithms Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems Nota de contenido: to residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerical algebraic geometry -- Four lectures on polynomial absolute factorization En línea: http://dx.doi.org/10.1007/b138957 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35276 Solving Polynomial Equations : Foundations, Algorithms, and Applications [documento electrónico] / SpringerLink (Online service) ; Bronstein, Manuel ; Cohen, Arjeh M ; Cohen, Henri ; Eisenbud, David ; Sturmfels, Bernd ; Dickenstein, Alicia ; Emiris, Ioannis Z . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 426 p. 44 illus., 11 illus. in color : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 14) .
ISBN : 978-3-540-27357-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Algebra Algorithms Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems Nota de contenido: to residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerical algebraic geometry -- Four lectures on polynomial absolute factorization En línea: http://dx.doi.org/10.1007/b138957 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35276 Ejemplares
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Título : Sparsity : Graphs, Structures, and Algorithms Tipo de documento: documento electrónico Autores: Nešetril, Jaroslav ; SpringerLink (Online service) ; Ossona de Mendez, Patrice Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Algorithms and Combinatorics, ISSN 0937-5511 num. 28 Número de páginas: XXIII, 459 p. 132 illus., 100 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-642-27875-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algorithms Computer science Convex geometry Discrete Mathematical logic Combinatorics in Science and Geometry Logic Foundations Algorithm Analysis Problem Complexity Clasificación: 51 Matemáticas Resumen: This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetril is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010 Nota de contenido: Part I Presentation: 1. Introduction -- 2. A Few Problems -- 3. Commented Contents -- Part II. The Theory: 4. Prolegomena -- 5. Measuring Sparsity -- 6. Classes and their Classification -- 7. Bounded Height Trees and Tree-Depth -- 8. Decomposition -- 9. Independence -- 10. First-Order Constraint Satisfaction Problems and Homomorphism Dualities -- 11. Restricted Homomorphism Dualities -- 12. Counting -- 13. Back to Classes -- Part III Applications: 14. Classes with Bounded Expansion – Examples -- 15. Property Testing, Hyperfiniteness and Separators -- 16. Algorithmic Applications -- 17. Other Applications -- 18. Conclusion -- Bibliography -- Index -- List of Symbols En línea: http://dx.doi.org/10.1007/978-3-642-27875-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32968 Sparsity : Graphs, Structures, and Algorithms [documento electrónico] / Nešetril, Jaroslav ; SpringerLink (Online service) ; Ossona de Mendez, Patrice . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012 . - XXIII, 459 p. 132 illus., 100 illus. in color : online resource. - (Algorithms and Combinatorics, ISSN 0937-5511; 28) .
ISBN : 978-3-642-27875-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algorithms Computer science Convex geometry Discrete Mathematical logic Combinatorics in Science and Geometry Logic Foundations Algorithm Analysis Problem Complexity Clasificación: 51 Matemáticas Resumen: This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetril is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010 Nota de contenido: Part I Presentation: 1. Introduction -- 2. A Few Problems -- 3. Commented Contents -- Part II. The Theory: 4. Prolegomena -- 5. Measuring Sparsity -- 6. Classes and their Classification -- 7. Bounded Height Trees and Tree-Depth -- 8. Decomposition -- 9. Independence -- 10. First-Order Constraint Satisfaction Problems and Homomorphism Dualities -- 11. Restricted Homomorphism Dualities -- 12. Counting -- 13. Back to Classes -- Part III Applications: 14. Classes with Bounded Expansion – Examples -- 15. Property Testing, Hyperfiniteness and Separators -- 16. Algorithmic Applications -- 17. Other Applications -- 18. Conclusion -- Bibliography -- Index -- List of Symbols En línea: http://dx.doi.org/10.1007/978-3-642-27875-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32968 Ejemplares
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