Algebraic And Symbolic Computation Methods In Dynamical Systems

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Algebraic and Symbolic Computation Methods in Dynamical Systems

Alban Quadrat,Eva Zerz
Algebraic and Symbolic Computation Methods in Dynamical Systems Book PDF

Author : Alban Quadrat,Eva Zerz
Publisher : Springer Nature
Page : 320 pages
File Size : 51,7 Mb
Release : 2020-05-30
Category : Science
ISBN : 9783030383565

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Algebraic and Symbolic Computation Methods in Dynamical Systems by Alban Quadrat,Eva Zerz Pdf

This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.

Differential Equations with Symbolic Computation

Dongming Wang,Zhiming Zheng
Differential Equations with Symbolic Computation Book PDF

Author : Dongming Wang,Zhiming Zheng
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 45,5 Mb
Release : 2006-03-16
Category : Mathematics
ISBN : 9783764374297

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Differential Equations with Symbolic Computation by Dongming Wang,Zhiming Zheng Pdf

This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.

Symbolic Methods in Control System Analysis and Design

N. Munro
Symbolic Methods in Control System Analysis and Design Book PDF

Author : N. Munro
Publisher : IET
Page : 424 pages
File Size : 41,6 Mb
Release : 1999
Category : Technology & Engineering
ISBN : 0852969430

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Symbolic Methods in Control System Analysis and Design by N. Munro Pdf

Fifteen contributions provide an up-to-date treatment of issues in system modeling, system analysis, design and synthesis methods, and nonlinear systems. Coverage includes the application of multidimensional Laplace transforms to the modeling of nonlinear elements, a survey of customized computer algebra modeling programs for multibody dynamical systems, robust control of linear systems using a new linear programming approach, the development and testing of a new branch-and-bound algorithm fir global optimization using symbolic algebra techniques, and dynamic sliding mode control design using symbolic algebra tools.

Computer Algebra Methods for Equivariant Dynamical Systems

Karin Gatermann
Computer Algebra Methods for Equivariant Dynamical Systems Book PDF

Author : Karin Gatermann
Publisher : Springer
Page : 163 pages
File Size : 43,5 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540465195

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Computer Algebra Methods for Equivariant Dynamical Systems by Karin Gatermann Pdf

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.

Symbolic Computation

Robert Grossman
Symbolic Computation Book PDF

Author : Robert Grossman
Publisher : SIAM
Page : 191 pages
File Size : 53,5 Mb
Release : 1989-01-01
Category : Technology & Engineering
ISBN : 1611971039

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Symbolic Computation by Robert Grossman Pdf

This is a monograph that describes current research efforts in the application of symbolic computation to several areas, including dynamical systems, differential geometry, Lie algebras, numerical analysis, fluid dynamics, perturbation theory, control theory, and mechanics. The chapters, which illustrate how symbolic computations can be used to study various mathematical structures, are outgrowths of the invited talks that were presented at the NASA-Ames Workshop on The Use of Symbolic Methods to Solve Algebraic and Geometric Problems Arising in Engineering. More than 100 people participated in the two-day conference, which took place in January 1987 at the NASA-Ames Research Center in Moffett Field, California. The field of symbolic computation is becoming increasingly important in science, engineering, and mathematics. The availability of powerful computer algebra systems on workstations has made symbolic computation an important tool for many researchers.

Computerized Symbolic Manipulation in Mechanics

Edwin Kreuzer
Computerized Symbolic Manipulation in Mechanics Book PDF

Author : Edwin Kreuzer
Publisher : Springer
Page : 265 pages
File Size : 50,6 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709130100

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Computerized Symbolic Manipulation in Mechanics by Edwin Kreuzer Pdf

The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.

Computational Methods in Commutative Algebra and Algebraic Geometry

Wolmer Vasconcelos
Computational Methods in Commutative Algebra and Algebraic Geometry Book PDF

Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 44,9 Mb
Release : 2004-05-18
Category : Mathematics
ISBN : 3540213112

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Computational Methods in Commutative Algebra and Algebraic Geometry by Wolmer Vasconcelos Pdf

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Elimination Methods

D. Wang
Elimination Methods Book PDF

Author : D. Wang
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 45,5 Mb
Release : 2001-01-05
Category : Computers
ISBN : 3211832416

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Elimination Methods by D. Wang Pdf

This book provides a systematic and uniform presentation of elimination methods and the underlying theories, along the central line of decomposing arbitrary systems of polynomials into triangular systems of various kinds. Highlighting methods based on triangular sets, the book also covers the theory and techniques of resultants and Gröbner bases. The methods and their efficiency are illustrated by fully worked out examples and their applications to selected problems such as from polynomial ideal theory, automated theorem proving in geometry and the qualitative study of differential equations. The reader will find the formally described algorithms ready for immediate implementation and applicable to many other problems. Suitable as a graduate text, this book offers an indispensable reference for everyone interested in mathematical computation, computer algebra (software), and systems of algebraic equations.

Challenging the Boundaries of Symbolic Computation

Janet Carne,Peter Mitic
Challenging the Boundaries of Symbolic Computation Book PDF

Author : Janet Carne,Peter Mitic
Publisher : Imperial College Press
Page : 438 pages
File Size : 42,8 Mb
Release : 2003
Category : Computers
ISBN : 184816131X

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Challenging the Boundaries of Symbolic Computation by Janet Carne,Peter Mitic Pdf

This volume consists of papers delivered at the International Mathematica Symposium 2003 OCo an interdisciplinary meeting bringing together users of Mathematica in research and education. It gathers research papers, reports on classroom practice, reports on the use of Mathematica in industry and commerce, and descriptions of fresh applications. List of contributors: J Nash, S Wolfram, R Maeder, B Buchberger and C McTague. Contents: Algebraic Computation; Applied Mathematics; Education; Physics; Pure Mathematics; Statistics and Probability; Visualisation; Miscellaneous. Readership: Users of Mathematica for research, education and industry; developers of Mathematica applications; users of symbolic computation methods."

Advances in the Design of Symbolic Computation Systems

Alfonso Miola,Marco Temperini
Advances in the Design of Symbolic Computation Systems Book PDF

Author : Alfonso Miola,Marco Temperini
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783709165317

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Advances in the Design of Symbolic Computation Systems by Alfonso Miola,Marco Temperini Pdf

New methodological aspects related to design and implementation of symbolic computation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific computation. The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction. In particular the proposed treatment of mathematical objects, via techniques for method abstraction, structures classification, and exact representation, the programming methodology which supports the design and implementation issues, and reasoning capabilities supported by the whole framework are described.

Computer Aided Analysis and Optimization of Mechanical System Dynamics

E. J. Haug
Computer Aided Analysis and Optimization of Mechanical System Dynamics Book PDF

Author : E. J. Haug
Publisher : Springer Science & Business Media
Page : 706 pages
File Size : 54,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783642524653

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Computer Aided Analysis and Optimization of Mechanical System Dynamics by E. J. Haug Pdf

These proceedings contain lectures presented at the NATO-NSF-ARO sponsored Advanced Study I~stitute on "Computer Aided Analysis and Optimization of Mechanical System Dynamics" held in Iowa City, Iowa, 1-12 August, 1983. Lectures were presented by free world leaders in the field of machine dynamics and optimization. Participants in the Institute were specialists from throughout NATO, many of whom presented contributed papers during the Institute and all of whom participated actively in discussions on technical aspects of the subject. The proceedings are organized into five parts, each addressing a technical aspect of the field of computational methods in dynamic analysis and design of mechanical systems. The introductory paper presented first in the text outlines some of the numerous technical considerations that must be given to organizing effective and efficient computational methods and computer codes to serve engineers in dynamic analysis and design of mechanical systems. Two substantially different approaches to the field are identified in this introduction and are given attention throughout the text. The first and most classical approach uses a minimal set of Lagrangian generalized coordinates to formulate equations of motion with a small number of constraints. The second method uses a maximal set of cartesian coordinates and leads to a large number of differential and algebraic constraint equations of rather simple form. These fundamentally different approaches and associated methods of symbolic computation, numerical integration, and use of computer graphics are addressed throughout the proceedings.

Computer Algebra in Scientific Computing

Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 55,6 Mb
Release : 2011-08-26
Category : Computers
ISBN : 9783642235672

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 13th International Workshop on Computer Algebra in Scientific Computing, CASC 2011, held in Kassel, Germany, in September 2011. The 26 full papers included in the book were carefully reviewed and selected from numerous submissions. The articles are organized in topical sections on the development of object oriented computer algebra software for the modeling of algebraic structures as typed objects; matrix algorithms; the investigation with the aid of computer algebra; the development of symbolic-numerical algorithms; and the application of symbolic computations in applied problems of physics, mechanics, social science, and engineering.

Computer Algebra and Symbolic Computation

Joel S. Cohen
Computer Algebra and Symbolic Computation Book PDF

Author : Joel S. Cohen
Publisher : A K PETERS
Page : 466 pages
File Size : 53,8 Mb
Release : 2020-09-30
Category : Algebra
ISBN : 0367659476

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Computer Algebra and Symbolic Computation by Joel S. Cohen Pdf

Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization. This book includes complexity analysis of algorithms and other recent developments. It is well-suited for self-study and can be used as the basis for a graduate course. Maintaining the style set by Elementary Algorithms, the author explains mathematical methods as needed while introducing advanced methods to treat complex operations.

Symbolic Integration I

Manuel Bronstein
Symbolic Integration I Book PDF

Author : Manuel Bronstein
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 49,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662033869

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Symbolic Integration I by Manuel Bronstein Pdf

This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.

Design and Implementation of Symbolic Computation Systems

John Fitch
Design and Implementation of Symbolic Computation Systems Book PDF

Author : John Fitch
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 55,7 Mb
Release : 1993-09-02
Category : Computers
ISBN : 3540572724

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Design and Implementation of Symbolic Computation Systems by John Fitch Pdf

DISCO 92 was held on the Newton Park campus of Bath College of Higher Education, England, April 13-15, 1992. Beside the formal lectures dedicated to design and implementation issues of computer algebra, there were several software demonstrations and an opportunity for system designers to compare systems. This volume presents the proceedings of the conference. It contains 18 papers on a variety of design and implementation issues. One general theme which clearly emerges is the need for interconnections between systems, as no one systems incorporates all the facilities that users want. Various effortsare being made to design such links, but generally in limited contexts (suchas the Maple project or the Posso project).