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Gröbner Bases in Symbolic Analysis by Markus Rosenkranz,Dongming Wang Pdf
This volume contains survey articles and original research papers, presenting the state of the art on applying the symbolic approach of Gröbner bases and related methods to differential and difference equations. The contributions are based on talks delivered at the Special Semester on Gröbner Bases and Related Methods hosted by the Johann Radon Institute of Computational and Applied Mathematics, Linz, Austria, in May 2006.
Numerical and Symbolic Scientific Computing by Ulrich Langer,Peter Paule Pdf
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
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.
Algebraic and Algorithmic Aspects of Differential and Integral Operators by Moulay Barkatou,Thomas Cluzeau,Georg Regensburger,Markus Rosenkranz Pdf
This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.
Formal Algorithmic Elimination for PDEs by Daniel Robertz Pdf
Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.
Mathematical Software - ICMS 2010 by Komei Fukuda,Joris van der Hoeven,Michael Joswig,Nobuki Takayama Pdf
This book constitutes the refereed proceedings of the Third International Congress on Mathematical Software, ICMS 2010, held in Kobe, Japan in September 2010. The 49 revised full papers presented were carefully reviewed and selected for presentation. The papers are organized in topical sections on computational group theory, computation of special functions, computer algebra and reliable computing, computer tools for mathematical editing and scientific visualization, exact numeric computation for algebraic and geometric computation, formal proof, geometry and visualization, Groebner bases and applications, number theoretical software as well as software for optimization and polyhedral computation.
Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by Kenji Iohara,Philippe Malbos,Masa-Hiko Saito,Nobuki Takayama Pdf
This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf
This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.
Mathematical Aspects of Computer and Information Sciences by Ilias S. Kotsireas,Siegfried M. Rump,Chee K. Yap Pdf
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, held in Berlin, Germany, in November 2015. The 48 revised papers presented together with 7 invited papers were carefully reviewed and selected from numerous submissions. The papers are grouped in topical sections on curves and surfaces, applied algebraic geometry, cryptography, verified numerical computation, polynomial system solving, managing massive data, computational theory of differential and difference equations, data and knowledge exploration, algorithm engineering in geometric computing, real complexity: theory and practice, global optimization, and general session.
Algebraic Biology by Katsuhisa Horimoto,Georg Regensburger,Markus Rosenkranz,Hiroshi Yoshida Pdf
This volume contains the proceedings of the Third International Conference on Algebraic Biology (AB 2008). Jointly organized by the National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, and the Research Institute for Symbolic Computation (RISC), Hagenberg, Austria, it was held from July 31 to August 2, 2008 in the Castle of Hagenberg. Algebraic biology is an interdisciplinary forum for research on all aspects of applying symbolic computation in biology. The ?rst conference on algebraic biology (AB 2005) was held November 28–30, 2005 in Tokyo, the second during July 2–4, 2007 in Hagenberg. The AB conference series is intended as a bridge between life sciences and symbolic computation: On the one hand, new insights inbiologyarefoundbypowerfulsymbolicmethods;ontheotherhand,biological problems suggestnew algebraicstructures andalgorithms.While this pro?le has been established in the previous proceedings, the papers in the present volume demonstrate the continuous growth of algebraic biology. We received 27 submissions from 14 countries (Australia, Austria, Canada, China, Colombia, France, Germany, Italy, Japan, Norway, Russia, Switzerland, UK, USA), and 14 papers were accepted for publication. Each submission was assigned to at least three ProgramCommittee members, who carefully reviewed the papers, in many cases with the help of external referees. The reviews were discussedby the ProgramCommittee for oneweekvia the EasyChairconference management system.
Algebraic and Numeric Biology by Katsuhisa Horimoto,Masahiko Nakatsui,Nikolaj Popov Pdf
This book constitutes the refereed proceedings of the 4th International Conference on Algebraic Biology, ANB 2010, held at the Castle of Hagenberg, Austria in July/August 2010. The conference is a follow up of the AB Conference. The 10 papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on mathematical modeling, system analysis and design, genomics, molecular structure analysis, automata theory, artificial intelligence, sequence analysis, automated reasoning, formal language and hybrid symbolic numerical methods.
Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Author : Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Publisher : Springer Science & Business Media Page : 507 pages File Size : 54,7 Mb Release : 2012-12-06 Category : Computers ISBN : 9783642602184
Computer Algebra in Scientific Computing CASC’99 by Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf
The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics.
Mathematical Congress of the Americas by Jimmy Petean Pdf
This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5-9, 2013, in Guanajuato, México. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents. The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.
