The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Grobner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature."
The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers a...
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...
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 ...
As the most complete text on closed form solutions of linear partial differential equations, this book's coverage of the generalization of Loewy's decomposition includes more than fifty worked out examples and exercises in addition to their solutions.
As the most complete text on closed form solutions of linear partial differential equations, this book's coverage of the generalization of Loewy's dec...
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field,...
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It...
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of how to use modern symbolic mathematics software systems for solving problems in calculus. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. MACSYMA is used as the software in which the example programs and calculations are given. However, by the experience gained in this book, the student will also be able to use any of the other major mathematical software systems,...
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledg...
The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to...
The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equatio...
The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability; obtaining a common understanding of verification needs in web applications; achieving a common understanding of the available rigorous approaches to system development, and the cases in which they have succeeded; identifying how rigorous software engineering methods can be exploited to develop suitable web applications; and at developing a European-scale research agenda combining theory, methods...
The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information...
This book focuses on advanced computer algebra methods and special functions that have applications in quantum field theory. It presents new methods for (infinite) multiple sums, multiple integrals, difference and differential equations.
This book focuses on advanced computer algebra methods and special functions that have applications in quantum field theory. It presents new methods f...
The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information systems, web services, and web interoperability;
The papers in this volume aim at obtaining a common understanding of the challenging research questions in web applications comprising web information...
In this book origami is treated as basic geometrical operations that are represented and manipulated symbolically and graphically by computers. The verification of origami is treated by computer software, with symbolic computation tools. The binary code of the origami software, called Eos and created by the author, is provided.
In this book origami is treated as basic geometrical operations that are represented and manipulated symbolically and graphically by computers. The ve...
