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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;

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a ¿mathematical model checker¿ by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material.

This volume gives an up-to-date review of the subject Integration in Finite Terms.

This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews.

The book is centered around the research areas of combinatorics, special functions, and computer algebra. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials.

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials.

In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers.

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;

Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation.

Focusing on linear partial differential equations, this volume presents a state-of-the-art overview of numerical and symbolic scientific computing. Topics include solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, and more.

George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g.

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory.

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 one of the most important mathematical software systems, namely, MACSYMA.

The well attended March 1994 HIse workshop in Amsterdam was a very lively con ference which stimulated much discussion and human-human interaction. The value of the effort was not only in generating new ideas, but in making people aware of work that has gone on on many fronts in using computers to make mathematics more understandable.

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 a la Hilbert and methods of natural deduction.

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.

" Dur ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita tive relations, as to establish the axiom system of geometry.

van der Waerden's elimination of the "elimination theory" chapter from from B. " 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.

This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory.