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Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory
AvJohannes Blümlein,Carsten Schneiderm. fl.
Inbunden, Engelska, 2019
2 421 kr
Skickas inom 10-15 vardagar
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.
Symbolic Computation of Integrability Structures for Partial Differential Equations
AvJoseph Krasil'shchik,Alexander Verbovetskym. fl.
Häftad, Engelska, 2018
1 214 kr
Skickas inom 10-15 vardagar
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. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.
Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra
In Honour of Peter Paule on his 60th Birthday
AvVeronika Pillwein,Carsten Schneider
Inbunden, Engelska, 2020
1 137 kr
Skickas inom 10-15 vardagar
The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.
Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra
In Honour of Peter Paule on his 60th Birthday
AvVeronika Pillwein,Carsten Schneider
Häftad, Engelska, 2021
1 137 kr
Skickas inom 10-15 vardagar
The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.
Invitation to Analytic Combinatorics
From One to Several Variables
AvStephen Melczer
Inbunden, Engelska, 2020
1 543 kr
Skickas inom 10-15 vardagar
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains.After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theorycan help refine some of these computability questions.Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
Invitation to Analytic Combinatorics
From One to Several Variables
AvStephen Melczer
Häftad, Engelska, 2021
1 543 kr
Skickas inom 10-15 vardagar
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains.After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theorycan help refine some of these computability questions.Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
Anti-Differentiation and the Calculation of Feynman Amplitudes
AvJohannes Blümlein,Carsten Schneider
Inbunden, Engelska, 2021
1 763 kr
Skickas inom 10-15 vardagar
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 aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Anti-Differentiation and the Calculation of Feynman Amplitudes
AvJohannes Blümlein,Carsten Schneider
Häftad, Engelska, 2022
1 763 kr
Skickas inom 10-15 vardagar
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 aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Thinking Programs
Logical Modeling and Reasoning About Languages, Data, Computations, and Executions
AvWolfgang Schreiner
Häftad, Engelska, 2022
961 kr
Skickas inom 5-8 vardagar
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly think about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single universal language, the formal language of logic. Apart from its universal elegance and expressiveness, this “logical” approach to the formal modeling of and reasoning about computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by software. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools thatare based on respectively make use of the presented logical underpinnings.
Integration in Finite Terms: Fundamental Sources
AvClemens G. Raab,Michael F. Singer
Inbunden, Engelska, 2022
1 873 kr
Skickas inom 10-15 vardagar
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Integration in Finite Terms: Fundamental Sources
AvClemens G. Raab,Michael F. Singer
Häftad, Engelska, 2023
1 873 kr
Skickas inom 10-15 vardagar
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Concrete Abstractions
Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker
AvWolfgang Schreiner
Inbunden, Engelska, 2023
830 kr
Skickas inom 10-15 vardagar
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.
Concrete Abstractions
Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker
AvWolfgang Schreiner
Häftad, Engelska, 2024
611 kr
Skickas inom 10-15 vardagar
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.
Thinking Programs
Logical Modeling and Reasoning About Languages, Data, Computations, and Executions
AvWolfgang Schreiner
Inbunden, Engelska, 2025
775 kr
Skickas inom 10-15 vardagar
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly think about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute wanted outputs from given inputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single, universal language, the formal language of logic. Apart from its universal elegance and expressiveness, this “logical” approach to the formal modeling of, and reasoning about, computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by software. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools that are based on or make use of the presented logical underpinnings.
Algorithms in Invariant Theory
AvBernd Sturmfels,Peter Paule
Häftad, Engelska, 2008
1 543 kr
Skickas inom 10-15 vardagar
J. Kung and G.-C. Rota, in their 1984 paper, write: “Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics”. The book of Sturmfels 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. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this “classical and new” area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
Mechanical Theorem Proving in Geometries
Basic Principles
AvWen-tsün Wu
Häftad, Engelska, 1994
556 kr
Skickas inom 10-15 vardagar
There seems to be no doubt that geometry originates from such practical activ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " 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. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti tative relations.
Polynomial Algorithms in Computer Algebra
AvFranz Winkler
Häftad, Engelska, 1996
556 kr
Skickas inom 10-15 vardagar
For several years now I have been teaching courses in computer algebra at the Universitat Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers of 1990 and 1992 I have organized and taught summer schools in computer algebra at the Universitat Linz. Gradually a set of course notes has emerged from these activities. People have asked me for copies of the course notes, and different versions of them have been circulating for a few years. Finally I decided that I should really take the time to write the material up in a coherent way and make a book out of it. Here, now, is the result of this work. Over the years many students have been helpful in improving the quality of the notes, and also several colleagues at Linz and elsewhere have contributed to it. I want to thank them all for their effort, in particular I want to thank B. Buchberger, who taught me the theory of Grabner bases nearly two decades ago, B. F. Caviness and B. D. Saunders, who first stimulated my interest in various problems in computer algebra, G. E. Collins, who showed me how to compute in algebraic domains, and J. R. Sendra, with whom I started to apply computer algebra methods to problems in algebraic geometry. Several colleagues have suggested improvements in earlier versions of this book. However, I want to make it clear that I am responsible for all remaining mistakes.
Computer - Human Interaction in Symbolic Computation
AvNorbert Kajler
Häftad, Engelska, 1998
1 137 kr
Skickas inom 10-15 vardagar
The well attended March 1994 HIse workshop in Amsterdam was a very lively con ference which stimulated much discussion and human-human interaction. As the editor of this volume points out, the Amsterdam meeting was just part of a year-long project that brought many people together from many parts of the world. 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 author was very glad he attended the workshop. * In thinking back over the conference and in reading the papers in this collection, the author feels there are perhaps four major conclusions to be drawn from the current state of work: 1. graphics is very important, but such features should be made as easy to use as possible; 2. symbolic mathematical computation is very powerful, but the user must be able to see "intermediate steps"; 3. system design has made much progress, but for semester-long coursework and book-length productions we need more tools to help composition and navigation; 4. monolithic systems are perhaps not the best direction for the future, as different users have different needs and may have to link together many kinds of tools. The editor of this volume and the authors of the papers presented here have also reached and documented similar conclusions.
Advances in the Design of Symbolic Computation Systems
AvAlfonso Miola,Marco Temperini
Häftad, Engelska, 1997
1 137 kr
Skickas inom 10-15 vardagar
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-supported Calculus
AvAdi Ben-Israel,Robert P. Gilbert
Inbunden, Engelska, 2002
885 kr
Skickas inom 10-15 vardagar
Das Symbolische Rechnen zur Losung mathematischer Probleme erlebt einen neuen Aufschwung durch den Einsatz speziell dafur entwickelter Softwaresysteme. Nach dem Erfolg von Mathematica und Maple erobert nun MACSYMA den Markt. MACSYMA wurde seit den spaten 60er Jahren am MIT entwickelt und uber die Jahre hin verbessert und weiterentwickelt. Es bietet die umfassendste Algorithmen-Bibliothek, die ein schnelles Losen der Aufgaben, besonders im Gebiet der Differential- und Integralrechnung, ermoglicht. Die Autoren geben in diesem Lehrbuch eine grundlegende Einfuhrung in das Symbolische Rechnen mit MACSYMA. Dem Band 2 liegt eine Diskette mit Aufgaben und Losungen bei, die Losungen werden in allen 3 gangigen Softwaresystemen Mathematica, Maple und MACSYMA dargestellt.
Elimination Methods
AvD. Wang
Häftad, Engelska, 2000
1 104 kr
Skickas inom 10-15 vardagar
The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " 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. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.
Approximate Commutative Algebra
AvLorenzo Robbiano,John Abbott
Häftad, Engelska, 2009
1 104 kr
Skickas inom 10-15 vardagar
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. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra.
Correct Software in Web Applications and Web Services
AvBernhard Thalheim,Klaus-Dieter Schewem. fl.
Inbunden, Engelska, 2015
556 kr
Skickas inom 10-15 vardagar
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 and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.
Correct Software in Web Applications and Web Services
AvBernhard Thalheim,Klaus-Dieter Schewem. fl.
Häftad, Engelska, 2016
572 kr
Skickas inom 10-15 vardagar
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 and tools that would lead to suitable web applications with the potential to implement systems for computation in the public domain.
Introduction to Computational Origami
AvTetsuo Ida
Inbunden, Engelska, 2020
1 929 kr
Skickas inom 10-15 vardagar
In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers. Focusing on how classical and modern geometrical problems are solved by means of origami, the book explains the methods not only with mathematical rigor but also by appealing to our scientific intuition, combining mathematical formulas and graphical images to do so. In turn, it discusses the verification of origami using computer software and symbolic computation tools. The binary code for the origami software, called Eos and created by the author, is also provided.
Symbolic Computation of Integrability Structures for Partial Differential Equations
AvJoseph Krasil'shchik,Alexander Verbovetskym. fl.
Inbunden, Engelska, 2018
1 214 kr
Skickas inom 10-15 vardagar
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. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.
Concrete Tetrahedron
Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates
AvManuel Kauers,Peter Paule
Häftad, Engelska, 2010
830 kr
Skickas inom 10-15 vardagar
The book treats four mathematical concepts which play a fundamental role in many different areas of mathematics: symbolic sums, recurrence (difference) equations, generating functions, and asymptotic estimates.Their key features, in isolation or in combination, their mastery by paper and pencil or by computer programs, and their applications to problems in pure mathematics or to "real world problems" (e.g. the analysis of algorithms) are studied. The book is intended as an algorithmic supplement to the bestselling "Concrete Mathematics" by Graham, Knuth and Patashnik.
Numerical and Symbolic Scientific Computing
Progress and Prospects
AvUlrich Langer,Peter Paule
Häftad, Engelska, 2011
1 104 kr
Skickas inom 10-15 vardagar
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.
Loewy Decomposition of Linear Differential Equations
AvFritz Schwarz
Inbunden, Engelska, 2012
1 104 kr
Skickas inom 10-15 vardagar
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 equations of higher order, in more variables or systems of such equations.
Computer Algebra in Quantum Field Theory
Integration, Summation and Special Functions
AvCarsten Schneider,Johannes Blümlein
Inbunden, Engelska, 2013
1 104 kr
Skickas inom 10-15 vardagar
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, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

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