This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

During the last few years, computers have evolved from pure number crunching machines to "intelligent" problem solving tools. Increasing effort has been spent on the investigation of new approaches and the application of solutions to real world problems. In this way, exciting new techniques have evolved providing support for an increasing number of technical and economical aspects. Applications range from the design and development of ultra highly integrated circuits to totally new man-machine interfaces, from software engineering tools to fault diagnosis systems, from decision support to even the analysis of unemployment. Following a first joint workshop on Advanced Information Processing held in July 1988 at the Institute for Problems of Informatics of the USSR Academy of Sciences (IPIAN) at Moscow, this was the second time that scientists and researchers from the USSR Academy of Sciences and Siemens AG, Corporate Research and Development, exchanged results and discussed recent advances in the field of applied computer sciences. Initiated by Prof. Dr. I. Mizin, Corresponding Member of the USSR Academy of Sciences and Director of IPIAN, and Prof. Dr. H. Schwartzel, Vice President of the Siemens AG and Head of the Applied Computer Science & Software Department, a joint symposium was arranged at the USSR Academy of Sciences in Moscow on June 5th and 6th 1990. The meetings on Information Processing and Software and Systems Design Automation provided a basis both for presentations of ongoing research and for discussions about specific problems.

This volume consists of papers presented in the special sessions on "Complex and Numerical Analysis", "Value Distribution Theory and Complex Domains", and "Use of Symbolic Computation in Mathematics Education" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT-9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense.

Systems and tools of computer algebra (Like AXIOM, Derive, FORM, Mathematica, Maple, Mupad, REDUCE, Macsyma…) let us manipulate extremely complex algebraic formulae symbolically on a computer. Contrary to numerics these computations are exact and there is no loss of accuracy. After decades of research and development, these tools are now becoming as indispensable in Science and Engineering as traditional number crunching already is.The ZiF'94 workshop is amongst the first devoted specifically to applications of computer algebra (CA) in Science and Engineering. The book documents the state of the art in this area and serves as an important reference for future work.

Contributed articles presented at the Conference, sponsored by National Science Foundation, USA [and others].

The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.

In the new era of technology and advanced communications, coding theory and cryptography play a particularly significant role with a huge amount of research being done in both areas. This book presents some of that research, authored by prominent experts in the field.The book contains articles from a variety of topics most of which are from coding theory. Such topics include codes over order domains, Groebner representation of linear codes, Griesmer codes, optical orthogonal codes, lattices and theta functions related to codes, Goppa codes and Tschirnhausen modules, s-extremal codes, automorphisms of codes, etc. There are also papers in cryptography which include articles on extremal graph theory and its applications in cryptography, fast arithmetic on hyperelliptic curves via continued fraction expansions, etc. Researchers working in coding theory and cryptography will find this book an excellent source of information on recent research.