Computer Algebra in Scientific Computing
16th International Workshop, CASC 2014, Warsaw, Poland, September 8-12, 2014. Proceedings
📘 About This Book
This book constitutes the proceedings of the 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, held in Warsaw, Poland, in September 2014. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as Studies in polynomial algebra are represented by contributions devoted to factoring sparse bivariate polynomials using the priority queue, the construction of irreducible polynomials by using the Newton index, real polynomial root finding by means of matrix and polynomial iterations, application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties, application of Gröbner systems for computing the (absolute) reduction number of polynomial ideals, the application of cylindrical algebraic decomposition for solving the quantifier elimination problems, certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact rational univariate representation from approximate numerical data, new parallel algorithms for operations on univariate polynomials (multi-point evaluation, interpolation) based on subproduct tree techniques.
📖 Summary
Computer Algebra in Scientific Computing, edited by Vladimir P. Gerdt, serves as the definitive proceedings volume for the 16th International Workshop on Computer Algebra in Scientific Computing, known as CASC 2014, which took place in Warsaw, Poland, during September 2014. Spanning 515 pages, this scholarly compilation brings together thirty-three carefully reviewed and selected full papers that highlight the latest advancements, theoretical breakthroughs, and practical applications at the intersection of computer algebra and scientific computation. The volume captures a vibrant snapshot of ongoing academic and industrial research, addressing complex computational challenges and showcasing innovative algorithmic techniques designed to handle intricate mathematical structures. At the core of the book is a heavy emphasis on polynomial algebra, a foundational pillar of symbolic computation. Several contributions delve into sophisticated methods for factoring sparse bivariate polynomials by employing priority queue data structures, optimizing the efficiency of algebraic manipulation. Other papers explore the construction of irreducible polynomials through the clever application of the Newton index, offering fresh perspectives on polynomial decomposition and classification. Real polynomial root finding is another major theme, with authors presenting advanced techniques utilizing matrix and polynomial iterations to approximate roots with high precision and reliability. The text also bridges the gap between pure algebraic theory and real-world engineering and physical sciences. A notable application highlighted in the collection involves the use of the eigenvalue method integrated with symmetry principles to solve complex polynomial systems. These systems frequently arise in the rigorous vibration analysis of mechanical structures that possess inherent symmetry properties, demonstrating how abstract algebraic tools can solve tangible mechanical engineering problems. Furthermore, the volume explores the application of Gröbner systems, a powerful framework in commutative algebra, for handling parametric polynomial systems and expanding the toolkit available to computational scientists. Throughout its pages, the book maintains a rigorous academic standard, reflecting the rigorous peer-review process that governed the selection of the thirty-three included papers. Researchers, software developers, and applied mathematicians will find the text to be a rich repository of specialized knowledge. By documenting the collaborative efforts and cutting-edge discoveries presented at CASC 2014, Vladimir P. Gerdt has curated an essential resource that not only preserves the historical record of a significant scientific gathering but also pushes forward the boundaries of what automated mathematical reasoning and computer algebra can achieve in modern scientific computing.
🎯 Key Lessons
⚖️ Pros & Cons
✅ Pros
Presents cutting-edge research from international experts in symbolic computation.
Includes rigorously reviewed and selected peer-reviewed papers.
Provides practical applications of algebra to mechanical engineering problems.
Offers deep dives into specialized topics like Gröbner systems and polynomial root finding.
⚠️ Cons
Highly specialized content may be too technical for general readers.
Format as a conference proceedings means topics span a wide array of sub-disciplines rather than a single narrative.
❓ FAQ
What is the main focus of Computer Algebra in Scientific Computing? +
The book focuses on advanced topics in computer algebra, particularly polynomial algebra, root finding, and their applications in scientific computing.
When and where was the workshop associated with this book held? +
The 16th International Workshop on Computer Algebra in Scientific Computing (CASC 2014) was held in Warsaw, Poland, in September 2014.
How many papers are included in the volume? +
The book contains 33 full papers that were carefully reviewed and selected for inclusion.
Who edited the book? +
The volume was edited by Vladimir P. Gerdt.
How many pages long is the book? +
The book spans 515 pages of specialized academic content.
