We present recent research of Eisenbud, FlΓΈystad, Schreyer, and others, which was discovered with the help of experimentation with Macaulay 2. In this invited, expository paper, we start by considering the exterior algebra, and the computation of GrΓΆbner bases. We then present, in an elementary mann
Computing in algebraic geometry: A quick start using SINGULAR
β Scribed by Wolfram Decker, Christoph Lossen
- Book ID
- 127420962
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 2 MB
- Series
- Algorithms and Computation in Mathematics
- Edition
- 1
- Category
- Library
- ISBN-13
- 9783540289920
No coin nor oath required. For personal study only.
β¦ Synopsis
This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations.
Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way, omitting proofs and detours, and they give references for further reading on some of the more advanced topics. In examples and exercises, the main emphasis is on explicit computations using the computer algebra system SINGULAR.
The book addresses both, students and researchers. It may serve as a basis for self-study, guiding the reader from his first steps into computing to writing his own procedures and libraries.
π SIMILAR VOLUMES
One way of using a computer algebra system to do research in finite geometry is to use the system to construct "small" order examples of various constructions, and then hope to recognize a pattern that can be generalized and eventually proven. Of course, initially one does not know if the "small" or
The author defines βGeometric Algebra Computingβ as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive m