Gröbner Deformations of Hypergeometric Differential Equations

1. Basic Notions.- 2. Solving Regular Holonomic Systems.- 3. Hypergeometric Series.- 4. Rank versus Volume.- 5. Integration of D-modules.- References.

From the reviews: "In recent years the theory of Gröbner bases has found several applications in various fields of symbolic computations, in particular in applications related to combinatorics. (...) The book is well written. (...) The monograph requires a consequent reading in order to discover all the beauties and the surprising connections between several different branches of mathematics, coming together in the text. This book contains a number of original research results on holonomic systems and hypergeometric functions. The reviewer is sure that it will be the standard reference for computational aspects and research on D-modules in the future. It raises many open problems for future work in this area. (Zentralblatt für Mathematik und ihre Grenzgebiete 0946.13021) "... The book is very well written and, despite the deep results it contains, it is easy to read. Each chapter provides good and nice examples illustrating all main notions. In the reviewer's opinion this book can be addressed not only to reearchers but also to beginners in D-module theory and especially in algorithmic D-module theory." (F. J. Castro-Jimenez, Mathematical Rezensions 2002).