Grobner Bases and Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Grobner Bases and Convex Polytopes write by Bernd Sturmfels. This book was released on 1996. Grobner Bases and Convex Polytopes available in PDF, EPUB and Kindle. This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.
Gröbner Bases and Convex Polytopes
Gröbner Bases and Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gröbner Bases and Convex Polytopes write by Bernd Sturmfels. This book was released on 1996. Gröbner Bases and Convex Polytopes available in PDF, EPUB and Kindle. This work is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics and polyhedral geometry.
Gröbner Bases
Gröbner Bases - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gröbner Bases write by Takayuki Hibi. This book was released on 2014-01-07. Gröbner Bases available in PDF, EPUB and Kindle. The idea of the Gröbner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Gröbner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Gröbner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer algebra system with the help of the Gröbner basis. Since then, rapid development on the Gröbner basis has been achieved by many researchers, including Bernd Sturmfels. This book serves as a standard bible of the Gröbner basis, for which the harmony of theory, application, and computation are indispensable. It provides all the fundamentals for graduate students to learn the ABC’s of the Gröbner basis, requiring no special knowledge to understand those basic points. Starting from the introductory performance of the Gröbner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). Then comes a deep discussion of how to compute the Gröbner basis (Chapter 3). These three chapters may be regarded as the first act of a mathematical play. The second act opens with topics on algebraic statistics (Chapter 4), a fascinating research area where the Gröbner basis of a toric ideal is a fundamental tool of the Markov chain Monte Carlo method. Moreover, the Gröbner basis of a toric ideal has had a great influence on the study of convex polytopes (Chapter 5). In addition, the Gröbner basis of the ring of differential operators gives effective algorithms on holonomic functions (Chapter 6). The third act (Chapter 7) is a collection of concrete examples and problems for Chapters 4, 5 and 6 emphasizing computation by using various software systems.
Minkowski Addition of Polytopes
Minkowski Addition of Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minkowski Addition of Polytopes write by Peter Gritzmann. This book was released on 1990. Minkowski Addition of Polytopes available in PDF, EPUB and Kindle.
An Introduction to Convex Polytopes
An Introduction to Convex Polytopes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Convex Polytopes write by Arne Brondsted. This book was released on 2012-12-06. An Introduction to Convex Polytopes available in PDF, EPUB and Kindle. The aim of this book is to introduce the reader to the fascinating world of convex polytopes. The highlights of the book are three main theorems in the combinatorial theory of convex polytopes, known as the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. All the background information on convex sets and convex polytopes which is m~eded to under stand and appreciate these three theorems is developed in detail. This background material also forms a basis for studying other aspects of polytope theory. The Dehn-Sommerville Relations are classical, whereas the proofs of the Upper Bound Theorem and the Lower Bound Theorem are of more recent date: they were found in the early 1970's by P. McMullen and D. Barnette, respectively. A famous conjecture of P. McMullen on the charac terization off-vectors of simplicial or simple polytopes dates from the same period; the book ends with a brief discussion of this conjecture and some of its relations to the Dehn-Sommerville Relations, the Upper Bound Theorem and the Lower Bound Theorem. However, the recent proofs that McMullen's conditions are both sufficient (L. J. Billera and C. W. Lee, 1980) and necessary (R. P. Stanley, 1980) go beyond the scope of the book. Prerequisites for reading the book are modest: standard linear algebra and elementary point set topology in [R1d will suffice.
