Author: DIMACS (GROUP) Publisher: ISBN: Category : Algorithms Languages : en Pages : 32
Book Description
Using the Minkowski addition of Newton polytopes, we show that the following problem can be solved in polynomial time for any finite set of polynomials [formula], where d is fixed: Does there exist a term order [tau] such that [Tau] is a Gröbner basis for its ideal with respect to [tau]? If not, find an optimal term order for [Tau] with respect to a natural Hilbert function criterion."
Author: Bernd Sturmfels Publisher: American Mathematical Soc. ISBN: 0821804871 Category : Mathematics Languages : en Pages : 176
Book Description
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.
Author: Ralf Fröberg Publisher: John Wiley & Sons ISBN: 9780471974420 Category : Mathematics Languages : en Pages : 198
Book Description
Grobner-Basen werden von Mathematikern und Informatikern zunehmend fur eine breite Palette von Anwendungen genutzt, in denen die algorithmische algebraische Geometrie eine Rolle spielt. Hier werden Grobner-Basen von einem konstruktiven, wenig abstrakten Standpunkt aus behandelt, wobei nur geringe Vorkenntnisse in linearer Algebra und komplexen Zahlen vorausgesetzt werden; zahlreiche Beispiele helfen bei der Durchdringung des Stoffes. Mit einer Ubersicht uber aktuell erhaltliche relevante Softwarepakete.
Author: Panayiotis Bozanis Publisher: Springer ISBN: 3540320911 Category : Computers Languages : en Pages : 890
Book Description
This volume contains a subset of the papers presented at the 10th Panhellenic Conference in Informatics (PCI 2005), which took place at the City of Volos, Greece, during November 11–13, 2005. After an international call for papers, 252 full papers were submitted. The number of the submitted papers constitutes a record number for the conf- ence and reveals its growing dynamics. The authors represented universities and institutes from the following countries: Algeria, Bulgaria, China, Cyprus, Czech Republic, Finland, Greece, The Netherlands, Hungary, Italy, Japan, Korea, The Kingdom of Saudi Arabia, Lebanon, Lithuania, Malaysia, Poland, Romania, Spain, Taiwan, Turkey, Ukraine, UK, and USA. Of the submitted papers, 81 were accepted for inclusion in this volume, giving an acceptance ratio of appr- imately 32. 2%. The papers are classi?ed into 17 thematic sections as follows: – data bases and data mining – algorithms and theoretical foundations – cultural and museum information systems – Internet-scale software/information systems – wearable and mobile computing – computer graphics, virtual reality and visualization – AI, machine learning and knowledge bases – languages, text and speech processing – bioinformatics – software engineering – educational technologies – e-business – computer and sensor hardware and architecture – computer security – image and video processing – signal processing and telecommunications – computer and sensor networks We would like to thank all the ProgramCommittee members and the additional reviewers for devoting time, e?ort and expertise so bounteously.
Author: Alicia Dickenstein Publisher: Springer Science & Business Media ISBN: 3540243267 Category : Computers Languages : en Pages : 433
Book Description
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Author: David A. Cox Publisher: Springer ISBN: 3319167219 Category : Mathematics Languages : en Pages : 664
Book Description
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to [email protected]. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly
Author: Bernd Sturmfels Publisher: American Mathematical Soc. ISBN: 9781470421571 Category : Mathematics Languages : en Pages : 162
Book Description
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.
Author: DIMACS (GROUP)
Author: Peter Gritzmann
Author: P. Gritzmann
Author: Peter Gritzmann
Author: Bernd Sturmfels
Author: Ralf Fröberg
Author: Panayiotis Bozanis
Author: Alicia Dickenstein
Author: David A. Cox
Author: Bernd Sturmfels