Description 
1 online resource (385 pages) 
Contents 
Preface; CONTENTS; Multidegree for Bifiltered Dmodules and Hypergeometric Systems R. Arcadias; Introduction; 1. Bifiltered free resolution of Dmodules; 2. Multidegree for bifiltered Dmodules; 3. Examples from the theory of hypergeometric systems; 3.1. V filtration along the origin; 3.2. V filtration along coordinate hyperplanes; 3.3. Dependency of the multidegree on the parameters; 3.4. Positivity; 4. Proof of Theorem 2.1; Acknowledgements; References; Desingularization Algorithms: A Comparison from the Practical Point of View R. Blanco and A. FruhbisKruger; 1. Introduction 

2. Algorithms re.ning Hironaka's approach in the general case3. Combinatorial algorithms for the binomial case; 4. Algorithmic resolution in low dimensions; 4.1. Resolution of surfaces by Jung's approach; 4.2. Beyond the geometric case: Lipman's construction for two dimensional schemes; 5. Comparisons and timings; Acknowledgments; References; Computing Localizations Iteratively F.J. CastroJimenez and A. Leykin; Introduction; 1. Preliminaries; 1.1. Weyl algebra; 1.2. Grobner bases; 1.3. Holonomic Dmodules; 2. Iterative algorithm; 2.1. Iterative approach; 2.2. Stopping criterion 

2.3. Annihilator order of a planar curve3. Discussion and open problems; 3.1. Isolated hypersurface singularities; 3.2. Weyl closure; 4. Acknowledgements; References; KNOPPIX/Math: A Live System for Mathematics T. Hamada and KNOPPIX/Math Committers; 1. Introduction; 2. History; 3. The objectives of KNOPPIX/Math; 4. How to boot KNOPPIX/Math; References; Running Markov Chain without Markov Basis H. Hara, S. Aoki and A. Takemura; 1. Introduction; 2. Markov basis and lattice basis; 3. Sampling contingency tables with a lattice basis; 3.1. Generating moves by using a lattice basis 

3.2. A lattice basis for higher Lawrence configuration4. Numerical experiments; 4.1. Nothreefactor interaction model; 4.2. Discrete logistic regression model; References; Degree Bounds for a Minimal Markov Basis for the Threestate Toric Homogeneous Markov Chain Model D. Haws, A. Martin del Campo and R. Yoshida; 1. Introduction; 2. Notation; 2.1. Model (a); 2.2. Model (b); 2.3. Model (c); 2.4. Model (d); 2.5. Sufficient statistics, ideals, and Markov basis; 2.6. State graph; 3. Smith Normal Form; 4. Semigroup; 4.1. Model (a); 4.2. Model (b); 4.3. Model (c); 4.4. Model (d) 

5. Polytope Structure6. Computational Results; 7. Conclusions and Open Problems; Appendix A. Supporting Hyperplanes; References; First Steps toward the Geometry of Cophylogeny P. Huggins, M. Owen and R. Yoshida; 1. Introduction; 2. Spaces of cophylogenetic trees; 3. Cophylogenetic reconstruction; 3.1. Retraction onto spaces of cophylogenetic trees; 3.2. Balanced minimum coevolution; 4. Cophylogenetic invariants; 5. Open problems; 6. Proof of Theorem 2.2; Acknowledgements; References 
Summary 
This volume consists of research papers and expository survey articles presented by the invited speakers of the conference on "Harmony of Gröbner Bases and the Modern Industrial Society". Topics include computational commutative algebra, algebraic statistics, algorithms of Dmodules and combinatorics. This volume also provides current trends on Gröbner bases and will stimulate further development of many research areas surrounding Gröbner bases 
Notes 
Cones of Elementary Imsets and Supermodular Functions: A Review and Some New Results T. Kashimura, T. Sei, A. Takemura and K. Tanaka 

Print version record 
Subject 
Associative rings.


Homology theory.


Representations of groups.


Rings (Algebra)

Form 
Electronic book

ISBN 
128066987X 

9781280669873 

9789814383462 

9814383465 
