The Resource Gröbner bases : statistics and software systems, Takayuki Hibi, editor
Gröbner bases : statistics and software systems, Takayuki Hibi, editor
Resource Information
The item Gröbner bases : statistics and software systems, Takayuki Hibi, editor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Gröbner bases : statistics and software systems, Takayuki Hibi, editor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
-
- eng
- jpn
- eng
- Extent
- 1 online resource
- Contents
-
- Convex Polytopes and Gröbner Bases
- Hidefumi Ohsugi
- Gröbner Basis for Rings of Differential Operators and Applications
- Nobuki Takayama
- Examples and Exercises
- Hiromasa Nakayama and Kenta Nishiyama
- A Quick Introduction to Gröbner Bases
- Takayuki Hibi
- Warm-Up Drills and Tips for Mathematical Software
- Tatsuyoshi Hamada
- Computation of Gröbner Bases
- Masayuki Noro
- Markov Bases and Designed Experiments
- Satoshi Aoki and Akimichi Takemura
- Isbn
- 9784431545743
- Label
- Gröbner bases : statistics and software systems
- Title
- Gröbner bases
- Title remainder
- statistics and software systems
- Statement of responsibility
- Takayuki Hibi, editor
- Language
-
- eng
- jpn
- eng
- Summary
- 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
- Cataloging source
- YDXCP
- Dewey number
- 519.5
- Index
- index present
- Language note
- Translated from the Japanese
- LC call number
- QA276
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorName
- Hibi, Takayuki
- http://library.link/vocab/subjectName
-
- Gröbner bases
- Mathematical statistics
- MATHEMATICS
- MATHEMATICS
- Gröbner bases
- Mathematical statistics
- Label
- Gröbner bases : statistics and software systems, Takayuki Hibi, editor
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Convex Polytopes and Gröbner Bases
- Hidefumi Ohsugi
- Gröbner Basis for Rings of Differential Operators and Applications
- Nobuki Takayama
- Examples and Exercises
- Hiromasa Nakayama and Kenta Nishiyama
- A Quick Introduction to Gröbner Bases
- Takayuki Hibi
- Warm-Up Drills and Tips for Mathematical Software
- Tatsuyoshi Hamada
- Computation of Gröbner Bases
- Masayuki Noro
- Markov Bases and Designed Experiments
- Satoshi Aoki and Akimichi Takemura
- Control code
- 869434722
- Dimensions
- unknown
- Extent
- 1 online resource
- File format
- unknown
- Form of item
- online
- Isbn
- 9784431545743
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1007/978-4-431-54574-3
- http://library.link/vocab/ext/overdrive/overdriveId
- 585540
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)869434722
- Label
- Gröbner bases : statistics and software systems, Takayuki Hibi, editor
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Convex Polytopes and Gröbner Bases
- Hidefumi Ohsugi
- Gröbner Basis for Rings of Differential Operators and Applications
- Nobuki Takayama
- Examples and Exercises
- Hiromasa Nakayama and Kenta Nishiyama
- A Quick Introduction to Gröbner Bases
- Takayuki Hibi
- Warm-Up Drills and Tips for Mathematical Software
- Tatsuyoshi Hamada
- Computation of Gröbner Bases
- Masayuki Noro
- Markov Bases and Designed Experiments
- Satoshi Aoki and Akimichi Takemura
- Control code
- 869434722
- Dimensions
- unknown
- Extent
- 1 online resource
- File format
- unknown
- Form of item
- online
- Isbn
- 9784431545743
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1007/978-4-431-54574-3
- http://library.link/vocab/ext/overdrive/overdriveId
- 585540
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)869434722
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Gr%C3%B6bner-bases--statistics-and-software-systems/VgVcbNxxY8M/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Gr%C3%B6bner-bases--statistics-and-software-systems/VgVcbNxxY8M/">Gröbner bases : statistics and software systems, Takayuki Hibi, editor</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data - Experimental
Data Citation of the Item Gröbner bases : statistics and software systems, Takayuki Hibi, editor
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Gr%C3%B6bner-bases--statistics-and-software-systems/VgVcbNxxY8M/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Gr%C3%B6bner-bases--statistics-and-software-systems/VgVcbNxxY8M/">Gröbner bases : statistics and software systems, Takayuki Hibi, editor</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
