000 03763nam a22004335i 4500
001 978-4-431-54574-3
003 DE-He213
005 20140220082927.0
007 cr nn 008mamaa
008 140107s2013 ja | s |||| 0|eng d
020 _a9784431545743
_9978-4-431-54574-3
024 7 _a10.1007/978-4-431-54574-3
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.5
_223
100 1 _aHibi, Takayuki.
_eeditor.
245 1 0 _aGröbner Bases
_h[electronic resource] :
_bStatistics and Software Systems /
_cedited by Takayuki Hibi.
264 1 _aTokyo :
_bSpringer Japan :
_bImprint: Springer,
_c2013.
300 _aXV, 474 p. 123 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aA Quick Introduction to Gröbner Bases -- Warm-up Drills and Tips for Mathematical Software -- Computation of Gröbner Bases -- Markov Bases and Designed Experiments -- Convex Polytopes and Gröbner Bases -- Gröbner Basis for Rings of Differential Operators and Applications -- Examples and Exercises.  .
520 _aThe 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.
650 0 _aStatistics.
650 0 _aMathematical statistics.
650 1 4 _aStatistics.
650 2 4 _aStatistical Theory and Methods.
650 2 4 _aStatistics and Computing/Statistics Programs.
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9784431545736
856 4 0 _uhttp://dx.doi.org/10.1007/978-4-431-54574-3
912 _aZDB-2-SMA
999 _c99096
_d99096