Details:
Title  Gr\"obner basis for rings of differential operators and applications.  Author(s)  Nobuki Takayama  Type  Book, Chapter in Book, Conference Proceeding  Abstract  We introduce the theory and present some applications of Gröbner bases for the rings of differential operators with rational function coefficients R and for those with polynomial coefficients D. The discussion with R, in the first half, is elementary. In the ring of polynomials, zerodimensional ideals form the biggest class, and this is also true in R. However, in D, there is no zerodimensional ideal, and holonomic ideals form the biggest class. Most algorithms for D use holonomic ideals. As an application, we present an algorithm for finding local minimums of holonomic functions; it can be applied to the maximumlikelihood estimate. The last part of this chapter considers Ahypergeometric systems; topics covered in other chapters will reappear in the study of Ahypergeometric systems. We have provided many of the proofs, but some technical proofs in the second half of this chapter have been omitted; these may be found in the references at the end of this chapter.  ISBN  9784431545736/hbk; 97844 
URL 
http://link.springer.com/chapter/10.1007%2F9784431545743_6 
Language  English  Pages  279344  Publisher  Tokyo: Springer  Year  2013  Edition  0  Translation 
No  Refereed 
No 
