Details:
Title  On computing Gr\"obner bases in rings of differential operators with coefficients in a ring.  Author(s)  Franz Winkler, Meng Zhou  Type  Article in Journal  Abstract  Following the definition of Gröbner bases in rings of differential operators given by Insa and Pauer (1998), we discuss some computational properties of Gröbner bases arising when the coefficient set is a ring. First we give examples to show that the generalization of Spolynomials is necessary for computation of Gröbner bases. Then we prove that under certain conditions the GSpolynomials can be reduced to be simpler than the original one. Especially for some simple case it is enough to consider Spolynomials in the computation of Gröbner bases. The algorithm for computation of Gröbner bases can thus be simplified. Last we discuss the elimination property of Gröbner bases in rings of differential operators and give some examples of solving PDE by elimination using Gröbner bases.  Keywords  Gröbner basis, rings of differential operators, GSpolynomials  ISSN  16618270; 16618289/e 
URL 
http://link.springer.com/article/10.1007%2Fs1178600700155 
Language  English  Journal  Math. Comput. Sci.  Volume  1  Number  2  Pages  211223  Publisher  Springer (Birkh\"auser), Basel  Year  2007  Edition  0  Translation 
No  Refereed 
No 
