Details:
Title  A bound for the Rosenfeld–Gröbner algorithm  Author(s)  Oleg D. Golubitsky, Marina Kondratieva, Marc Moreno Maza, Alexey Ovchinnikov  Type  Article in Journal  Abstract  We consider the Rosenfeld–Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F , let M (F) be the sum of maximal orders of differential indeterminates occurring in F . We propose a modification of the Rosenfeld–Gröbner algorithm, in which for every intermediate polynomial system F , the bound M(F) ⩽ (n−1)!(F_0) holds, where F 0 is the initial set of generators of the radical ideal. In particular, the resulting regular systems satisfy the bound. Since regular ideals can be decomposed into characterizable components algebraically, the bound also holds for the orders of derivatives occurring in a characteristic decomposition of a radical differential ideal.  Keywords  Differential algebra, Characteristic sets, Radical differential ideals, Decomposition into regular components  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108000035 
Language  English  Journal  Journal of Symbolic Computation  Volume  43  Number  8  Pages  582  610  Year  2008  Edition  0  Translation 
No  Refereed 
No 
