Details:
Title  Gröbner fan and universal characteristic sets of prime differential ideals  Author(s)  Oleg D. Golubitsky  Type  Article in Journal  Abstract  The concepts of Gröbner cone, Gröbner fan, and universal Gröbner basis are generalized to the case of characteristic sets of prime differential ideals. It is shown that for each cone there exists a set of polynomials which is characteristic for every ranking from this cone; this set is called a strong characteristic set, and an algorithm for its construction is given. Next, it is shown that the set of all differential Gröbner cones is finite for any differential ideal. A subset of the ideal is called its universal characteristic set, if it contains a characteristic set of the ideal w.r.t. any ranking. It is shown that every prime differential ideal has a finite universal characteristic set, and an algorithm for its construction is given. The question of minimality of this set is addressed in an example. The example also suggests that construction of a universal characteristic set can help in solving a system of nonlinear PDE’s, as well as maybe providing a means for more efficient parallel computation of characteristic sets.  Keywords  Differential algebra, Prime differential ideal, Characteristic set  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106000484 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  10  Pages  1091  1104  Year  2006  Edition  0  Translation 
No  Refereed 
No 
