Details:
Title  The Gröbner basis of the ideal of vanishing polynomials  Author(s)  GertMartin Greuel, Frank Seelisch, Oliver Wienand  Type  Article in Journal  Abstract  We construct an explicit minimal strong Gröbner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m ≥ 2 . The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Gröbner basis is independent of the monomial order and that the set of leading terms of the constructed Gröbner basis is unique, up to multiplication by units. We also present a fast algorithm to compute reduced normal forms, and furthermore, we give a recursive algorithm for building a Gröbner basis in Z/m[x_1,x_2, … ,x_n] along the prime factorization of m . The obtained results are not only of mathematical interest but have immediate applications in formal verification of data paths for microelectronic systemsonchip.  Keywords  Gröbner bases, Polynomial rings and ideals, Polynomials over commutative rings, Vanishing ideal  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110001756 
Language  English  Journal  Journal of Symbolic Computation  Volume  46  Number  5  Pages  561  570  Year  2011  Note  Groebner Bases and Applications  Edition  0  Translation 
No  Refereed 
No 
