The Groebner basis of the ideal of vanishing polynomials

Details The Groebner basis of the ideal of vanishing polynomials The Groebner basis of the ideal of vanishing polynomials

2007-09-19

arxiv.org/abs/0709.2978v5

Mathematics

Commutative Algebra

15 pages, 1 table, 2 algorithms (corrected version with new Prop. 3.8 and proof); Journal of Symbolic Computation 46 (2011)

Scientific paper

10.1016/j.jsc.2010.10.006

We construct an explicit minimal strong Groebner 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 Groebner basis is independent of the monomial order and that the set of leading terms of the constructed Groebner 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 Groebner 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 systems-on-chip.

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