A generalization of Groebner bases and a synthesis algorithm of multisequence over Z/(m)

摘要

A generalization of Grobner bases over ring (Z/(p~e)[x_1,…,x_n])[I is given, where Z is the ring of integers, p is a prime, e ≥ 1, and I is an ideal of Z/(p~e)[x_1,…,x_n]. By applying this generalization, an algorithm is presented, which can synthesize multisequence with an equal or unequal length over Z[(m). The computational complexity of this algorithm is O(N~2).