On modular computation of Groebner bases with integer coefficients
نویسنده
چکیده
A as a subset of Q[X], so, if I is an ideal of A, then QI is the ideal of Q[X] generated by I. Given a ring R, we denote the natural mapping A → A ⊗ R = R[X] by ι R. This note is devoted to the following algorithmic problem (see [1] for a definition and properties of Gröbner bases of ideals in polynomial rings over Z). Problem (P). Suppose that we have an infinite sequence f 1 , f 2 ,. .. of elements of A (a blackbox producing them one by one). Let I = (f 1 , f 2 ,. . .) be the ideal generated by all the f i 's. Compute the Gröbner base of I under the assumption that the Gröbner base of QI and the Gröbner bases of ι Z/mZ (I), m ∈ Z, are known.
منابع مشابه
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عنوان ژورنال:
- CoRR
دوره abs/1312.6331 شماره
صفحات -
تاریخ انتشار 2013