Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain

Algorithm 4

Algorithm for computing the module of syzygies.

Input: polynomials and a monomial ordering

Output:  

(1) Compute a strong Gröbner basis for w.r.t

(2) Compute the set of all syzygies for .

(3) Arrange elements of as columns of the matrix

as explained in the Remark 23

(4) Compute . Assume that has columns .

(5) Return .