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

Algorithm 2

Buchberger’s algorithm.

Input: given an ideal and a monomial ordering on .

Output: a strong Gröbner basis for .

1  

2

3 while    do

4 choose and denote by the remainder of the division’s algorithm of by

if    then

5

6 end

7 else

8 ;

9 ;

10

11 end

12 end

13 return