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

Algorithm 1

Division’s algorithm.

Input:   and a monomial ordering .

Output:    and such that .

1  Initialization:   and ;

2  while    do

3  

4  

5  while    do

6  if    then

7  

8  

9  

10 end

11 else

12 

13 end

14 end

15 if    then

16 

17 

18 end

19  end