Effective Localization Using Double Ideal Quotient and Its Implementation
In this paper, we propose a new method for localization of polynomial ideal, which we call “Local Primary Algorithm”. For an ideal I and a prime ideal P, our method computes a P-primary component of I after checking if P is associated with I by using double ideal quotient (I : (I : P)) and its variants which give us a lot of information about localization of I.
KeywordsGröbner basis Primary decomposition Localization
The authors would like to thank the referees for their helpful comments to improve the presentation of this paper. The authors are also grateful to Masayuki Noro for technical assistance with the computer experiments and coding on Risa/Asir.