Effective Localization Using Double Ideal Quotient and Its Implementation

Yuki Ishihara; Kazuhiro Yokoyama

doi:10.1007/978-3-319-99639-4_19

paper

Effective Localization Using Double Ideal Quotient and Its Implementation

arXiv:2003.00220 · doi:10.1007/978-3-319-99639-4_19

Abstract

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 $I$ .