# Effective Localization Using Double Ideal Quotient and Its Implementation

@inproceedings{Ishihara2018EffectiveLU, title={Effective Localization Using Double Ideal Quotient and Its Implementation}, author={Yuki Ishihara and Kazuhiro Yokoyama}, booktitle={CASC}, year={2018} }

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.

## 4 Citations

### Modular techniques for effective localization and double ideal quotient

- MathematicsISSAC
- 2020

This paper applies modular techniques effectively to computation of such double ideal quotient and its variants, where first the authors compute them modulo several prime numbers and then lift them up over rational numbers by Chinese Remainder Theorem and rational reconstruction.

### Computation of a Primary Component of an Ideal from Its Associated Prime by E ﬀ ective Localization

- Mathematics
- 2020

This is an enhanced full paper version of [Ishihara-Yokoyama, 2018] and contains detailed proofs, additional examples and new algorithms. In [Ishihara-Yokoyama, 2018], we proposed e ﬀ ective methods…

### Modular Techniques for Intermediate Primary Decomposition

- Mathematics, Computer ScienceISSAC
- 2022

An algorithm for ''Strong Intermediate Primary Decomposition" via maximal independent sets by using modular techniques, utilizing double ideal quotients to check whether a candidate from modular computations is an intersection of prime divisors or not is devised.

### Constructive arithmetics in Ore localizations enjoying enough commutativity

- MathematicsJ. Symb. Comput.
- 2021

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