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. 

Modular techniques for effective localization and double ideal quotient

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

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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.

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