论文标题
有效本地化和双重理想商的模块化技术
Modular Techniques for Effective Localization and Double Ideal Quotient
论文作者
论文摘要
通过双重理想商，我们的意思是$（i：（i：j））$，其中理想$ i $和$ j $。在我们以前的工作[11]中，双重理想商及其变体被证明对于检查素数和生成主要组件非常有用。结合这些属性，我们可以有效地计算“直接定位”，与完整的主要分解相比。在本文中，我们将模块化技术有效地应用于这种双重理想商及其变体的计算，首先我们将它们计算为Modulo几个质数，然后通过中文剩余定理和合理的重建来提高它们的理性数字。作为双重理想商及其变体的一种新的模块化技术，我们设计了模块化计算输出的标准。另外，我们将模块化技术应用于中间的主要分解。我们通过对单数的初步计算经验来研究模块化技术的有效性。
By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining those properties, we can compute "direct localization" effectively, comparing with full primary decomposition. In this paper, we apply modular techniques effectively to computation of such double ideal quotient and its variants, where first we compute them modulo several prime numbers and then lift them up over rational numbers by Chinese Remainder Theorem and rational reconstruction. As a new modular technique for double ideal quotient and its variants, we devise criteria for output from modular computations. Also, we apply modular techniques to intermediate primary decomposition. We examine the effectiveness of our modular techniques for several examples by preliminary computational experiences on Singular.
