有效局部化和双理想商的模技术
Modular Techniques for Effective Localization and Double Ideal Quotient
摘要：
通过双理想商，我们表示$(I:(I:J))$，其中理想$I$和$J$。在我们以前的工作[11]中，双理想商及其变体被证明对于检查素除子和生成素成分是非常有用的。与完全准素分解相比，结合这些性质，我们可以有效地计算“直接局部化”。本文将模技术有效地应用于这类双理想商及其变体的计算，首先计算它们对若干素数取模，然后利用孙子剩余定理和有理重构将它们提升到有理数上.作为一种新的模技术的双理想商及其变种，我们设计的标准，从模计算的输出。此外，我们将模块化技术应用于中间准素分解。我们检查我们的模块化技术的有效性，通过初步的计算经验奇异的几个例子。
英文摘要：
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.
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