莫拉的圣杯：在素理想上局部化计算的算法
Mora's holy grail: Algorithms for computing in localizations at prime ideals
摘要：
本文利用标准基技术讨论了仿射坐标环A在素理想L上的局部化A_L及其相应的分次环Gr_a（A_L）的计算处理。在Mora工作的基础上，我们提出了两个中心命题的替代证明，并扩展了Mora所提到的应用：理想的分解，参数系统和Hilbert多项式，以及A_L的维数和正则性。所有算法都在计算机代数系统Singular的graal.lib库中实现。
英文摘要：
This article discusses a computational treatment of the localization A_L of an affine coordinate ring A at a prime ideal L and its associated graded ring Gr_a(A_L) with the means of standard basis techniques. Building on Mora's work, we present alternative proofs on two of the central statements and expand on the applications mentioned by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of A_L. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.
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