等维多项式理想的模绝对分解
Modular absolute decomposition of equidimensional polynomial ideals
摘要：
本文提出了一种模策略，它描述了由有理系数多项式定义的等维多项式理想的绝对准素分解的关键性质。我们设计的算法是基于经典的消除变量和冒号理想的技术，并使用了一个棘手的选择素数工作。由于这种技术，我们可以获得绝对不可约分量的数量，它们的次数，重数以及约化分量的仿射Hilbert函数（即它们的初始理想w.r.t.度相容项排序）。
英文摘要：
In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on the classical technique of elimination of variables and colon ideals and uses a tricky choice of prime integers to work with. Thanks to this technique, we can obtain the number of absolute irreducible components, their degree, multiplicity and also the affine Hilbert function of the reduced components (namely, their initial ideal w.r.t. a degree-compatible term ordering) .
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