摘要翻译:
对于m>=2,我们构造了Z/M上多项式环中消失多项式理想的显式极小强Groebner基。证明是以纯粹组合的方式进行的。一个显著的事实是,构造的Groebner基是独立于单项式的,并且构造的Groebner基的导项集是唯一的,直到单位相乘。给出了求约化规范形的快速算法,并给出了在Z/M[x_1,x_2,...,x_n]中沿M的素因子分解建立Groebner基的递推算法。所得结果不仅具有数学意义,而且在微电子片上系统数据路径的形式化验证中具有直接的应用。
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英文标题:
《The Groebner basis of the ideal of vanishing polynomials》
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作者:
G.-M. Greuel, F. Seelisch, O. Wienand
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最新提交年份:
2011
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分类信息:
一级分类:Mathematics 数学
二级分类:Commutative Algebra 交换代数
分类描述:Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环,模,理想,同调代数,计算方面,不变理论,与代数几何和组合学的联系
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner basis is independent of the monomial order and that the set of leading terms of the constructed Groebner basis is unique, up to multiplication by units. We also present a fast algorithm to compute reduced normal forms, and furthermore, we give a recursive algorithm for building a Groebner basis in Z/m[x_1,x_2,...,x_n] along the prime factorization of m. The obtained results are not only of mathematical interest but have immediate applications in formal verification of data paths for microelectronic systems-on-chip.
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PDF链接:
https://arxiv.org/pdf/0709.2978