摘要翻译：
在已知多项式的理想为0维的情况下，当多项式个数等于变量个数时，利用有界根泛函的扩张运算，给出了求所有根泛函的理想基和空间基的算法。该算法的计算复杂度为d^O(n)}运算，其中n为多项式个数和变量个数，d为多项式的极大次。可拓运算与多元贝走田结构有联系。
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英文标题：
《Determination of the basis of the space of all root functionals of a
  system of polynomial equations and of the basis of its ideal by the operation
  of the extension of bounded root functionals》
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作者：
Timur R. Seifullin
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最新提交年份：
2008
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分类信息：

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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一级分类：Computer Science        计算机科学
二级分类：Symbolic Computation        符号计算
分类描述：Roughly includes material in ACM Subject Class I.1.
大致包括ACM学科第一类1的材料。
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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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英文摘要：
  It is proposed the algorithm that find a basis of the ideal and a basis of the space of all root functionals by using the extension operation for bounded root functionals, when the number of polynomials is equal to the number of variables, if it is known that the ideal of polynomials is 0-dimensional. The asyptotic complexity of this algorithm is d^{O(n)} operations, where n is the number of polynomials and the number of variables, d is the maximal degree of polynomials. The extension operation has connection with the multivariate Bezoutian construction.
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PDF链接：
https://arxiv.org/pdf/0805.4543