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首页> 外文期刊>urnal of Symbolic Computation >Exact resultants for corner-cut unmixed multivariate polynomial systems using the Dixon formulation
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Exact resultants for corner-cut unmixed multivariate polynomial systems using the Dixon formulation

机译：使用Dixon公式获得角切无混合多元多项式系统的精确结果

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摘要

Structural conditions on the support of a multivariate polynomial system are developed for which the Dixon-based resultant methods compute exact resultants. The concepts of a corner-cut support and almost corner-cut support of an unmixed polynomial system are introduced. For generic unmixed polynomial systems with corner-cut and almost corner-cut supports, the Dixon based methods can be used to compute their resultants exactly. These structural conditions on supports are based on analyzing how such supports differ from box supports of d-degree systems for which the Dixon formulation is known to compute resultants exactly. Such an analysis also gives a sharper bound on the complexity of resultant computation using the Dixon formulation in terms of the support and the mixed volume of the Newton polytope of the support. These results are a direct generalization of the authors' results on bivariate systems including the results of Zhang and Goldman as well as of Chionh for generic unmixed bivariate polynomial systems with corner-cut supports.
机译：开发了在多元多项式系统支持下的结构条件，基于狄克逊的结果方法可以计算出精确的结果。介绍了未混合多项式系统的角点支持和几乎角点支持的概念。对于具有切角和几乎切角支持的通用非混合多项式系统，可以使用基于Dixon的方法精确计算其结果。支座上的这些结构条件是基于以下分析的：这些支座与d级系统的箱形支座有何不同，已知Dixon公式可以精确计算出结果。就载体和载体的牛顿多表位的混合体积而言，这种分析还对使用Dixon制剂的结果计算的复杂性给出了更清晰的界限。这些结果是作者对双变量系统的结果的直接概括，包括带有角切支持的通用非混合双变量多项式系统的Zhang和Goldman以及Chionh的结果。

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