粘附性优于邻接性:使用CAD计算黎曼索引

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI:10.1145/1073884.1073892

James C. Beaumont, R. Bradford, J. Davenport, Nalina Phisanbut

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引用次数: 8

摘要

给定一个具有代数分支切割的初等函数，我们展示了如何决定我们在任何给定点上的相关黎曼曲面的哪一张。我们通过建立由分支切割定义的复平面的柱面代数分解(CAD)与黎曼曲面的有限片子集之间的对应关系来做到这一点。关键的优点是我们不再需要处理困难的“恒定问题”。

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Adherence is better than adjacency: computing the Riemann index using CAD

Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.

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Proceedings of the 2005 international symposium on Symbolic and algebraic computation

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