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Received: 2008-07-16

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Crosschecked: 2008-10-27

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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.12 P.1685-1693


Computing the topology of an arrangement of implicitly defined real algebraic plane curves

Author(s):  Jorge CARAVANTES, Laureano GONZALEZ-VEGA

Affiliation(s):  Department of Mathematics, Statistics and Computation, University of Cantabria, Santander, 39005, Cantabria, Spain

Corresponding email(s):   jorge.caravantes@unican.es, laureano.gonzalez@unican.es

Key Words:  Topology computation, Real plane curves, Sweeping method

Jorge CARAVANTES, Laureano GONZALEZ-VEGA. Computing the topology of an arrangement of implicitly defined real algebraic plane curves[J]. Journal of Zhejiang University Science A, 2008, 9(12): 1685-1693.

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J0 - Journal of Zhejiang University Science A
VL - 9
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SP - 1685
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A08GMP01

We introduce a new algebraic approach dealing with the problem of computing the topology of an arrangement of a finite set of real algebraic plane curves presented implicitly. The main achievement of the presented method is a complete avoidance of irrational numbers that appear when using the sweeping method in the classical way for solving the problem at hand. Therefore, it is worth mentioning that the efficiency of the proposed method is only assured for low-degree curves.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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