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On the Computation of the Topology of a Non-Reduced Implicit Space Curve

Daouda Niang Diatta 1 Bernard Mourrain 2 Olivier Ruatta 1 
1 DMI
XLIM - XLIM
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure (PLS) isotopic to the original space curve. The algorithm is designed to provide the exact result for all inputs. It's a symbolic-numeric algorithm based on subresultant computation. Simple algebraic criteria are given to certify the output of the algorithm. The algorithm uses only one projection of the non-reduced space curve augmented with adjacency information around some "particular points" of the space curve. The algorithm is implemented with the Mathemagix Computer Algebra System (CAS) using the SYNAPS library as a backend.
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https://hal.archives-ouvertes.fr/hal-00218271
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Submitted on : Friday, March 7, 2008 - 3:14:15 PM
Last modification on : Saturday, June 25, 2022 - 10:58:41 PM
Long-term archiving on: : Thursday, April 29, 2010 - 7:49:31 PM

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Daouda Niang Diatta, Bernard Mourrain, Olivier Ruatta. On the Computation of the Topology of a Non-Reduced Implicit Space Curve. ISSAC, Jul 2008, Linz, Austria. pp.47-54, ⟨10.1145/1390768.1390778⟩. ⟨hal-00218271⟩

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