On the computation of the topology of a non-reduced implicit space curve

Authors:
Diatta Niang Daouda;Bernard Mourrain;Olivier Ruatta
Affiliations:
University of Limoges and INRIA Sophia-Antipolis, Limoges, France;GALAAD, INRIA, Sophia-Antipolis, France;University of Limoges, Limoges, France
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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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.