Computing the singularities of rational space curves

Authors:
Xiaoran Shi;Falai Chen
Affiliations:
University of Science and Technology of China, Hefei, Anhui, P.R. China;University of Science and Technology of China, Hefei, Anhui, P.R. China
Venue:
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Year:
2010

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Abstract

In this paper, we discuss the singularities of rational space curves. Two methods are provided to compute the singularities of arbitrary degree curves. These methods are a generalization of the paper (Chen, Wang and Liu. Computing singular points of plane rational curves. Journal of Symbolic Computation 43, 92--117, 2008), which are based on the μ-basis of the rational space curve and on random technique. The μ-basis induces a matrix M which contains all the information about the singularities including the parameter values corresponding to the singularities, multiplicities and infinitely near singularities. These information can be obtained by computing the Smith form of the matrix M. We compare our methods with previous approaches such as generalized resultants, and provide some examples to illustrate the effectiveness of our methods.