TY - GEN
T1 - Computing the singularities of rational space curves
AU - Shi, Xiaoran
AU - Chen, Falai
PY - 2010
Y1 - 2010
N2 - 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 μbasis 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.
AB - 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 μbasis 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.
KW - Rational space curve
KW - Singularities
KW - μ-basis
UR - https://www.scopus.com/pages/publications/77956297683
U2 - 10.1145/1837934.1837970
DO - 10.1145/1837934.1837970
M3 - 会议稿件
AN - SCOPUS:77956297683
SN - 9781450301503
T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
SP - 171
EP - 178
BT - Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
PB - Association for Computing Machinery (ACM)
T2 - 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
Y2 - 25 July 2010 through 28 July 2010
ER -