Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods
Keyword(s):
We present an algorithm that computes the singular points of projective plane algebraic curves and determines their multiplicities and characters. The feasibility of the algorithm is analyzed. We prove that the algorithm has the polynomial time complexity on the degree of the algebraic curve. The algorithm involves the combined applications of homotopy continuation methods and a method of root computation of univariate polynomials. Numerical experiments show that our algorithm is feasible and efficient.
1988 ◽
Vol 133
(1)
◽
pp. 109-121
◽
1987 ◽
Vol 11
(1)
◽
pp. 7-25
◽
2008 ◽
Vol 51
(1)
◽
pp. 29-54
◽
2006 ◽
Vol 25
(1)
◽
pp. 66-78
◽
2000 ◽
Vol 114
(2-3)
◽
pp. 233-247
◽