Symbolic Homotopy Construction

Jan Verschelde and Ronald Cools

Abstract:

Homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system. Computations will be performed more efficiently if the symmetric structure of the system can be exploited. This paper presents the construction of a symmetric homotopy. Using this homotopy, only the paths according to the generating solutions have to be traced during continuation.

J. Comput. Appl. Math. 50:572-592, 1994.