Finding all solutions to a system of polynomial equations. (English) Zbl 0567.55002

Wright, Alden H.

Math. Comput. 44, 125-133 (1985).

This paper shows that the number of solutions to a system of n polynomial equations in complex variables is the product of the degrees of the equations. The proof is based on a homotopy, or deformation, from a standard system of equations with the same degrees and known solutions. This homotopy provides a computational method of approximating all solutions. Computational results demonstrating the feasibility of this method are also presented.

Reviewer: N.F.F.Ebecken

MSC:

55M99	Classical topics in algebraic topology
65F99	Numerical linear algebra
65H99	Nonlinear algebraic or transcendental equations
12D10	Polynomials in real and complex fields: location of zeros (algebraic theorems)

Keywords:

system of polynomial equations; homotopy method; fundamental theorem of algebra; number of solutions