Computing all solutions to polynomial systems using homotopy continuation

Errata Computing All Solutions to Polynomial Systems using Homotopy Continuation* Alexander P. Morgan and Andrew J. Sommese

The hypothesis

of Theorem

1 on page 119 must be strengthened

in the

case that the start system G(z) has singular solutions. In the sentence in the paragraph preceding the statement of the theorem “Assume that, for all s E S, the multiplicity of s as a solution of G( xl - 0 is less than or equal to the multiplicity of s as a solution of F(z) = 0” substitute for “F(z) = 0” the phrase “H(z,t) = 0 for a generic choice of t.” This result is then a special case of Theorem 3 on pages 131-133 of “Coefficient-Parameter Polynomial Continuation” by Alexander P. Morgan and Andrew J. Sommese, Applied Mathematics and Computation, 29:123-160 (19891, upon noting (see page 137 of this same reference) that isolated solutions of polynomial systems without side conditions are stable, geometrically isolated solutions. We would like to thank T.-Y. Li for pointing the mistake out by sending us his preprint “Solving Deficient Polynomial Systems with Homotopies which Keep Subschemes at Infinity Invariant,” by T.-Y. Li and Xiaoshen Wang.

l

A&.

Math. Cornput., 24:115-138 (1987).

APPLIED MATHEMATICS

AND COMPUTATION

51:209 (1992)

209

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