Solving deficient polynomial systems with homotopies which keep the subschemes at infinity invariant

Authors:
T. Y. Li and Xiao Shen Wang

Journal:
Math. Comp. **56** (1991), 693-710

MSC:
Primary 65H10; Secondary 65H20

DOI:
https://doi.org/10.1090/S0025-5718-1991-1066835-2

MathSciNet review:
1066835

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Abstract: By a *deficient* polynomial system of *n* polynomial equations in *n* unknowns we mean a system that has fewer solutions than that predicted by the total degree, or the Bézout number, of the system. If the system is *m*-homogeneous, the Bézout number can be considerably reduced. In this paper, we introduce a homotopy for numerically determining all isolated solutions of deficient *m*-homogeneous systems. The initial polynomial system *Q* is chosen which keeps the *subschemes* of at infinity invariant when *t* varies in [0, 1).

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1066835-2

Article copyright:
© Copyright 1991
American Mathematical Society