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Mathematics of Computation

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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
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 $ H(x,t) = (1 - t)aQ(x) + tP(x)$ at infinity invariant when t varies in [0, 1).

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Article copyright: © Copyright 1991 American Mathematical Society