Abstract
Let p 1, … p t be polynomials in C n with a variety V of common zeros contained in a suitable open set U. Explicit formulas are provided to construct rational functions λ 1, … λ s such that Σ i=1 s p i λ i 1, and such that the singularities of the λ i are contained in U. This result is applied to compute rational functions-valued 1-inverses of matrices with polynomial coefficients, which do not have constant rank, while retaining control over the location of the singularities of the rational functions themselves.
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