Abstract.
We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient conditions that implies existence of a local implicit function as well as another system of sufficient conditions that guarantees absence of a local implicit function. The results obtained are applied to proving new and classical results on flexibility and rigidity of polyhedra and frameworks.
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(Received 13 July 2000; in revised form 11 December 2000)
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Alexandrov, V. Implicit Function Theorem for Systems of Polynomial Equations with Vanishing Jacobian and Its Application to Flexible Polyhedra and Frameworks. Mh Math 132, 269–288 (2001). https://doi.org/10.1007/s006050170034
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DOI: https://doi.org/10.1007/s006050170034