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A uniformly computable Implicit Function Theorem
Author(s) -
McNicholl Timothy H.
Publication year - 2008
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710040
Subject(s) - corollary , differentiable function , mathematics , inverse function theorem , implicit function theorem , function (biology) , computable function , pure mathematics , inverse , taylor's theorem , computable analysis , discrete mathematics , mathematical analysis , picard–lindelöf theorem , fixed point theorem , geometry , evolutionary biology , biology
We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non‐differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler (2006). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)