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- W63355359 abstract "It is shown that within a coordinate aligned rectangle in the real plane there exists a cylindrical decomposition of the zero set of any function of two variables which can be written as a polynomial in x , e x , y , e y . Also the construction of such a cylindrical decomposition is Turing reduced to problems involving definable constants. In this way the topology of the zero set of such a function is computable in a bounded coordinate aligned rectangle, depending on an oracle to solve the constant problem. This result is then generalized to functions which can be written as polynomials in x, y and any number of basic functions in x or in y which belong to a large class of analytic functions, including all those which satisfy first order algebraic differential equations. The techniques used are false derivatives and local Sturm sequences." @default.
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- W63355359 date "1992-12-01" @default.
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- W63355359 title "Computing the topology of a bounded non algebraic curve in the plane" @default.
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- W63355359 doi "https://doi.org/10.1016/s0747-7171(19)80004-4" @default.
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