Abstract
We study the problem of deciding whether a system of real polynomial equations and inequalities has solutions, and if yes finding a sample solution. For polynomials with exact rational number coefficients the problem can be solved using a variant of the cylindrical algebraic decomposition (CAD) algorithm. We investigate how the CAD algorithm can be adapted to the situation when the coefficients are inexact, or, more precisely, Mathematica arbitrary-precision floating point numbers. We investigate what changes need to be made in algorithms used by CAD, and how reliable are the results we get.
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Strzebonski, A. (1999). A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_26
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DOI: https://doi.org/10.1007/978-94-017-1247-7_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5350-3
Online ISBN: 978-94-017-1247-7
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