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A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic

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Reliable Computing

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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Authors and Affiliations

  1. Wolfram Research Inc. and Jagiellonian University, 100 Trade Centre Drive, Champaign, IL, 61820, USA

    Adam Strzebonski

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  1. Adam Strzebonski
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Strzebonski, A. A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic. Reliable Computing 5, 337–346 (1999). https://doi.org/10.1023/A:1009924521389

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