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

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.