APPROXIMATE GCD OF MULTIVARIATE POLYNOMIALS

Abstract

Problem. Given two multivariate polynomials with inexact coefficients, how to produce a ‘satisfactory ’ GCD for a given error tolerance $\\epsilon$? $F $ $= $ $C(x_{1}, \\ldots, x_{n})\\overline{F}(x_{1}, \\ldots, x_{n})+\\mathrm{O}(\\epsilon(x_{1}, \\ldots, x_{n}))$