We discuss computation of Gröbner bases using approximate
arithmetic for coefficients. We show how certain considerations
of tolerance, corresponding roughly to absolute and relative error
from numeric computation, allow us to obtain good approximate solutions
to problems that are overdetermined. We provide examples of solving
overdetermined systems of polynomial equations. As a secondary feature
we show handling of approximate polynomial GCD computations, using
benchmarks from the literature.
On Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph Coloring