  Quadratically optimized polynomials are described which are useful in
multi-bosonic algorithms for Monte Carlo simulations of quantum field theories
with fermions. Algorithms for the computation of the coefficients and roots of
these polynomials are described and their implementation in the algebraic
manipulation language Maple is discussed. Tests of the evaluation of
polynomials on dynamical fermion configurations are performed. In a simple
special case the obtained polynomial approximations are compared to Chebyshev
polynomials.
