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 coeffici
ents and roots of these polynomials are described and their implementa
tion in the algebraic manipulation language Maple is discussed. Tests
of the evaluation of polynomials on dynamical fermion configurations a
re performed. In a simple special case the obtained polynomial approxi
mations are compared to Chebyshev polynomials. (C) 1998 Elsevier Scien
ce B.V.