Symbolic computation of divided differences

Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x)-f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulations. This paper provides a guide to divided difference theory and practice, with a special eye toward the needs of computer algebra systems that should be programmed to deal with these often-messy formulas.