  We present an algebraic approach to one-loop tensor integral reduction. The
integrals are presented in terms of scalar one- to four-point functions. The
reduction is worked out explicitly until five-point functions of rank five. The
numerical C++ package PJFry evaluates tensor coefficients in terms of a basis
of scalar integrals, which is provided by an external library, e.g. QCDLoop. We
shortly describe installation and use of PJFry. Examples for numerical results
are shown, including a special treatment for small or vanishing inverse
four-point Gram determinants. An extremely efficient application of the
formalism is the immediate evaluation of complete contractions of the tensor
integrals with external momenta. This leads to the problem of evaluating sums
over products of signed minors with scalar products of chords. Chords are
differences of external momenta. These sums may be evaluated analytically in a
systematic way. The final expressions for the numerical evaluation are then
compact combinations of the contributing basic scalar functions.
