REDUCTION OF FEYNMAN GRAPH AMPLITUDES TO A MINIMAL SET OF BASIC INTEGRALS

An algorithm for the reduction of Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is pro posed. The method is based on the new algorithms for evaluating tensor integrals, representation of generalized recurrence relations fora. g iven kind of integrals as a linear system of PDEs and the reduction of this system to a standard form. Basic integrals reveal as parametric derivatives of the system in the standard form and the number of basic integrals in the minimal set is determined by the dimension of the so lution space of the system of PDEs.