Precise evaluation of the electron (g-2) at 4 loops: the algebraic way

It is expected that the next generation of (g-2) experiments will pin down the error below the 1ppb (parts per billion) level; to cope with such a precision, the current error on the theoretical value of the 4 loop QED contribution must be reduced by at least a factor ten. To avoid the rounding problems which affect the numerical calculation, we developed and implemented as computer code various exact algebraic algorithms for reducing the very many integrals appearing in the calculation to a much smaller number of master integrals