Abstract We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections. as well as a direct derivation of the differential equations satisfied by the master integrals. employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers. https://www.roneverhart.com/Gretsch-G5210T-P90-Electromatic-Jet-Two-90-Single-Cut-Electric-Guitar-w-Bigsby-Mako-p23063/