  This work studies limits of Pfaffian systems, a class of first-order PDEs
appearing in the Feynman integral calculus. Such limits appear naturally in the
context of scattering amplitudes when there is a separation of scale in a given
set of kinematic variables. We model these limits, which are often singular,
via restrictions of D-modules. We thereby develop two different restriction
algorithms: one based on gauge transformations, and another relying on the
Macaulay matrix. These algorithms output Pfaffian systems containing fewer
variables and of smaller rank. We show that it is also possible to retain
logarithmic corrections in the limiting variable. The algorithms are showcased
in many examples involving Feynman integrals and hypergeometric functions
coming from GKZ systems.
