Regular bb-functions of DD-modules

Let MM be an algebraic DD-module defined on an affine space XX and YY be a linear submanifold of XX. We give an algorithm to determine if MM is regular specializable along YY, and to find, if so, its regular bb-function. (MM has a regular bb-function by definition if and only if MM is regular specializable.) We also prove that the AA-hypergeometric system of Gelfand–Kapranov–Zelevinsky is always regular specializable along the origin.