en.wikipedia.org/wiki/D-modules In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein?Sato polynomial.
The methods of D-module theory have always been drawn from sheaf theory and other techniques with inspiration from the work of Alexander Grothendieck in algebraic geometry.
The Bernstein-Sato functional equation is used in computations of some of the more complex kinds of singular integrals occurring in quantum field theory (Tkachov 1997). Such computations are needed for precision measurements in elementary particle physics as practiced e.g. at CERN (see the papers citing (Tkachov 1997)). However, the most interesting cases require a simple generalization of the Bernstein-Sato functional equation to the product of two polynomials ・・Devising ways to bypass the combinatorial explosion of the brute force algorithm would be of great value in such applications.
