Bernstein–Sato polynomial

In mathematics, the Bernstein–Sato polynomial is a polynomial related to differential operators, introduced independently by Joseph Bernstein (1971) and Mikio Sato and Takuro Shintani (1972, 1974), Sato (1990).

Kashiwara (1976) proved that all roots of the Bernstein–Sato polynomial are negative rational numbers.

[citation needed] Nero Budur, Mircea Mustață, and Morihiko Saito (2006) generalized the Bernstein–Sato polynomial to arbitrary varieties.

There are implementations of related algorithms in computer algebra systems RISA/Asir, Macaulay2, and SINGULAR.

Daniel Andres, Viktor Levandovskyy, and Jorge Martín-Morales (2009) presented algorithms to compute the Bernstein–Sato polynomial of an affine variety together with an implementation in the computer algebra system SINGULAR.