  In D-module theory, we have the notion of the restriction of a module along a
smooth variety. T. Oaku and N. Takayama have described a process to compute the
restriction, which starts from a free resolution adapted to the V-filtration of
Kashiwara-Malgrange. By using the theory of free resolutions adapted to the
(order and V)-bifiltration (from T. Oaku , N. Takayama and M. Granger), we
endow the restriction with an order filtration and we show that the process of
Oaku and Takayama respects the order filtration. In consequence, we compute a
minimal presentation of the algebraic local cohomology module associated with a
quasi-homogeneous polynomial with an isolated singularity, viewed as a D-module
and endowed with a kind of a pole order filtration.
