2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113935We give an algorithm to compute the local $b$ function. In this algorithm, we use the Mora division algorithm in the ring of differential operators and an approximate division algorithm in the ring of differential operators with power series coefficient.19 pagesRings and AlgebrasAn Algorithm Computing the Local $b$ Function by an Approximate Division Algorithm in $\hat{\mathcal{D}}$text