Algebraic power series are formal power series which satisfy a univariate
polynomial equation over the polynomial ring in n variables. This relation
determines the series only up to conjugacy. Via the Artin-Mazur theorem and the
implicit function theorem it is possible to describe algebraic series
completely by a vector of polynomials in n+p variables. This vector will be the
code of the series. In the paper, it is then shown how to manipulate algebraic
series through their code. In particular, the Weierstrass division and the
Grauert-Hironaka-Galligo division will be performed on the level of codes, thus
providing a finite algorithm to compute the quotients and the remainder of the
division.Comment: 35 page