@inproceedings{BoGoPeSc05, author = {Bostan, A. and Gonz{\'a}lez-Vega, L. and Perdry, H. and Schost, {\'E}.}, title = {From {N}ewton sums to coefficients: complexity issues in characteristic $p$}, booktitle = {MEGA'05}, year = {2005}, note = {Eighth International Symposium on Effective Methods in Algebraic Geometry, Porto Conte, Alghero, Sardinia (Italy), May 27th -- June 1st}, abstract = {We consider the following problem: given the first $d$ Newton sums of a degree $d$ polynomial $P$, recover the coefficients of $P$. We propose fast algorithms to perform this conversion for polynomials over the $p$-adic ring $\Z_p$. As an application, we deduce a new algorithm to compute the \emph{composed product} of polynomials over the finite field $\F_p$, whose bit-complexity improves the known results by a factor of $\,\log d$ in many cases.}, }