Re: Need algorithm to convert general continued fraction to simple continued fraction

*To*: mathgroup at smc.vnet.net*Subject*: [mg70197] Re: Need algorithm to convert general continued fraction to simple continued fraction*From*: dimmechan at yahoo.com*Date*: Sat, 7 Oct 2006 07:07:26 -0400 (EDT)*References*: <eg4seq$fdp$1@smc.vnet.net>

Although is not quite clear to me what you really want, I will make an attempt to answer you. Here we are... lst = {1/(t^2 + t + 1), t^4 - t, t^2 - t, t^4 - t, 1/(t^3 + 3*t^2), t + t^4 + 6*t^7, 1/(t^12 + 5*t^5 + 6*t + 8)}; ReplacePart[lst, 0, Position[lst, 1/_]] {0, -t + t^4, -t + t^2, -t + t^4, 0, t + t^4 + 6*t^7, 0} Diana wrote: > Math folks, > > I have a general continued fraction, the partial quotients of which are > comprised of arbitrary polynomials in t. These arbitrary polynomials do > not repeat in a regular fashion, but I have the continued fraction > expansion available to any desired length. > > I would like to know if there is an alogrithm which I could use, and > then code with Mathematica, which would allow me to convert this > fraction to a simple continued fraction. > > In other words, I would like to replace a non-zero a_0 term with 0. > > So, is there a way to convert: > > [{1/(t^2+t+1), t^4-t, t^2-t, t^4-t, ...}] (These polynomials in t are > arbitrary but known.) > > to: > > [{0, ...}]?