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MathGroup Archive 2006

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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, ...}]?


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