Re: Program to calculate rational function with imbedded continued fraction

• To: mathgroup at smc.vnet.net
• Subject: [mg69912] Re: Program to calculate rational function with imbedded continued fraction
• From: "Diana" <diana.mecum at gmail.com>
• Date: Wed, 27 Sep 2006 06:05:05 -0400 (EDT)
• References: <efarkg\$7up\$1@smc.vnet.net>

```Dimitris,

Thank you so much. I will try to be more clear.

I am writing a thesis related to analogs of "e" in the function field
case.

e(1) is written as a continued fraction.

One example of e(1) for characteristic 2 is the following: [i] = T^2^i
- T

e(1) - 1 = [0, [1], [2], [1], [3], [1], [2], [1], [4], [1], [2], [1],
[3], [1], [2], [1], [5], [1], [2], [1], [3], [1], [2], [1], [4], [1],
[2], [1], [3], [1], [2], [1], [6], [1], [2], [1], [3], [1], [2], [1],
[4], [1], [2], [1], [3], [1], [2], [1], [5], [1], [2], [1], [3], [1],
[2], [1], [4], [1], [2], [1], [3], [1], [2], [1], [7] ...]

You see that the pattern does not repeat or terminate. I will only be
able to provide a finite length of the sequence.

Then, I am trying to calculate, for various x, y, z, w, xw - yz != 0

(xe(1) - y)/(ze(1) - w).

x, y, z, and w are polynomials of T in characteristic 2.

For example, (e(1) -t)(t^2e - 1)

I am able to calculate FromContinuedFraction of each of the top and
bottom expressions, but then need a program to calculate the continued
fraction of that. I have attached a Mathematica file for which I need
to calculate the continued fraction.

So, for example, I would like to be able to calculate the continued
fraction of

(FromContinuedFraction[0, [1], [2], [1], [3], [1], [2], [4]] - T)/(T^2
FromContinuedFraction[0, [1], [2], [1], [3], [1], [2], [4]] -1)