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MathGroup Archive 2006

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Program to add continued fractions with polynomial partial quotients

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70103] Program to add continued fractions with polynomial partial quotients
  • From: "Diana" <diana.mecum at gmail.com>
  • Date: Wed, 4 Oct 2006 05:58:36 -0400 (EDT)

Hello all,

I am trying to write a program which will evaluate the sum of two
continued fractions.

An example of the two continued fractions are as follows:

(A) {0, T^2 + T + 1}

(B) {0, -T + T^4, T - T^2, T - T^4, -((-T + T^8)/(1 + T + T^2)), -T +
T^4,  -T + T^2, T - T^4, T - T^2 + T^4 - T^5 + T^7 - T^8 + T^10 - T^11
+  T^13 - T^14, -T + T^4, T - T^2, T - T^4, (-T + T^8)/(1 + T + T^2),
-T + T^4, -T + T^2, T - T^4, -((-T + T^32)/(1 + T + T^2)), -T + T^4,  T
- T^2, T - T^4, -((-T + T^8)/(1 + T + T^2)), -T + T^4, -T + T^2,  T -
T^4, -T + T^2 - T^4 + T^5 - T^7 + T^8 - T^10 + T^11 - T^13 + T^14,  -T
+ T^4}

Would someone know of a program to do this?

I would like it to be adaptable to different continued fractions with
polynomial T, for any specified length of input.

My understanding is that with the odd terms, you add the partial
quotients and then determine the polynomial quotient and remainder.
With the even terms, you add the partial quotients, divide the sum by
the product of the partial quotients, and then determine the polynomial
quotient and remainder.

Thanks,

Diana M.


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