Continued fraction from rational polynomial?
- To: mathgroup at smc.vnet.net
- Subject: [mg127007] Continued fraction from rational polynomial?
- From: dr DanW <dmaxwarren at gmail.com>
- Date: Sat, 23 Jun 2012 04:16:27 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Does Mathematica have a function to develop a continued fraction from a rational polynomial? I have managed to implement the Euclidian Algorithm for polynomials as below:
PolynomialContinuedFraction[a_, b_, s_Symbol] /; PolynomialQ[a, s] && PolynomialQ[b, s] :=
Block[{q, r},
Flatten[Reap[NestWhile[Function[ab, {q, r} = PolynomialQuotientRemainder[ab[[1]], ab[[2]], s];
Sow[q]; {ab[[2]], r}], {a, b}, Function[ab, ab[[2]] =!= 0]]; ][[2]]]]
but I cannot shake the feeling that this is something the Mathematica can already do and I just don't know what it is called. ContinuedFraction[] only works with numbers. Interestingly, FromContinuedFraction[] works just fine with the symbolic output of my function.
Daniel