does anyone have a program for the period length of a continued fraction?

*To*: mathgroup at smc.vnet.net*Subject*: [mg23216] does anyone have a program for the period length of a continued fraction?*From*: "Matthew Herman" <Henayni at hotmail.com>*Date*: Mon, 24 Apr 2000 01:12:23 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I am working on a program for pell's equation, and I need this. In the meantime, here is a program for the {a1,a2...an} list of a finite or infinite continued fraction and another for the convergents. If anyone has any comments or suggestions.. let me know. FullExtendedGCD is taken from Stan Wagon's "Mathematica in Action". contfrac[a_,b_]:= If[IntegerQ[a = b],Part[FullExtendedGCD[a,b],2],Floor[NestList[r,a,b-1]]] r[x_] := 1/(x - Floor[x]) FullExtendedGCD[a_, b_] := FullExtendedGCD[a, b, {a}, {}] FullExtendedGCD[a_, b_, r_, q_] := FullExtendedGCD[ b, Mod[a,b], Append[r, b], Append[q, Floor[a/b]]] FullExtendedGCD[a_, 0, r_, q_] := Block[{s = {1, 0}, t = {0, 1}}, Scan[(AppendTo[t, t[[-2]] - t[[-1]] #]; AppendTo[s, s[[-2]] - s[[-1]] #]) &, q]; {r, q, s, t}] (conv[a_, b_] := Table[p[a, b, k]/q[a, b, k], {k, 1, Length[contfrac[a, b]]}] p[a_,b_,n_]:=Part[contfrac[a,b],n]p[a,b,n-1]+p[a,b,n-2] p[a_,b_,2]:=Part[contfrac[a,b],1]*Part[contfrac[a,b],2]+1 p[a_,b_,1]:=Part[contfrac[a,b],1] q[a_,b_,1]:=1 q[a_,b_,2]:=Part[contfrac[a,b],2] q[a_,b_,n_]:=Part[contfrac[a,b],n]q[a,b,n-1]+q[a,b,n-2] thanks, matt