Periodic continued fractions -- suggestions wanted
- To: mathgroup at smc.vnet.net
- Subject: [mg23242] Periodic continued fractions -- suggestions wanted
- From: "Matthew Herman" <Henayni at hotmail.com>
- Date: Sat, 29 Apr 2000 22:04:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Here it is. I would like some suggestions to make it more efficient period::usage = "period[a,b] returns the period length of the reduced quadratic irrational a, after iterating b times; if period[a,b] returns 0, it means that the pre-periodic part is the same as the periodic part. For instance period[2+Sqrt[5],10] returns 0 because the CF expansion is [4]" period[a_, b_] := If[IntegerQ[a^2], Part[Part[Position[contfrac[a, Floor[4 a Log[a]]], 2 Floor[a]] - 1,1], 1], Part[Part[Position[FullSimplify[ FullSimplify[NestList[r, a, b - 1]] - Part[FullSimplify[NestList[r, a, b - 1]], 2]], 0], 2] - 2, 1]] r[x_] := 1\(x - Floor[x]) contfrac[a_, b_] := If[IntegerQ[a b], Part[FullExtendedGCD[a, b], 2], Floor[NestList[r, a, b - 1]]] Thanks, Matt