Re: How to do Continued fraction of polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg53206] Re: [mg53052] How to do Continued fraction of polynomials*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Tue, 28 Dec 2004 23:12:43 -0500 (EST)*References*: <200412220952.EAA04405@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Milind Gupta wrote: > How can we do a continued fraction expansion in Mathematica. > > Suppose we have > x^3 + 2x > ------------ > x^2 + 1 > > and we want: > > x + 1 > ------------- > x + 1 > ---- > x > > Can we get this by using some function or some technique in Mathematica?? > > Regards, One method is to iterate taking a quotient and remainder, keeping the quotients and dividing previous remainders by new ones. polynomialContinuedFraction[p1_,p2_,x_] := Module[{quot,rem,res}, Reap[NestWhileList[ ({quot,rem} = Developer`PolynomialDivision[#[[1]],#[[2]],x]; Sow[quot,res]; {#[[2]],rem})&, {p1,p2}, !Developer`ZeroQ[#[[2]]]&]][[2,1]] ] For your example: In[12]:= convergents = polynomialContinuedFraction[x^3+2*x, x^2+1, x] Out[12]= {x, x, x} To change to the customary format you can use pcfForm[{l1_}] := l1 pcfForm[ll_List] := First[ll] + 1/pcfForm[Rest[ll]] In[16]:= InputForm[pcfForm[convergents]] Out[16]//InputForm= x + (x^(-1) + x)^(-1) Daniel Lichtblau Wolfram Research

**References**:**How to do Continued fraction of polynomials***From:*Milind Gupta <milind.gupta@gmail.com>