Re: Alternative cf format.
- To: mathgroup at smc.vnet.net
- Subject: [mg21573] Re: Alternative cf format.
- From: Tobias Oed <tobias at physics.odu.edu>
- Date: Sat, 15 Jan 2000 02:04:16 -0500 (EST)
- Organization: Old Dominion University
- References: <85ml1f$1ql@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Alan W.Hopper" wrote: > > Dear Math group, > > A message I meant to go to mathworld at wolfram.com i.e. Eric Weisstein's > encyclopedia project at Wolfram , http://mathworld.wolfram.com was > posted > inadvertantly as [mg21478] , I apologize for this, but if anyone has > some > comments to make about that CyclicDecimals notebook of mine, I would be > > interested to know about it. > > But here is a separate little question for the mathgroup. > > with Mathematica 3.0 ; > > In[1]:= <<NumberTheory`ContinuedFractions` > > In[2]:= cf = ContinuedFraction[87 / 37] > > 1 > Out[2]:= 2 + --------- > 1 > 2 + ------- > 1 > 1 + ------- > 1 > 5 + ------- > 2 > > In[3]:= Normal[cf] > > Out[3]= 87 / 33 > > Or has Mathematica 4 gone back to the old list format of Mathematica 2, > (much more convenient for long periods), > > as ; > > In[4]:= List @@ cf > > Out[4]= {{2,2,1,5,2}} > > Now an alternative way of representing continued fractions is with the > nested form ; > > In[5]:= 2+1/(2+1/(1+1/(5+1/2))) > > Out[5]= 87 / 33 > > My HP-48SX calculator can convert from the 'standard' to the nested > formats (for short cont. frs) at the press of a key, and I imagine it > would > be straightforward to compose some Mathematica code, for the same > purpose. > Does anyone know a way to convert from the standard to the nested form, > via the list form ? > > Best wishes to all for the new year/decade/millenium , > > Alan W. Hopper > > Katoomba, Australia. > > awhopper at hermes.net.au I think this does what you want last/: Power[last,-1]=last last/: Hold[last]=0 Fold[(#2+Hold[Evaluate[1/#1]] /. HoldForm[x_]:>x /. Hold->HoldForm)&,last,Reverse[First[cf]]] enjoy, Tobias