[Date Index] [Thread Index] [Author Index]

Alternative cf format.

• To: mathgroup at smc.vnet.net
• Subject: [mg21514] Alternative cf format.
• From: "Alan W.Hopper" <awhopper at hermes.net.au>
• Date: Fri, 14 Jan 2000 02:43:32 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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