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MathGroup Archive 2000

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Re: matrices, dot products and convergents of continued fractions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23406] Re: [mg23402] matrices, dot products and convergents of continued fractions
  • From: "Richard Finley" <rfinley at medicine.umsmed.edu>
  • Date: Sat, 6 May 2000 19:14:14 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Matt,
Perhaps I am just not understanding what you are trying to do, but your definition of contfrac1 always gives an integer result so your definition of aak will always give an error if b>0 (since it exceeds the depth of the atomic result).  Perhaps you could explain what you actually want them to compute.  
regards, RF

>>> "Matthew Herman" <henayni at hotmail.com> 05/06/00 12:26AM >>>
hi,

It is known that you can compute convergents of continued fractions using 
matrices and dot products. I am having a problem, maybe you guys could help.

aak2[x_, y_] := Table[aak[x, b, y], {b, 1, y}]
aak[x_, b_, y_] := {{1, contfrac1[x, y][[b]]}, {1, 1}}
contfrac1[a_,b_]:=
  If[IntegerQ[Numerator[a]] && IntegerQ[Denominator[a]],
    ContinuedFraction[a][[1]],ContinuedFraction[a,b][[1]]]

I want to take Dot[aak[x,b,y]], but there are 2 braces on the outside that 
prevent me from doing this. Anyone have an idea on how to workaround that?

Matt


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