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Re: DigitDifferences?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg60754] Re: DigitDifferences?
*From*: "Ray Koopman" <koopman at sfu.ca>
*Date*: Tue, 27 Sep 2005 03:45:24 -0400 (EDT)
*References*: <dh2tfe$d69$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Paul Abbott wrote:
> I would like some suggestions on good implementations of the following
> idea: suppose that you have two numbers whose floating point
> representation has many common digits, say
>
> 2`50 Sum[(-1)^(k - 1)/(2 k - 1), {k, 1, 50000}]
>
> 1.5707863267948976192313211916397520520985833146875579625874449850433
>
> and
>
> N[Pi/2, 50]
>
> 1.5707963267948966192313216916397514420985846996875529104874722962622
>
> Although these two numbers disagree in the 5th decimal place, they still
> have a great many common digits from that point onwards.
>
> (By the way, if you are using OS X you can use the "Evaluate to Text"
> MathService under the Services menu to do inline Mathematica evaluations
> in your favourite newsreader, avoiding much of the cutting and pasting
> to and from Mathematica. I used that here for the numerical evaluations.)
>
> I would like to display the differences between these numbers a la
> Borwein Borwein and Dilcher (1989) in "Pi, Euler numbers and asymptotic
> expansions", Amer. Math. Monthly 96 (1989), 681-687. To get an idea,
> paste either cell below into a Notebook. These attempts were done by
> hand -- so automated code for their production would be nice -- and they
> have one unfortunate problem: the spacing between numbers is not
> uniform. Suggestions for a DigitDifferences function most welcome.
>
> Cheers,
> Paul
>
> Here my two attempts to display the sort of formatting required -- there
> may be other better solutions:
>
> Cell[BoxData[
> FormBox[
> RowBox[{"1.5707",
> UnderscriptBox["8",
> UnderscriptBox["_", "1"]], "632679489",
> UnderscriptBox[
> UnderscriptBox["7", "_"],
> RowBox[{"-", "1"}]], "619231321",
> UnderscriptBox["1",
> UnderscriptBox["_", "5"]], "9163975",
> UnderscriptBox[
> UnderscriptBox["205", "_"],
> RowBox[{"-", "61"}]], "209858",
> UnderscriptBox["3314",
> UnderscriptBox["_", "1385"]], "6876"}],
> TraditionalForm]], "Text"]
>
>
>
> Cell[BoxData[
> FormBox[
> RowBox[{"1.5707", " ",
> UnderscriptBox["8",
> UnderscriptBox["_", "1"]], " ", "632679489", " ",
> OverscriptBox[
> OverscriptBox["7", "_"], "1"], " ", "619231321", " ",
> UnderscriptBox["1",
> UnderscriptBox["_", "5"]], " ", "9163975", " ",
> OverscriptBox[
> OverscriptBox["205", "_"], "61"], " ", "209858", " ",
> UnderscriptBox["3314",
> UnderscriptBox["_", "1385"]], " ", "6876"}],
> TraditionalForm]], "Text"]
>
> _______________________________________________________________________
> Paul Abbott Phone: 61 8 6488 2734
> School of Physics, M013 Fax: +61 8 6488 1014
> The University of Western Australia (CRICOS Provider No 00126G)
> AUSTRALIA http://physics.uwa.edu.au/~paul
I suppose it depends on why one is comparing the numbers,
but I find this a little easier to read:
Cell["\n
8 7 1 205 3314 \n
1.5707 632679489 619231321 9163975 209858 6876\n
9 6 6 144 4699 \n",
Text, LineSpacing->{.40,0}]
Adjust LineSpacing to suit the output device.
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