DigitDifferences?

*To*: mathgroup at smc.vnet.net*Subject*: [mg60677] DigitDifferences?*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Sat, 24 Sep 2005 02:55:22 -0400 (EDT)*Organization*: The University of Western Australia*Sender*: owner-wri-mathgroup at wolfram.com

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