(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 153361, 3634]*) (*NotebookOutlinePosition[ 154005, 3656]*) (* CellTagsIndexPosition[ 153961, 3652]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Functions for generating and displaying cross sections of Pascal's \ simplices\ \>", "Title"], Cell[TextData[{ "Eric Rowland, 09/17/03\n", ButtonBox["http://www.math.rutgers.edu/~erowland", ButtonData:>{ URL[ "http://www.math.rutgers.edu/~erowland"], None}, ButtonStyle->"Hyperlink"] }], "Subsubtitle"], Cell[CellGroupData[{ Cell["Functions", "Section"], Cell["Evaluate this section to load the functions.", "Text"], Cell[TextData[{ StyleBox["Simplex", "Input"], " gives the ", Cell[BoxData[ \(TraditionalForm\`m\)]], "th ", Cell[BoxData[ \(TraditionalForm\`\((n - 1)\)\)]], "-dimensional cross section of Pascal's ", Cell[BoxData[ \(TraditionalForm\`n\)]], "-simplex." }], "Text"], Cell[BoxData[{ \(\(Simplex[1, m_] = 1;\)\), "\[IndentingNewLine]", \(Simplex[n_, m_] := \(Simplex[n, m] = Table[Binomial[m, i] Simplex[n - 1, i], {i, 0, m}]\)\)}], "Input"], Cell["\<\ This not particularly elegant function inserts a space between every other \ element in a list.\ \>", "Text"], Cell[BoxData[ \(Sparsify[list_] := Insert[list, "\<\>", List /@ Range[2, Length[list]]]\)], "Input"], Cell[TextData[{ StyleBox["TriangleFormat", "Input"], " puts a two dimensional (lower) triangular table into nice triangular \ format (assuming that the first row is of length 1 and each row after the \ first is 1 element longer than the preceding). (I tried to build slightly \ more generality into the function (by defining ", StyleBox["m", "Input"], "), but the way it pads the rows to make a square matrix ends up deleting \ entries if the matrix is not in the exactly specified form.)\nThe rest of \ these functions just provide spiffy-looking computing and formatting \ shortcuts. However, one source of confusion may be that, for example, ", StyleBox["Tetrahedron", "Input"], " does not output a tetrahedron but rather a triangle (the cross section of \ a tetrahedron). 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