(************** Content-type: application/mathematica ************** 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[ 355908, 7745]*) (*NotebookOutlinePosition[ 356785, 7775]*) (* CellTagsIndexPosition[ 356741, 7771]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ PolytopeSkeleton.m Visualizing Convex Polytope Skeletons (with cddmathlink)\ \>", "Title", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[StyleBox["Komei Fukuda, fukuda@ifor.math.ethz.ch\nSwiss Federal \ Institute of Technology, Lausanne and Zurich\nDecember 17, 2002", FontSize->17, FontSlant->"Italic"]], "Subtitle", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Preparation (reading Packages)", "Section", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["Off[General::spell1]; Off[General::spell]", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["$Path = Append[$Path,\"~/Math\"]; ", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "We use an extra graphics package available from ", StyleBox["MathSource", FontSlant->"Italic"], ". It is called View3D which is a part of ExtendGraphics package wrtten \ by Tom Wickham-Jones . The package is available at ", StyleBox["http://www.mathsource.com/", FontFamily->"Courier", FontWeight->"Bold"], ". If you install it in a directory which in not in the $Path, you need to \ append the directory to $Path." }], "Text", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["$Path", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \({"/Users/fukuda/Library/Mathematica/4.1/Kernel", "/Users/fukuda/Library/Mathematica/4.1/AddOns/Autoload", "/Users/fukuda/Library/Mathematica/4.1/AddOns/Applications", "/Library/Mathematica/Kernel/", "/Library/Mathematica/Autoload/", "/Library/Mathematica/Applications/", "/Library/Mathematica/", ".", "/Users/fukuda", "/Applications/LocalApps/Mathematica 4.1.app/AddOns/StandardPackages", "/Applications/LocalApps/Mathematica \ 4.1.app/AddOns/StandardPackages/StartUp", "/Applications/LocalApps/Mathematica 4.1.app/AddOns/Autoload", "/Applications/LocalApps/Mathematica 4.1.app/AddOns/Applications", "/Applications/LocalApps/Mathematica 4.1.app/AddOns/ExtraPackages", "/Applications/LocalApps/Mathematica \ 4.1.app/SystemFiles/Graphics/Packages", "/Applications/LocalApps/Mathematica 4.1.app/Configuration/Kernel", "~/Math", "~/Math"}\)], "Output"] }, Open ]], Cell["Needs[\"ExtendGraphics`View3D`\"];", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "cddmathlink is a ", StyleBox["MathLink", FontSlant->"Italic"], " version of libcdd for doing the vertex enumeration and the facet \ enumeration of a convex polyhedron. cddlib-080.tar.gz is available from \ Fukuda's Homepage: http:///www.ifor.math.ethz.ch/staff/fukuda/fukuda.html \ . Look for \"cdd Homepage\"." }], "Text", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["cddml=Install[\"~/Math/cddmathlink2gmp\"]", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \(LinkObject["/Users/fukuda/Math/cddmathlink2gmp", 4, 2]\)], "Output"] }, Open ]], Cell[TextData[{ "The following packages come with libcdd package and should be installed in \ your favorite directory. Here I assume it is in \"~/Math\" directory. They \ are separately available from Fukuda's Homepage: \ http:///www.ifor.math.ethz.ch/staff/fukuda/fukuda.html . Look for ", StyleBox["Mathematica", FontSlant->"Italic"], " Projects." }], "Text", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["<< PolytopeSkeleton.m", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["<< IOPolyhedra.m", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}], Cell["<< UnfoldPolytope.m", "Input", InitializationCell->True, ImageRegion->{{0, 1}, {0, 1}}] }, Open ]], Cell[CellGroupData[{ Cell["Compute theVertices of a Polytope by using cddmathlink", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["FileNames[\"*\",\"~/Math/ine_3d\"]", "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ \({"~/Math/ine_3d/cube3a.ine", "~/Math/ine_3d/cube3b.ine", "~/Math/ine_3d/cube3.ine", "~/Math/ine_3d/cubocta.ine", "~/Math/ine_3d/cuboctaT.ine", "~/Math/ine_3d/denault1.ine", "~/Math/ine_3d/dodeca.ine", "~/Math/ine_3d/dodecaT.ine", "~/Math/ine_3d/glopt1.ine", "~/Math/ine_3d/grcubocta.ine", "~/Math/ine_3d/grcuboctaT.ine", "~/Math/ine_3d/hexocta.ine", "~/Math/ine_3d/hexoctaT.ine", "~/Math/ine_3d/icododeca.ine", "~/Math/ine_3d/icododecaT.ine", "~/Math/ine_3d/icosaT.ine", "~/Math/ine_3d/rcubocta.ine", "~/Math/ine_3d/rcuboctaT.ine", "~/Math/ine_3d/rhomtria.ine", "~/Math/ine_3d/rhomtriaT.ine", "~/Math/ine_3d/scube3.ine", "~/Math/ine_3d/zono3_10.ine"}\)], "Output"] }, Open ]], Cell["\<\ The file test.ine is the main output file of cdd+, which gives the \ inequality (facet) representation of the polytope.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ MatrixForm[inedata= \tReadPolyhedraData[\"~/Math/ine_3d/glopt1.ine\"]];\ \>", "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ InterpretationBox[\("m="\[InvisibleSpace]17\[InvisibleSpace]", n="\ \[InvisibleSpace]4\[InvisibleSpace]" type="\[InvisibleSpace]"rational"\), SequenceForm[ "m=", 17, ", n=", 4, " type=", "rational"], Editable->False]], "Print"] }, Open ]], Cell["\<\ amat=-Transpose[Drop[Transpose[inedata],1]]; 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