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In particular, users have reported good results with the Cloog code generator (both in terms of the code generated, and in terms of ability to control trade-offs when generating code), and with the algorithms for counting integer solutions (Alexander Barvinok's [21] work requires a vertex description of the polytope, which is not supported in ...
PDFCreator is an application for converting documents into Portable Document Format format on Microsoft Windows operating systems. It works by creating a virtual printer that prints to PDF files, and thereby allows practically any application to create PDF files by choosing to print from within the application and then printing to the PDFCreator printer.
The composition of a standard OFF file is as follows: [4] First line (optional): the letters OFF to mark the file type. Second line: the number of vertices, number of faces, and number of edges, in order (the latter can be ignored by writing 0 instead). List of vertices: X, Y and Z coordinates.
The PDF 1.4 specification allowed form submissions in XML format, but this was replaced by submissions in XFDF format in the PDF 1.5 specification. XFDF conforms to the XML standard. XFDF can be used in the same way as FDF; e.g., form data is submitted to a server, modifications are made, then sent back and the new form data is imported in an ...
A unitary reflection generator for a 1-polytope with p vertices is e 2πi/p = cos(2π/p) + i sin(2π/p). When p = 2, the generator is e πi = –1, the same as a point reflection in the real plane. In higher complex polytopes, 1-polytopes form p-edges. A 2-edge is similar to an ordinary real edge, in that it contains two vertices, but need not ...
The first diagram makes clear that the power set is a graded poset.The second diagram has the same graded structure, but by making some edges longer than others, it emphasizes that the 4-dimensional cube is a combinatorial union of two 3-dimensional cubes, and that a tetrahedron (abstract 3-polytope) likewise merges two triangles (abstract 2-polytopes).