00001 ///////////////////////////////////////////////////////////////////////////// 00002 /// 00003 /// \file 00004 /// 00005 /// A cubical version of the Alexander-Whitney diagonal. 00006 /// 00007 ///////////////////////////////////////////////////////////////////////////// 00008 00009 // Copyright (C) 2009-2011 by Pawel Pilarczyk. 00010 // 00011 // This file is part of my research software package. This is free software: 00012 // you can redistribute it and/or modify it under the terms of the GNU 00013 // General Public License as published by the Free Software Foundation, 00014 // either version 3 of the License, or (at your option) any later version. 00015 // 00016 // This software is distributed in the hope that it will be useful, 00017 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00018 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00019 // GNU General Public License for more details. 00020 // 00021 // You should have received a copy of the GNU General Public License 00022 // along with this software; see the file "license.txt". If not, 00023 // please, see <http://www.gnu.org/licenses/>. 00024 00025 // Started on March 24, 2009. Last revision: March 6, 2011. 00026 00027 00028 #ifndef _CHAINCON_AWDIAGCUB_H_ 00029 #define _CHAINCON_AWDIAGCUB_H_ 00030 00031 00032 // include some standard C++ header files 00033 #include <istream> 00034 #include <ostream> 00035 00036 // include selected header files from the CHomP library 00037 #include "chomp/system/config.h" 00038 00039 // include relevant local header files 00040 #include "chaincon/cubcell.h" 00041 #include "chaincon/combtensor.h" 00042 00043 00044 // -------------------------------------------------- 00045 // ------------------ AW diagonal ------------------- 00046 // -------------------------------------------------- 00047 00048 /// Computes the Alexander-Whitney diagonal of a cubical cell 00049 /// using the formula from Serre's paper. 00050 /// Please, note that this formula has only been implemented 00051 /// for 2-dimensional cells at the moment; the general formula 00052 /// will be implemented soon. 00053 template <class CoordT> 00054 inline tCombTensor<tCubCell<CoordT> > AWdiagonal (const tCubCell<CoordT> &c) 00055 { 00056 // abort the program if the dimension is different than two 00057 if (c. dim () != 2) 00058 throw "A-W diagonal implemented for 2-dim cubes only."; 00059 00060 // extract the coordinates of the four vertices of the cubical cell 00061 int dim = c. spaceDim (); 00062 CoordT coord [4] [chomp::homology::MaxBasDim]; 00063 int indices [2]; 00064 int index = 0; 00065 for (int i = 0; i < dim; ++ i) 00066 { 00067 coord [0] [i] = c. left (i); 00068 coord [3] [i] = c. right (i); 00069 if (coord [0] [i] != coord [3] [i]) 00070 { 00071 coord [1] [i] = index ? coord [3] [i] : 00072 coord [0] [i]; 00073 coord [2] [i] = index ? coord [0] [i] : 00074 coord [3] [i]; 00075 indices [index ++] = i; 00076 } 00077 else 00078 { 00079 coord [1] [i] = coord [0] [i]; 00080 coord [2] [i] = coord [0] [i]; 00081 } 00082 } 00083 00084 // create the products of respective cells 00085 tCombTensor<tCubCell<CoordT> > tensor; 00086 tensor. add (tCubCell<CoordT> (dim, coord [0], coord [2]), 00087 tCubCell<CoordT> (dim, coord [2], coord [3])); 00088 tensor. add (tCubCell<CoordT> (dim, coord [0], coord [1]), 00089 tCubCell<CoordT> (dim, coord [1], coord [3])); 00090 00091 return tensor; 00092 } /* AWdiagonal */ 00093 00094 00095 #endif // _CHAINCON_AWDIAGCUB_H_ 00096
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