The ChainCon Software (Release 0.03)
awdiagsimgen.h
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1 /////////////////////////////////////////////////////////////////////////////
2 ///
3 /// \file
4 ///
5 /// A version of the Alexander-Whitney diagonal for general simplicial sets.
6 ///
7 /////////////////////////////////////////////////////////////////////////////
8 
9 // Copyright (C) 2009-2016 by Pawel Pilarczyk.
10 //
11 // This file is part of my research software package. This is free software:
12 // you can redistribute it and/or modify it under the terms of the GNU
13 // General Public License as published by the Free Software Foundation,
14 // either version 3 of the License, or (at your option) any later version.
15 //
16 // This software is distributed in the hope that it will be useful,
17 // but WITHOUT ANY WARRANTY; without even the implied warranty of
18 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 // GNU General Public License for more details.
20 //
21 // You should have received a copy of the GNU General Public License
22 // along with this software; see the file "license.txt". If not,
23 // please, see <http://www.gnu.org/licenses/>.
24 
25 // Started on March 24, 2009. Last revision: December 3, 2014.
26 
27 
28 #ifndef _CHAINCON_AWDIAGSIMGEN_H_
29 #define _CHAINCON_AWDIAGSIMGEN_H_
30 
31 
32 // include some standard C++ header files
33 #include <istream>
34 #include <ostream>
35 
36 // include selected header files from the CHomP library
37 #include "chomp/system/config.h"
38 
39 // include relevant local header files
40 #include "chaincon/combtensor.h"
41 #include "chaincon/tensor.h"
42 #include "chaincon/ez_aw.h"
43 
44 
45 // --------------------------------------------------
46 // ------------------ AW diagonal -------------------
47 // --------------------------------------------------
48 
49 /// Computes the Alexander-Whitney diagonal of a simplicial cell.
50 template <class SimCellT>
51 inline void AWdiagonal (const SimCellT &s,
53 {
54  EZ_AW (s, s, t);
55  return;
56 } /* AWdiagonal */
57 
58 /// Computes the Alexander-Whitney diagonal of a simplicial cell.
59 template <class SimCellT, class CoefT>
60 inline void AWdiagonal (const SimCellT &s,
62 {
63  EZ_AW (s, s, t);
64  return;
65 } /* AWdiagonal */
66 
67 
68 #endif // _CHAINCON_AWDIAGSIMGEN_H_
69 
A tensor of chains with coefficients in an arbitrary commutative ring.
Tensor of chains.
Definition: tensor.h:52
Combinatorial tensor of cells.
Definition: combtensor.h:53
A combinatorial tensor (for coefficients in Z_2).
void EZ_AW(const SimCellT &s1, const SimCellT &s2, tCombTensor< SimCellT, SimCellT > &t)
Computes the Alexander-Whitney operator on a product of simplicial cells.
Definition: ez_aw.h:76
The Alexander-Whitney operator as a component of the Eilenberg-Zilber chain contraction.
void AWdiagonal(const SimCellT &s, tCombTensor< SimCellT, SimCellT > &t)
Computes the Alexander-Whitney diagonal of a simplicial cell.
Definition: awdiagsimgen.h:51