chaincon/combchain.h

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/////////////////////////////////////////////////////////////////////////////
///
/// \file
///
/// A combinatorial chain, that is, a chain with Z_2 coefficients.
///
/////////////////////////////////////////////////////////////////////////////

// Copyright (C) 2009-2011 by Pawel Pilarczyk.
//
// This file is part of my research software package. This is free software:
// you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// This software is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this software; see the file "license.txt". If not,
// please, see <http://www.gnu.org/licenses/>.

// Started on March 24, 2009. Last revision: March 6, 2011.


#ifndef _CHAINCON_COMBCHAIN_H_
#define _CHAINCON_COMBCHAIN_H_


// include some standard C++ header files
#include <istream>
#include <ostream>

// include selected header files from the CHomP library
#include "chomp/system/config.h"
#include "chomp/struct/hashsets.h"


// --------------------------------------------------
// -------------- combinatorial chain ---------------
// --------------------------------------------------

/// A combinatorial chain. This is in fact a finite set of cells.
/// It corresponds to chains with coefficients in F_2 (a.k.a. Z_2).
template <class CellT>
class tCombChain
{
public:
        /// The type of cells in the combinatorial chain.
        typedef CellT CellType;

        /// The default constructor of an empty combinatorial chain.
        tCombChain ();

        /// The constructor of a combinatorial chain containing one cell.
        explicit tCombChain (const CellT &c);

        /// Returns the number of elements in the combinatorial chain.
        int_t size () const;

        /// Returns true if and only if the chain is zero (empty set).
        bool empty () const;

        /// Returns the n-th element of the combinatorial chain.
        const CellT &operator [] (int_t n) const;

        /// Returns the position of the given cell in the chain
        /// or -1 if the cell is not there.
        int_t position (const CellT &c) const;

        /// Checks if the given cell appears in the chain.
        bool contains (const CellT &c) const;

        /// Adds a given cell to the combinatorial chain.
        void add (const CellT &c);

        /// Adds a given chain to the combinatorial chain.
        void add (const tCombChain<CellT> &ch);

        /// Compares if the two chains are equal.
        bool operator == (const tCombChain<CellT> &ch) const;

        /// Swaps the data with another chain.
        void swap (tCombChain<CellT> &ch);

private:
        /// The set of elements in the combinatorial chain.
        chomp::homology::hashedset<CellT> cells;

}; /* class tCombChain */

// --------------------------------------------------

template <class CellT>
inline tCombChain<CellT>::tCombChain ():
        cells (1)
{
        return;
} /* tCombChain::tCombChain */

template <class CellT>
inline tCombChain<CellT>::tCombChain (const CellT &c):
        cells (1)
{
        cells. add (c);
        return;
} /* tCombChain::tCombChain */

template <class CellT>
inline int_t tCombChain<CellT>::size () const
{
        return cells. size ();
} /* tCombChain::size */

template <class CellT>
inline bool tCombChain<CellT>::empty () const
{
        return cells. empty ();
} /* tCombChain::empty */

template <class CellT>
inline const CellT &tCombChain<CellT>::operator [] (int_t n) const
{
        return cells [n];
} /* tCombChain::operator [] */

template <class CellT>
inline int_t tCombChain<CellT>::position (const CellT &c) const
{
        return cells. getnumber (c);
} /* tCombChain::position */

template <class CellT>
inline bool tCombChain<CellT>::contains (const CellT &c) const
{
        return (cells. getnumber (c) >= 0);
} /* tCombChain::contains */

template <class CellT>
inline void tCombChain<CellT>::add (const CellT &c)
{
        int_t n = cells. getnumber (c);
        if (n < 0)
                cells. add (c);
        else
                cells. removenum (n);
        return;
} /* tCombChain::add */

template <class CellT>
inline void tCombChain<CellT>::add (const tCombChain<CellT> &ch)
{
        int_t size = ch. size ();
        for (int_t i = 0; i < size; ++ i)
                this -> add (ch [i]);
        return;
} /* tCombChain::add */

template <class CellT>
inline bool tCombChain<CellT>::operator == (const tCombChain<CellT> &ch)
        const
{
        int_t size = cells. size ();
        int_t chSize = ch. cells. size ();
        if (size != chSize)
                return false;
        for (int_t i = 0; i < size; ++ i)
        {
                if (!ch. cells. check (cells [i]))
                        return false;
        }
        return true;
} /* tCombChain::operator == */

template <class CellT>
inline void tCombChain<CellT>::swap (tCombChain<CellT> &ch)
{
        cells. swap (ch. cells);
        return;
} /* tCombChain::swap */

// --------------------------------------------------

/// Writes a combinatorial chain to an output stream.
template <class CellT>
std::ostream &operator << (std::ostream &out, const tCombChain<CellT> &c)
{
        int_t size = c. size ();
        for (int_t i = 0; i < size; ++ i)
        {
                if (i)
                        out << "+";
                out << c [i];
        }
        return out;
} /* operator << */

/// Reads a combinatorial chain from an input stream.
template <class CellT>
std::istream &operator >> (std::istream &in, tCombChain<CellT> &c)
{
        throw "Operator >> not implemented for tCombChain.";
        return in;
} /* operator >> */

// --------------------------------------------------

template <class CellT>
tCombChain<CellT> operator + (const tCombChain<CellT> &a,
        const tCombChain<CellT> &b)
{
        tCombChain<CellT> c (a);
        c. add (b);
        return c;
} /* operator + */

// --------------------------------------------------

/// Adds the boundary of a given cell to the provided chain.
template <class CellT>
inline void computeBoundary (const CellT &c, tCombChain<CellT> &b)
{
        // determine the length of the boundary of this cell
        int length = c. boundaryLength ();

        // process all the cells in its boundary
        for (int i = 0; i < length; ++ i)
        {
                // create the subsequent boundary cell
                CellT bc (c, i);

                // add the boundary cell to the given chain
                b. add (bc);
        }
        return;
} /* computeBoundary */

/// Returns the boundary of a given cell.
template <class CellT>
inline tCombChain<CellT> boundary (const CellT &c)
{
        // prepare a chain that is going to contain the boundary of c
        tCombChain<CellT> b;

        // add the boundary of the cell to b
        computeBoundary (c, b);

        // return the computed boundary chain
        return b;
} /* boundary */

/// Adds the boundary of a given chain to the provided chain.
template <class CellT>
inline void computeBoundary (const tCombChain<CellT> &c,
        tCombChain<CellT> &b)
{
        int_t size = c. size ();
        for (int_t i = 0; i < size; ++ i)
                computeBoundary (c [i], b);
        return;
} /* computeBoundary */

/// Returns the boundary of a given chain.
template <class CellT>
inline tCombChain<CellT> boundary (const tCombChain<CellT> &c)
{
        // prepare a chain that is going to contain the boundary of c
        tCombChain<CellT> b;

        // add the boundary of each cell in the chain to b
        computeBoundary (c, b);

        // return the computed boundary chain
        return b;
} /* boundary */


#endif // _CHAINCON_COMBCHAIN_H_