chains.h File Reference

This file contains classes and functions related to algebraic chain complexes and chain maps, including homology computation. More...

#include "chomp/system/config.h"
#include "chomp/system/textfile.h"
#include <iostream>
#include <fstream>
#include <cstdlib>
#include <iomanip>

Go to the source code of this file.

Classes
class	chomp::homology::chain< euclidom >
	This class defines objects which represent chains as finite sequences of elements identified by integral numbers with coefficients in a given Euclidean domain. More...
class	chomp::homology::simplelist< element >
	This class defines a simple list of pointers to objects of the given type. More...
class	chomp::homology::mmatrix< euclidom >
	A class for representing sparse matrices containing elements of the 'euclidom' type. More...
class	chomp::homology::chaincomplex< euclidom >
	This is an implementation of a chain complex over an arbitrary ring. More...
class	chomp::homology::chainmap< euclidom >
	This class defines a chain map between two chain complexes. More...
Namespaces
namespace	chomp
	This namespace contains the entire CHomP library interface.
namespace	chomp::homology
	This namespace contains the core of the homology computation procedures and related classes and templates contained in the CHomP C++ library.
Defines
#define	CHAINFIXED   0
Functions
template<class euclidom >
outputstream &	chomp::homology::show_homology (outputstream &out, const chain< euclidom > &c)
	Shows a chain as a list of generators of one level of a homology module.
template<class euclidom >
std::ostream &	chomp::homology::show_homology (std::ostream &out, const chain< euclidom > &c)
	Shows a chain as a list of generators of one level of a homology module.
template<class euclidom >
std::ostream &	chomp::homology::operator<< (std::ostream &out, const chain< euclidom > &c)
	Outputs the given chain to a standard output stream in the text mode.
template<class euclidom >
std::istream &	chomp::homology::operator>> (std::istream &in, chain< euclidom > &c)
	Reads a chain from a standard input stream in the text mode.
template<class euclidom >
std::ostream &	chomp::homology::operator<< (std::ostream &out, const mmatrix< euclidom > &m)
	Writes a matrix to the output stream as a map in terms of columns.
template<class euclidom >
std::ostream &	chomp::homology::operator<< (std::ostream &out, const chaincomplex< euclidom > &c)
	Writes a chain complex to an output stream in the text format.
template<class euclidom >
std::ostream &	chomp::homology::operator<< (std::ostream &out, const chainmap< euclidom > &m)
	Writes a chain map to an output stream in the text format.

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Detailed Description

This file contains classes and functions related to algebraic chain complexes and chain maps, including homology computation.

The templates in this file are prepared for a Euclidean domain. This ring type should have the following methods defined in it: operator +, operator *, unary operator -, operator <<, operator >>, assignment from an integer (only 0 and 1), function "normalized", operators == and != (used only to compare with 0 and with 1), operators / and % (for division with remainder), function delta (from the definition of the Euclidean domain), and a static member function "const char *euclidom::ringsymbol ()".

Author:

Pawel Pilarczyk

Definition in file chains.h.

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Define Documentation

#define CHAINFIXED   0

Definition at line 91 of file chains.h.

Referenced by chomp::homology::chain< euclidom >::allocated().