chomp::homology::chainmap< euclidom > Class Template Reference

This class defines a chain map between two chain complexes. More...

#include <chains.h>

Public Member Functions
	chainmap (const chaincomplex< euclidom > &domain, const chaincomplex< euclidom > &range)
	The default constructor of a chain map between the two given chain complexes. More...
	chainmap (const chainmap< euclidom > &c)
	Copy constructor. More...
chainmap< euclidom > &	operator= (const chainmap< euclidom > &c)
	The assignment operator. More...
	~chainmap ()
	The destructor. More...
int	dim () const
	Returns the dimension of the chain map. More...
const mmatrix< euclidom > &	operator[] (int i) const
	Returns the matrix of the chain map at the given level. More...
void	add (int q, int_t m, int_t n, euclidom e)
	Adds a coefficient to the selected matrix of the map: M_q [m, n] += e. More...
void	invert (void)
	Inverts the chain map. More...
void	compose (const chainmap< euclidom > &m1, const chainmap< euclidom > &m2)
	Composes two given chain maps. More...
outputstream &	show (outputstream &out, const char *maplabel="f", const char *xtxt=NULL, const char *ytxt=NULL, const int *level=NULL) const
	Writes the chain map to an output stream in the text format using specified labels for the map and elements in the domain and in the codomain of the map. More...
std::ostream &	show (std::ostream &out, const char *maplabel="f", const char *xtxt=NULL, const char *ytxt=NULL, const int *level=NULL) const
	Writes the chain map to an output stream in the text format using specified labels for the map and elements in the domain and in the codomain of the map. More...
void	take_homology (const chainmap< euclidom > &m, const chain< euclidom > *hom_domain, const chain< euclidom > *hom_range)
	Creates a chain map that represents the map induced in homology by the chain map between the two given chain complexes which have been previously transformed to the simple form. More...
outputstream &	show_homology (outputstream &out, const chain< euclidom > *hom_domain, const chain< euclidom > *hom_range, const int *level=NULL, const char *xtxt=NULL, const char *ytxt=NULL) const
	Writes to an output stream the map induced in homology. More...
std::ostream &	show_homology (std::ostream &out, const chain< euclidom > *hom_domain, const chain< euclidom > *hom_range, const int *level=NULL, const char *xtxt=NULL, const char *ytxt=NULL) const
	Writes to an output stream the map induced in homology. More...

Private Attributes
int	len
	The number of matrices (dimension of the chain map + 1). More...
mmatrix< euclidom > *	map
	The matrices in each dimension. More...

Detailed Description

template<class euclidom>
class chomp::homology::chainmap< euclidom >

This class defines a chain map between two chain complexes.

The chain complexes must exist and not change durign the existence of the chain map.

Definition at line 3242 of file chains.h.

Constructor & Destructor Documentation

chainmap() [1/2]

template<class euclidom >

chomp::homology::chainmap< euclidom >::chainmap ( const chaincomplex< euclidom > &  domain, const chaincomplex< euclidom > &  range  )

inline

The default constructor of a chain map between the two given chain complexes.

Definition at line 3328 of file chains.h.

{
        // set the dimension
        len = domain. len;
        if (range. len < domain. len)
                len = range. len;
 
        // allocate new matrices
        if (len)
                map = new mmatrix<euclidom> [len];
        else
                map = NULL;
 
        for (int i = 0; i < len; ++ i)
        {
                // define the size of the matrix (number of rows and columns)
                map [i]. define (range. getnumgen (i),
                        domain. getnumgen (i));
 
                // link the matrices to the ones in the chain complexes
                domain. boundary [i]. dom_dom. add (map [i]);
                range. boundary [i]. dom_img. add (map [i]);
                if (i < domain. len - 1)
                        domain. boundary [i + 1]. img_dom. add (map [i]);
                if (i < range. len - 1)
                        range. boundary [i + 1]. img_img. add (map [i]);
        }
 
        return;
} /* chainmap<euclidom>::chainmap */

chainmap() [2/2]

template<class euclidom >

chomp::homology::chainmap< euclidom >::chainmap ( const chainmap< euclidom > &  c )

inline

Copy constructor.

Definition at line 3361 of file chains.h.

{
        len = c. len;
        if (len)
                map = new mmatrix<euclidom> [len];
        else
                map = 0;
 
        for (int i = 0; i < len; ++ i)
                map [i] = c. map [i];
 
        return;
} /* chainmap<euclidom>::chainmap */

~chainmap()

template<class euclidom >

chomp::homology::chainmap< euclidom >::~chainmap

inline

The destructor.

Definition at line 3395 of file chains.h.

{
        if (map)
                delete [] map;
        return;
} /* chainmap<euclidom>::~chainmap */

Member Function Documentation

add()

template<class euclidom >

void chomp::homology::chainmap< euclidom >::add ( int  q, int_t  m, int_t  n, euclidom  e  )

inline

Adds a coefficient to the selected matrix of the map: M_q [m, n] += e.

In other words, the image of n += e * m.

Definition at line 3417 of file chains.h.

{
        map [q]. add (m, n, e);
        return;
} /* chainmap<euclidom>::add */

compose()

template<class euclidom >

void chomp::homology::chainmap< euclidom >::compose ( const chainmap< euclidom > &  m1, const chainmap< euclidom > &  m2  )

inline

Composes two given chain maps.

The chain map is replaced by the result of this composition.

Definition at line 3473 of file chains.h.

{
        if ((m1. len < len) || (m2. len < len))
                throw "Trying to compose chain maps with too few levels.";
        for (int q = 0; q < len; ++ q)
                map [q]. multiply (m1. map [q], m2. map [q]);
        return;
} /* chainmap<euclidom>::compose */

dim()

template<class euclidom >

int chomp::homology::chainmap< euclidom >::dim

inline

Returns the dimension of the chain map.

Definition at line 3403 of file chains.h.

{
        return len - 1;
} /* chainmap<euclidom>::dim */

invert()

template<class euclidom >

void chomp::homology::chainmap< euclidom >::invert ( void  )

inline

Inverts the chain map.

Definition at line 3465 of file chains.h.

{
        for (int q = 0; q < len; ++ q)
                map [q]. invert ();
        return;
} /* chainmap<euclidom>::invert */

operator=()

template<class euclidom >

chainmap< euclidom > & chomp::homology::chainmap< euclidom >::operator= ( const chainmap< euclidom > &  c )

inline

The assignment operator.

Definition at line 3376 of file chains.h.

{
        if (map)
                delete [] map;
 
        len = c. len;
        if (len)
                map = new mmatrix<euclidom> [len];
        else
                map = 0;
 
        for (int i = 0; i < len; ++ i)
                map [i] = c. map [i];
 
        return *this;
} /* chainmap<euclidom>::operator = */

operator[]()

template<class euclidom >

const mmatrix< euclidom > & chomp::homology::chainmap< euclidom >::operator[] ( int  i ) const

inline

Returns the matrix of the chain map at the given level.

Definition at line 3409 of file chains.h.

{
//      if ((i < 0) || (i >= len))
//              throw "Chain map level out of range.";
        return map [i];
} /* chainmap<euclidom>::operator [] */

show() [1/2]

template<class euclidom >

outputstream & chomp::homology::chainmap< euclidom >::show ( outputstream &  out, const char *  maplabel = "f", const char *  xtxt = NULL, const char *  ytxt = NULL, const int *  level = NULL  ) const

inline

Writes the chain map to an output stream in the text format using specified labels for the map and elements in the domain and in the codomain of the map.

Definition at line 3484 of file chains.h.

{
        for (int q = 0; q < len; ++ q)
        {
                if (level && !level [q])
                        continue;
                out << "Dim " << q << ":";
                map [q]. showmap (out, maplabel, xtxt, ytxt);
        }
        return out;
} /* chainmap<euclidom>::show */

show() [2/2]

template<class euclidom >

std::ostream & chomp::homology::chainmap< euclidom >::show ( std::ostream &  out, const char *  maplabel = "f", const char *  xtxt = NULL, const char *  ytxt = NULL, const int *  level = NULL  ) const

inline

Writes the chain map to an output stream in the text format using specified labels for the map and elements in the domain and in the codomain of the map.

Definition at line 3499 of file chains.h.

{
        outputstream tout (out);
        show (tout, maplabel, xtxt, ytxt, level);
        return out;
} /* chainmap<euclidom>::show */

show_homology() [1/2]

template<class euclidom >

outputstream & chomp::homology::chainmap< euclidom >::show_homology ( outputstream &  out, const chain< euclidom > *  hom_domain, const chain< euclidom > *  hom_range, const int *  level = NULL, const char *  xtxt = NULL, const char *  ytxt = NULL  ) const

inline

Writes to an output stream the map induced in homology.

If the array of levels is provided, only these homology levels are displayed for which the array has a nonzero entry.

Definition at line 3509 of file chains.h.

{
        int max_len = len - 1;
        while ((max_len >= 0) && !hom_domain [max_len]. size ())
                -- max_len;
        ++ max_len;
        for (int q = 0; q < max_len; ++ q)
        {
                if (!level || level [q])
                {
                        out << "Dim " << q << ":";
                        int hlen = hom_domain [q]. size ();
                        if (!hlen)
                                out << "\t0" << '\n';
                        for (int i = 0; i < hlen; ++ i)
                        {
                                out << "\tf (";
                                if (xtxt)
                                        out << xtxt;
                                out << (i + 1) << ") = ";
                                map [q]. show_hom_col (out,
                                        hom_domain [q]. num (i),
                                        hom_range [q], ytxt);
                                out << '\n';
                        }
                }
        }
        return out;
} /* chainmap<euclidom>::show_homology */

show_homology() [2/2]

template<class euclidom >

std::ostream & chomp::homology::chainmap< euclidom >::show_homology ( std::ostream &  out, const chain< euclidom > *  hom_domain, const chain< euclidom > *  hom_range, const int *  level = NULL, const char *  xtxt = NULL, const char *  ytxt = NULL  ) const

inline

Writes to an output stream the map induced in homology.

If the array of levels is provided, only these homology levels are displayed for which the array has a nonzero entry.

Definition at line 3543 of file chains.h.

{
        outputstream tout (out);
        show_homology (tout, hom_domain, hom_range, level, xtxt, ytxt);
        return out;
} /* chainmap<euclidom>::show_homology */

References chomp::homology::show_homology().

take_homology()

template<class euclidom >

void chomp::homology::chainmap< euclidom >::take_homology ( const chainmap< euclidom > &  m, const chain< euclidom > *  hom_domain, const chain< euclidom > *  hom_range  )

inline

Creates a chain map that represents the map induced in homology by the chain map between the two given chain complexes which have been previously transformed to the simple form.

Definition at line 3424 of file chains.h.

{
        if (!hom_domain || !hom_range)
                return;
 
        for (int q = 0; q < len; ++ q)
        {
                int_t dlen = hom_domain [q]. size ();
                const chain<euclidom> &r = hom_range [q];
                int_t rlen = r. size ();
                map [q]. define (rlen, dlen);
                // go through the homology generators in the domain
                for (int_t i = 0; i < dlen; ++ i)
                {
                        // retrieve the real number of the homology generator
                        int_t x = hom_domain [q]. num (i);
 
                        // get the image of this element by the chain map
                        const chain<euclidom> &img = m [q]. getcol (x);
 
                        // transform numbers in this image to hom. generators
                        int_t j = 0;
                        for (int_t k = 0; k < img. size (); ++ k)
                        {
                                // find the current element in the range
                                while ((j < rlen) &&
                                        (r. num (j) < img. num (k)))
                                        ++ j;
 
                                // if found in the range, add it
                                if ((j < rlen) &&
                                        (r. num (j) == img. num (k)))
                                        map [q]. add (j, i, img. coef (k));
                        }
                }
        }
        return;
} /* chainmap<euclidom>::take_homology */

Member Data Documentation

len

template<class euclidom >

int chomp::homology::chainmap< euclidom >::len

private

The number of matrices (dimension of the chain map + 1).

Definition at line 3318 of file chains.h.

map

template<class euclidom >

mmatrix<euclidom>* chomp::homology::chainmap< euclidom >::map

private

The matrices in each dimension.

Definition at line 3321 of file chains.h.

---

The documentation for this class was generated from the following file:

• chomp/homology/chains.h