chomp::homengin::algstruct< euclidom > Class Template Reference

An algebraic structure that represents a finitely generated Abelian group with gradation. More...

#include <algstruct.h>

Public Member Functions
	algstruct ()
	The default constructor. More...
	~algstruct ()
	The destructor. More...
int	countLevels () const
	Returns the number of levels of gradation stored in the structure. More...
void	setBetti (int level, int number)
	Sets a specific Betti number. More...
void	addBetti (int level, int howmuch)
	Increases a specific Betti number. More...
int	getBetti (int level) const
	Returns a specific Betti number. More...
void	addTorsion (int level, euclidom coef)
	Adds a torsion coefficient. More...
const euclidom &	getTorsion (int level, int n) const
	Returns a torsion coefficient. More...
int	countTorsion (int level) const
	Says how many torsion coefficients exist at the given level. More...
std::ostream &	describe (std::ostream &out) const
	Describes the homology group in a human-readable way. More...
std::ostream &	showBetti (std::ostream &out) const
	Shows the Betti numbers as a space-sperated sequence. More...

Private Attributes
std::vector< int >	betti
	The Betti numbers. More...
std::vector< std::vector< euclidom > >	torsion
	The torsion coefficients. More...

Detailed Description

template<class euclidom>
class chomp::homengin::algstruct< euclidom >

An algebraic structure that represents a finitely generated Abelian group with gradation.

Definition at line 67 of file algstruct.h.

Constructor & Destructor Documentation

algstruct()

template<class euclidom >

chomp::homengin::algstruct< euclidom >::algstruct

inline

The default constructor.

Definition at line 115 of file algstruct.h.

{
 return;
} /* algstruct::algstruct */

~algstruct()

template<class euclidom >

chomp::homengin::algstruct< euclidom >::~algstruct

inline

The destructor.

Definition at line 121 of file algstruct.h.

{
 return;
} /* algstruct::~algstruct */

Member Function Documentation

addBetti()

template<class euclidom >

void chomp::homengin::algstruct< euclidom >::addBetti ( int  level, int  howmuch  )

inline

Increases a specific Betti number.

Definition at line 153 of file algstruct.h.

{
 if (level < 0)
  return;
 if (static_cast<unsigned> (level) < betti. size ())
  betti [level] += howmuch;
 else
  setBetti (level, howmuch);
 return;
} /* algstruct::addBetti */

addTorsion()

template<class euclidom >

void chomp::homengin::algstruct< euclidom >::addTorsion ( int  level, euclidom  coef  )

inline

Adds a torsion coefficient.

Definition at line 176 of file algstruct.h.

{
 if (level < 0)
  return;
 std::vector<euclidom> empty;
 for (int nTorsion = torsion. size (); nTorsion <= level; ++ nTorsion)
  torsion. push_back (empty);
 torsion [level]. push_back (coef);
 return;
} /* algstruct::addTorsion */

countLevels()

template<class euclidom >

int chomp::homengin::algstruct< euclidom >::countLevels

inline

Returns the number of levels of gradation stored in the structure.

Definition at line 129 of file algstruct.h.

{
 int nBetti = betti. size ();
 int nTorsion = torsion. size ();
 return (nBetti > nTorsion) ? nBetti : nTorsion;
} /* algstruct::countLevels */

countTorsion()

template<class euclidom >

int chomp::homengin::algstruct< euclidom >::countTorsion ( int  level ) const

inline

Says how many torsion coefficients exist at the given level.

Definition at line 203 of file algstruct.h.

{
 if (level < 0)
  return 0;
 if (static_cast<unsigned> (level) < torsion. size ())
  return torsion [level]. size ();
 return 0;
} /* algstruct::countTorsion */

describe()

template<class euclidom >

std::ostream & chomp::homengin::algstruct< euclidom >::describe

(

std::ostream &

out

)

const

Describes the homology group in a human-readable way.

Definition at line 228 of file algstruct.h.

{
 int nBetti = betti. size ();
 int nTorsion = torsion. size ();
 for (int i = 0; (i < nBetti) || (i < nTorsion); ++ i)
 {
  if (i)
   out << ", ";
  else
   out << '(';
  bool zero = true;
  if ((i < nBetti) && (betti [i] > 0))
  {
   zero = false;
   out << ringsymbol<euclidom> ();
   if (betti [i] > 1)
    out << '^' << betti [i];
   if ((i < nTorsion) && (torsion [i]. size ()))
    out << " + ";
  }
  if (i < nTorsion)
  {
   std::vector<euclidom> tor = torsion [i];
   for (unsigned j = 0; j < tor. size (); ++ j)
   {
    zero = false;
    if (j)
     out << " + ";
    out << ringsymbol<euclidom> () <<
     '_' << tor [j];
   }
  }
  if (zero)
   out << 0;
 }
 if (nBetti || nTorsion)
  out << ')';
 else
  out << '0';
 return out;
} /* algstruct::describe */

getBetti()

template<class euclidom >

int chomp::homengin::algstruct< euclidom >::getBetti ( int  level ) const

inline

Returns a specific Betti number.

Definition at line 165 of file algstruct.h.

{
 if (level < 0)
  return 0;
 if (static_cast<unsigned> (level) < betti. size ())
  return betti [level];
 else
  return 0;
} /* algstruct::getBetti */

getTorsion()

template<class euclidom >

const euclidom & chomp::homengin::algstruct< euclidom >::getTorsion ( int  level, int  n  ) const

inline

Returns a torsion coefficient.

Definition at line 188 of file algstruct.h.

{
 static euclidom e;
 
 if ((level < 0) || (n < 0))
  return e;
 if ((static_cast<unsigned> (level) < torsion. size ()) &&
  (static_cast<unsigned> (n) < torsion [level]. size ()))
  return torsion [level] [n];
 else
  return e;
} /* algstruct::getTorsion */

setBetti()

template<class euclidom >

void chomp::homengin::algstruct< euclidom >::setBetti ( int  level, int  number  )

inline

Sets a specific Betti number.

Definition at line 137 of file algstruct.h.

{
 if (level < 0)
  return;
 if (number <= 0)
  return;
 for (int nBetti = betti. size (); nBetti < level; ++ nBetti)
  betti. push_back (0);
 if (static_cast<unsigned> (level) < betti. size ())
  betti [level] = number;
 else
  betti. push_back (number);
 return;
} /* algstruct::setBetti */

showBetti()

template<class euclidom >

std::ostream & chomp::homengin::algstruct< euclidom >::showBetti

(

std::ostream &

out

)

const

Shows the Betti numbers as a space-sperated sequence.

Definition at line 271 of file algstruct.h.

{
 bool first = true;
 for (std::vector<int>::const_iterator it = betti. begin ();
  it != betti. end (); ++ it)
 {
  if (first)
   first = false;
  else
   out << ' ';
  out << *it;
 }
 return out;
} /* algstruct::showBetti */

Member Data Documentation

betti

template<class euclidom >

std::vector<int> chomp::homengin::algstruct< euclidom >::betti

private

The Betti numbers.

Definition at line 106 of file algstruct.h.

torsion

template<class euclidom >

std::vector<std::vector<euclidom> > chomp::homengin::algstruct< euclidom >::torsion

private

The torsion coefficients.

Definition at line 109 of file algstruct.h.

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

• capd/homengin/algstruct.h